Address some of the comments by Irene and Andreas
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appendix.md
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# Appendix
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: Cross Section limits using 2016 data and the N-subjettiness tagger for the decay to qW
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| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
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|------------|-----------------|------------------|------------------|-----------------|
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| 1.6 | 0.10406 | 0.14720 | 0.07371 | 0.08165 |
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| 1.8 | 0.07656 | 0.10800 | 0.05441 | 0.04114 |
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| 2.0 | 0.05422 | 0.07605 | 0.03879 | 0.04043 |
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| 2.5 | 0.02430 | 0.03408 | 0.01747 | 0.04052 |
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| 3.0 | 0.01262 | 0.01775 | 0.00904 | 0.02109 |
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| 3.5 | 0.00703 | 0.00992 | 0.00502 | 0.00399 |
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| 4.0 | 0.00424 | 0.00603 | 0.00300 | 0.00172 |
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| 4.5 | 0.00355 | 0.00478 | 0.00273 | 0.00249 |
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| 5.0 | 0.00269 | 0.00357 | 0.00211 | 0.00240 |
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| 6.0 | 0.00103 | 0.00160 | 0.00068 | 0.00062 |
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| 7.0 | 0.00063 | 0.00105 | 0.00039 | 0.00086 |
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: Cross Section limits using 2016 data and the deep boosted tagger for the decay to qW
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| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
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|------------|-----------------|------------------|------------------|-----------------|
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| 1.6 | 0.17750 | 0.25179 | 0.12572 | 0.38242 |
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| 1.8 | 0.11125 | 0.15870 | 0.07826 | 0.11692 |
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| 2.0 | 0.08188 | 0.11549 | 0.05799 | 0.09528 |
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| 2.5 | 0.03328 | 0.04668 | 0.02373 | 0.03653 |
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| 3.0 | 0.01648 | 0.02338 | 0.01181 | 0.01108 |
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| 3.5 | 0.00840 | 0.01195 | 0.00593 | 0.00683 |
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| 4.0 | 0.00459 | 0.00666 | 0.00322 | 0.00342 |
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| 4.5 | 0.00276 | 0.00412 | 0.00190 | 0.00366 |
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| 5.0 | 0.00177 | 0.00271 | 0.00118 | 0.00401 |
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| 6.0 | 0.00110 | 0.00175 | 0.00071 | 0.00155 |
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| 7.0 | 0.00065 | 0.00108 | 0.00041 | 0.00108 |
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: Cross Section limits using 2016 data and the N-subjettiness tagger for the decay to qZ
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| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
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|------------|-----------------|------------------|------------------|-----------------|
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| 1.6 | 0.08687 | 0.12254 | 0.06174 | 0.06987 |
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| 1.8 | 0.06719 | 0.09477 | 0.04832 | 0.03424 |
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| 2.0 | 0.04734 | 0.06640 | 0.03405 | 0.03310 |
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| 2.5 | 0.01867 | 0.02619 | 0.01343 | 0.03214 |
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| 3.0 | 0.01043 | 0.01463 | 0.00744 | 0.01773 |
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| 3.5 | 0.00596 | 0.00840 | 0.00426 | 0.00347 |
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| 4.0 | 0.00353 | 0.00500 | 0.00250 | 0.00140 |
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| 4.5 | 0.00233 | 0.00335 | 0.00164 | 0.00181 |
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| 5.0 | 0.00157 | 0.00231 | 0.00110 | 0.00188 |
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| 6.0 | 0.00082 | 0.00126 | 0.00054 | 0.00049 |
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| 7.0 | 0.00050 | 0.00083 | 0.00031 | 0.00066 |
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: Cross Section limits using 2016 data and deep boosted tagger for the decay to qZ
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| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
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|------------|-----------------|------------------|------------------|-----------------|
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| 1.6 | 0.16687 | 0.23805 | 0.11699 | 0.35999 |
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| 1.8 | 0.12750 | 0.17934 | 0.09138 | 0.12891 |
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| 2.0 | 0.09062 | 0.12783 | 0.06474 | 0.09977 |
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| 2.5 | 0.03391 | 0.04783 | 0.02422 | 0.03754 |
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| 3.0 | 0.01781 | 0.02513 | 0.01277 | 0.01159 |
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| 3.5 | 0.00949 | 0.01346 | 0.00678 | 0.00741 |
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| 4.0 | 0.00494 | 0.00711 | 0.00349 | 0.00362 |
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| 4.5 | 0.00293 | 0.00429 | 0.00203 | 0.00368 |
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| 5.0 | 0.00188 | 0.00284 | 0.00127 | 0.00426 |
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| 6.0 | 0.00102 | 0.00161 | 0.00066 | 0.00155 |
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| 7.0 | 0.00053 | 0.00085 | 0.00034 | 0.00085 |
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: Cross Section limits using the combined data and the N-subjettiness tagger for the decay to qW
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| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
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|------------|-----------------|------------------|------------------|-----------------|
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| 1.6 | 0.05703 | 0.07999 | 0.04088 | 0.03366 |
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| 1.8 | 0.03953 | 0.05576 | 0.02833 | 0.04319 |
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| 2.0 | 0.02844 | 0.03989 | 0.02045 | 0.04755 |
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| 2.5 | 0.01270 | 0.01781 | 0.00913 | 0.01519 |
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| 3.0 | 0.00658 | 0.00923 | 0.00473 | 0.01218 |
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| 3.5 | 0.00376 | 0.00529 | 0.00269 | 0.00474 |
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| 4.0 | 0.00218 | 0.00309 | 0.00156 | 0.00114 |
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| 4.5 | 0.00132 | 0.00188 | 0.00094 | 0.00068 |
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| 5.0 | 0.00084 | 0.00122 | 0.00060 | 0.00059 |
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| 6.0 | 0.00044 | 0.00066 | 0.00030 | 0.00041 |
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| 7.0 | 0.00022 | 0.00036 | 0.00014 | 0.00043 |
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: Cross Section limits using the combined data and the deep boosted tagger for the decay to qW
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| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
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|------------|-----------------|------------------|------------------|-----------------|
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| 1.6 | 0.06656 | 0.09495 | 0.04698 | 0.12374 |
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| 1.8 | 0.04281 | 0.06141 | 0.03001 | 0.05422 |
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| 2.0 | 0.03297 | 0.04650 | 0.02363 | 0.04658 |
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| 2.5 | 0.01328 | 0.01868 | 0.00950 | 0.01109 |
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| 3.0 | 0.00650 | 0.00917 | 0.00464 | 0.00502 |
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| 3.5 | 0.00338 | 0.00479 | 0.00241 | 0.00408 |
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| 4.0 | 0.00182 | 0.00261 | 0.00129 | 0.00127 |
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| 4.5 | 0.00107 | 0.00156 | 0.00074 | 0.00123 |
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| 5.0 | 0.00068 | 0.00102 | 0.00046 | 0.00149 |
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| 6.0 | 0.00038 | 0.00060 | 0.00024 | 0.00034 |
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| 7.0 | 0.00021 | 0.00035 | 0.00013 | 0.00046 |
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: Cross Section limits using the combined data and the N-subjettiness tagger for the decay to qZ
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| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
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|------------|-----------------|------------------|------------------|-----------------|
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| 1.6 | 0.05125 | 0.07188 | 0.03667 | 0.02993 |
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| 1.8 | 0.03547 | 0.04989 | 0.02551 | 0.03614 |
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| 2.0 | 0.02523 | 0.03539 | 0.01815 | 0.04177 |
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| 2.5 | 0.01059 | 0.01485 | 0.00761 | 0.01230 |
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| 3.0 | 0.00576 | 0.00808 | 0.00412 | 0.01087 |
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| 3.5 | 0.00327 | 0.00460 | 0.00234 | 0.00425 |
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| 4.0 | 0.00190 | 0.00269 | 0.00136 | 0.00097 |
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| 4.5 | 0.00119 | 0.00168 | 0.00084 | 0.00059 |
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| 5.0 | 0.00077 | 0.00110 | 0.00054 | 0.00051 |
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| 6.0 | 0.00039 | 0.00057 | 0.00026 | 0.00036 |
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| 7.0 | 0.00019 | 0.00031 | 0.00013 | 0.00036 |
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: Cross Section limits using the combined data and deep boosted tagger for the decay to qZ
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| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
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|------------|-----------------|------------------|------------------|-----------------|
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| 1.6 | 0.07719 | 0.10949 | 0.05467 | 0.14090 |
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| 1.8 | 0.05297 | 0.07493 | 0.03752 | 0.06690 |
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| 2.0 | 0.03875 | 0.05466 | 0.02768 | 0.05855 |
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| 2.5 | 0.01512 | 0.02126 | 0.01080 | 0.01160 |
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| 3.0 | 0.00773 | 0.01088 | 0.00554 | 0.00548 |
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| 3.5 | 0.00400 | 0.00565 | 0.00285 | 0.00465 |
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| 4.0 | 0.00211 | 0.00301 | 0.00149 | 0.00152 |
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| 4.5 | 0.00118 | 0.00172 | 0.00082 | 0.00128 |
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| 5.0 | 0.00073 | 0.00108 | 0.00050 | 0.00161 |
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| 6.0 | 0.00039 | 0.00060 | 0.00025 | 0.00036 |
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| 7.0 | 0.00021 | 0.00034 | 0.00013 | 0.00045 |
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appendix.tex
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appendix.tex
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\newpage
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\hypertarget{appendix}{%
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\section*{Appendix}\label{appendix}}
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\begin{longtable}[]{@{}lllll@{}}
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\caption{Cross Section limits using 2016 data and the N-subjettiness
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tagger for the decay to qW}\tabularnewline
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endfirsthead
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endhead
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1.6 & 0.10406 & 0.14720 & 0.07371 & 0.08165\tabularnewline
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1.8 & 0.07656 & 0.10800 & 0.05441 & 0.04114\tabularnewline
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2.0 & 0.05422 & 0.07605 & 0.03879 & 0.04043\tabularnewline
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2.5 & 0.02430 & 0.03408 & 0.01747 & 0.04052\tabularnewline
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3.0 & 0.01262 & 0.01775 & 0.00904 & 0.02109\tabularnewline
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3.5 & 0.00703 & 0.00992 & 0.00502 & 0.00399\tabularnewline
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4.0 & 0.00424 & 0.00603 & 0.00300 & 0.00172\tabularnewline
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4.5 & 0.00355 & 0.00478 & 0.00273 & 0.00249\tabularnewline
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5.0 & 0.00269 & 0.00357 & 0.00211 & 0.00240\tabularnewline
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6.0 & 0.00103 & 0.00160 & 0.00068 & 0.00062\tabularnewline
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7.0 & 0.00063 & 0.00105 & 0.00039 & 0.00086\tabularnewline
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\bottomrule
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\end{longtable}
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\begin{longtable}[]{@{}lllll@{}}
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\caption{Cross Section limits using 2016 data and the deep boosted
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tagger for the decay to qW}\tabularnewline
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endfirsthead
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endhead
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1.6 & 0.17750 & 0.25179 & 0.12572 & 0.38242\tabularnewline
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1.8 & 0.11125 & 0.15870 & 0.07826 & 0.11692\tabularnewline
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2.0 & 0.08188 & 0.11549 & 0.05799 & 0.09528\tabularnewline
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2.5 & 0.03328 & 0.04668 & 0.02373 & 0.03653\tabularnewline
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3.0 & 0.01648 & 0.02338 & 0.01181 & 0.01108\tabularnewline
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3.5 & 0.00840 & 0.01195 & 0.00593 & 0.00683\tabularnewline
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4.0 & 0.00459 & 0.00666 & 0.00322 & 0.00342\tabularnewline
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4.5 & 0.00276 & 0.00412 & 0.00190 & 0.00366\tabularnewline
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5.0 & 0.00177 & 0.00271 & 0.00118 & 0.00401\tabularnewline
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6.0 & 0.00110 & 0.00175 & 0.00071 & 0.00155\tabularnewline
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7.0 & 0.00065 & 0.00108 & 0.00041 & 0.00108\tabularnewline
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\bottomrule
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\end{longtable}
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\begin{longtable}[]{@{}lllll@{}}
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\caption{Cross Section limits using 2016 data and the N-subjettiness
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tagger for the decay to qZ}\tabularnewline
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endfirsthead
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endhead
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1.6 & 0.08687 & 0.12254 & 0.06174 & 0.06987\tabularnewline
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1.8 & 0.06719 & 0.09477 & 0.04832 & 0.03424\tabularnewline
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2.0 & 0.04734 & 0.06640 & 0.03405 & 0.03310\tabularnewline
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2.5 & 0.01867 & 0.02619 & 0.01343 & 0.03214\tabularnewline
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3.0 & 0.01043 & 0.01463 & 0.00744 & 0.01773\tabularnewline
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3.5 & 0.00596 & 0.00840 & 0.00426 & 0.00347\tabularnewline
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4.0 & 0.00353 & 0.00500 & 0.00250 & 0.00140\tabularnewline
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4.5 & 0.00233 & 0.00335 & 0.00164 & 0.00181\tabularnewline
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5.0 & 0.00157 & 0.00231 & 0.00110 & 0.00188\tabularnewline
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6.0 & 0.00082 & 0.00126 & 0.00054 & 0.00049\tabularnewline
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7.0 & 0.00050 & 0.00083 & 0.00031 & 0.00066\tabularnewline
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\bottomrule
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\end{longtable}
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\begin{longtable}[]{@{}lllll@{}}
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\caption{Cross Section limits using 2016 data and deep boosted tagger
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for the decay to qZ}\tabularnewline
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endfirsthead
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endhead
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1.6 & 0.16687 & 0.23805 & 0.11699 & 0.35999\tabularnewline
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1.8 & 0.12750 & 0.17934 & 0.09138 & 0.12891\tabularnewline
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2.0 & 0.09062 & 0.12783 & 0.06474 & 0.09977\tabularnewline
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2.5 & 0.03391 & 0.04783 & 0.02422 & 0.03754\tabularnewline
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3.0 & 0.01781 & 0.02513 & 0.01277 & 0.01159\tabularnewline
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3.5 & 0.00949 & 0.01346 & 0.00678 & 0.00741\tabularnewline
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4.0 & 0.00494 & 0.00711 & 0.00349 & 0.00362\tabularnewline
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4.5 & 0.00293 & 0.00429 & 0.00203 & 0.00368\tabularnewline
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5.0 & 0.00188 & 0.00284 & 0.00127 & 0.00426\tabularnewline
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6.0 & 0.00102 & 0.00161 & 0.00066 & 0.00155\tabularnewline
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7.0 & 0.00053 & 0.00085 & 0.00034 & 0.00085\tabularnewline
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\bottomrule
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\end{longtable}
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\begin{longtable}[]{@{}lllll@{}}
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\caption{Cross Section limits using the combined data and the
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N-subjettiness tagger for the decay to qW}\tabularnewline
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endfirsthead
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endhead
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1.6 & 0.05703 & 0.07999 & 0.04088 & 0.03366\tabularnewline
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1.8 & 0.03953 & 0.05576 & 0.02833 & 0.04319\tabularnewline
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2.0 & 0.02844 & 0.03989 & 0.02045 & 0.04755\tabularnewline
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2.5 & 0.01270 & 0.01781 & 0.00913 & 0.01519\tabularnewline
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3.0 & 0.00658 & 0.00923 & 0.00473 & 0.01218\tabularnewline
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3.5 & 0.00376 & 0.00529 & 0.00269 & 0.00474\tabularnewline
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4.0 & 0.00218 & 0.00309 & 0.00156 & 0.00114\tabularnewline
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4.5 & 0.00132 & 0.00188 & 0.00094 & 0.00068\tabularnewline
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5.0 & 0.00084 & 0.00122 & 0.00060 & 0.00059\tabularnewline
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6.0 & 0.00044 & 0.00066 & 0.00030 & 0.00041\tabularnewline
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7.0 & 0.00022 & 0.00036 & 0.00014 & 0.00043\tabularnewline
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\bottomrule
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\end{longtable}
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\begin{longtable}[]{@{}lllll@{}}
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\caption{Cross Section limits using the combined data and the deep
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boosted tagger for the decay to qW}\tabularnewline
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endfirsthead
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\toprule
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Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
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limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
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\midrule
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\endhead
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1.6 & 0.06656 & 0.09495 & 0.04698 & 0.12374\tabularnewline
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1.8 & 0.04281 & 0.06141 & 0.03001 & 0.05422\tabularnewline
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2.0 & 0.03297 & 0.04650 & 0.02363 & 0.04658\tabularnewline
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2.5 & 0.01328 & 0.01868 & 0.00950 & 0.01109\tabularnewline
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3.0 & 0.00650 & 0.00917 & 0.00464 & 0.00502\tabularnewline
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||||
3.5 & 0.00338 & 0.00479 & 0.00241 & 0.00408\tabularnewline
|
||||
4.0 & 0.00182 & 0.00261 & 0.00129 & 0.00127\tabularnewline
|
||||
4.5 & 0.00107 & 0.00156 & 0.00074 & 0.00123\tabularnewline
|
||||
5.0 & 0.00068 & 0.00102 & 0.00046 & 0.00149\tabularnewline
|
||||
6.0 & 0.00038 & 0.00060 & 0.00024 & 0.00034\tabularnewline
|
||||
7.0 & 0.00021 & 0.00035 & 0.00013 & 0.00046\tabularnewline
|
||||
\bottomrule
|
||||
\end{longtable}
|
||||
|
||||
\begin{longtable}[]{@{}lllll@{}}
|
||||
\caption{Cross Section limits using the combined data and the
|
||||
N-subjettiness tagger for the decay to qZ}\tabularnewline
|
||||
\toprule
|
||||
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
||||
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
||||
\midrule
|
||||
\endfirsthead
|
||||
\toprule
|
||||
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
||||
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
||||
\midrule
|
||||
\endhead
|
||||
1.6 & 0.05125 & 0.07188 & 0.03667 & 0.02993\tabularnewline
|
||||
1.8 & 0.03547 & 0.04989 & 0.02551 & 0.03614\tabularnewline
|
||||
2.0 & 0.02523 & 0.03539 & 0.01815 & 0.04177\tabularnewline
|
||||
2.5 & 0.01059 & 0.01485 & 0.00761 & 0.01230\tabularnewline
|
||||
3.0 & 0.00576 & 0.00808 & 0.00412 & 0.01087\tabularnewline
|
||||
3.5 & 0.00327 & 0.00460 & 0.00234 & 0.00425\tabularnewline
|
||||
4.0 & 0.00190 & 0.00269 & 0.00136 & 0.00097\tabularnewline
|
||||
4.5 & 0.00119 & 0.00168 & 0.00084 & 0.00059\tabularnewline
|
||||
5.0 & 0.00077 & 0.00110 & 0.00054 & 0.00051\tabularnewline
|
||||
6.0 & 0.00039 & 0.00057 & 0.00026 & 0.00036\tabularnewline
|
||||
7.0 & 0.00019 & 0.00031 & 0.00013 & 0.00036\tabularnewline
|
||||
\bottomrule
|
||||
\end{longtable}
|
||||
|
||||
\begin{longtable}[]{@{}lllll@{}}
|
||||
\caption{Cross Section limits using the combined data and deep boosted
|
||||
tagger for the decay to qZ}\tabularnewline
|
||||
\toprule
|
||||
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
||||
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
||||
\midrule
|
||||
\endfirsthead
|
||||
\toprule
|
||||
Mass {[}TeV{]} & Exp. limit {[}pb{]} & Upper limit {[}pb{]} & Lower
|
||||
limit {[}pb{]} & Obs. limit {[}pb{]}\tabularnewline
|
||||
\midrule
|
||||
\endhead
|
||||
1.6 & 0.07719 & 0.10949 & 0.05467 & 0.14090\tabularnewline
|
||||
1.8 & 0.05297 & 0.07493 & 0.03752 & 0.06690\tabularnewline
|
||||
2.0 & 0.03875 & 0.05466 & 0.02768 & 0.05855\tabularnewline
|
||||
2.5 & 0.01512 & 0.02126 & 0.01080 & 0.01160\tabularnewline
|
||||
3.0 & 0.00773 & 0.01088 & 0.00554 & 0.00548\tabularnewline
|
||||
3.5 & 0.00400 & 0.00565 & 0.00285 & 0.00465\tabularnewline
|
||||
4.0 & 0.00211 & 0.00301 & 0.00149 & 0.00152\tabularnewline
|
||||
4.5 & 0.00118 & 0.00172 & 0.00082 & 0.00128\tabularnewline
|
||||
5.0 & 0.00073 & 0.00108 & 0.00050 & 0.00161\tabularnewline
|
||||
6.0 & 0.00039 & 0.00060 & 0.00025 & 0.00036\tabularnewline
|
||||
7.0 & 0.00021 & 0.00034 & 0.00013 & 0.00045\tabularnewline
|
||||
\bottomrule
|
||||
\end{longtable}
|
||||
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|
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|
|||
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|
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|
||||
pandoc thesis.md -o thesis.tex --biblatex --bibliography=bibliography.bib -N --listings --pdf-engine=lualatex -s --filter pandoc-crossref
|
||||
pandoc thesis.md -o thesis.tex --biblatex --bibliography=bibliography.bib -N --listings --pdf-engine=lualatex -s --filter pandoc-crossref --include-after-body=appendix.tex
|
||||
lualatex thesis
|
||||
biber thesis
|
||||
lualatex thesis
|
||||
|
|
|
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@ -265,3 +276,4 @@
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\abx@aux@defaultrefcontext{0}{TAU21_TAGGER}{nty/global//global/global}
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15
thesis.bcf
15
thesis.bcf
|
|
@ -1995,12 +1995,19 @@
|
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<bcf:datasource type="file" datatype="bibtex">bibliography.bib</bcf:datasource>
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</bcf:bibdata>
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<bcf:section number="0">
|
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<bcf:citekey order="1">website</bcf:citekey>
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<bcf:citekey order="1">PREV_RESEARCH</bcf:citekey>
|
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<bcf:citekey order="2">QSTAR_THEORY</bcf:citekey>
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<bcf:citekey order="3">PREV_RESEARCH</bcf:citekey>
|
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<bcf:citekey order="4">QSTAR_THEORY</bcf:citekey>
|
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<bcf:citekey order="5">PREV_RESEARCH</bcf:citekey>
|
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<bcf:citekey order="6">PREV_RESEARCH</bcf:citekey>
|
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<bcf:citekey order="4">website</bcf:citekey>
|
||||
<bcf:citekey order="5">ANTIKT</bcf:citekey>
|
||||
<bcf:citekey order="6">ANTIKT</bcf:citekey>
|
||||
<bcf:citekey order="7">PREV_RESEARCH</bcf:citekey>
|
||||
<bcf:citekey order="8">PREV_RESEARCH</bcf:citekey>
|
||||
<bcf:citekey order="9">QSTAR_THEORY</bcf:citekey>
|
||||
<bcf:citekey order="10">PREV_RESEARCH</bcf:citekey>
|
||||
<bcf:citekey order="11">PREV_RESEARCH</bcf:citekey>
|
||||
<bcf:citekey order="12">PREV_RESEARCH</bcf:citekey>
|
||||
<bcf:citekey order="13">PREV_RESEARCH</bcf:citekey>
|
||||
<bcf:citekey order="0" nocite="1">*</bcf:citekey>
|
||||
</bcf:section>
|
||||
<!-- SORTING TEMPLATES -->
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52
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|||
[0] Config.pm:304> INFO - This is Biber 2.12
|
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[0] Config.pm:307> INFO - Logfile is 'thesis.blg'
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[20] biber:315> INFO - === Mi Okt 16, 2019, 13:44:43
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[37] Biber.pm:371> INFO - Reading 'thesis.bcf'
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[102] Biber.pm:4093> INFO - Processing section 0
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[111] Biber.pm:4254> INFO - Looking for bibtex format file 'bibliography.bib' for section 0
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[183] Utils.pm:193> WARN - month field 'Nov' in entry 'HADRONIZATION' is not an integer - this will probably not sort properly.
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[2551] Utils.pm:193> WARN - month field 'Mar' in entry 'TAU21_TAGGER' is not an integer - this will probably not sort properly.
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[6640] bbl.pm:739> INFO - Output to thesis.bbl
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[6642] Biber.pm:110> INFO - WARNINGS: 12
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[20] biber:315> INFO - === Fr Okt 25, 2019, 10:00:15
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[39] Biber.pm:371> INFO - Reading 'thesis.bcf'
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[118] bibtex.pm:1523> INFO - LaTeX decoding ...
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[2634] Utils.pm:193> WARN - month field 'Nov' in entry 'HADRONIZATION' is not an integer - this will probably not sort properly.
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[2939] Utils.pm:193> WARN - month field 'Apr' in entry 'MONTECARLO' is not an integer - this will probably not sort properly.
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||||
[2970] Utils.pm:193> WARN - month field 'May' in entry 'LHC' is not an integer - this will probably not sort properly.
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||||
[2973] Utils.pm:193> WARN - month field 'Jan' in entry 'PARTICLE_FLOW' is not an integer - this will probably not sort properly.
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||||
[3046] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'variable = shifted' with 'variable = non-ignorable'
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[3046] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'normalization = NFD' with 'normalization = prenormalized'
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[3047] Biber.pm:3927> INFO - No sort tailoring available for locale 'en-GB'
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[3132] bbl.pm:636> INFO - Writing 'thesis.bbl' with encoding 'UTF-8'
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[7189] bbl.pm:739> INFO - Output to thesis.bbl
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[7190] Biber.pm:110> INFO - WARNINGS: 12
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506
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687
thesis.md
687
thesis.md
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@ -8,7 +8,6 @@ header-includes: |
|
|||
\usepackage{tikz-feynman}
|
||||
\usepackage{csquotes}
|
||||
\pagenumbering{gobble}
|
||||
\setlength{\parindent}{1.0em}
|
||||
\setlength{\parskip}{0.5em}
|
||||
\bibliographystyle{lucas_unsrt}
|
||||
abstract: |
|
||||
|
|
@ -41,49 +40,59 @@ The Standard Model is a very successful theory in describing most of the effects
|
|||
lot of shortcomings that show that it isn't yet a full "theory of everything". To solve these shortcomings, lots of
|
||||
theories beyond the standard model exist that try to explain some of them.
|
||||
|
||||
One category of such theories is based on a composite quark model. They predict that quarks consist of particles unknown
|
||||
to us so far or can bind to other particles using unknown forces. This could explain some symmetries between particles
|
||||
One category of such theories is based on a composite quark model. Quarks are currently considered elementary particles
|
||||
by the Standard Model. The composite quark models on the other hand predict that quarks consist of particles unknown
|
||||
to us so far or can bind to other particles using unknown forces. This could explain the symmetries between particles
|
||||
and reduce the number of constants needed to explain the properties of the known particles. One common prediction of
|
||||
those theories are excited quark states. Those are quark states of higher energy that can decay to an unexcited quark
|
||||
under the emission of a boson. These decays are the topic of this thesis.
|
||||
under the emission of a boson. This thesis will search for their decay to a quark and a W/Z boson. The W/Z boson then
|
||||
decays in the hadronic channel, to two more quarks. The endstate of this decay has only quarks, making Quantum
|
||||
Chromodynamics effects the main background.
|
||||
|
||||
In previous research, a lower limit for the mass of an excited quark has already been set using data from the 2016 run
|
||||
of the Large Hadron Collider with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$. Since then, a lot more data
|
||||
has been collected, totalling to $\SI{137.19}{\per\femto\barn}$. This thesis uses this new data as well as a new
|
||||
technique to identify decays of highly boosted particles based on a deep neural network to further improve this limit
|
||||
and therefore exclude the excited quark particle to even higher masses. It will also compare this new tagging technique
|
||||
to an older tagger based on jet substructure studies used in the previous research.
|
||||
In a previous research [@PREV_RESEARCH], a lower limit for the mass of an excited quark has already been set using data
|
||||
from the 2016 run of the Large Hadron Collider with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$. Since
|
||||
then, a lot more data has been collected, totalling to $\SI{137.19}{\per\femto\barn}$ of data usable for research. This
|
||||
thesis uses this new data as well as a new technique to identify decays of highly boosted particles based on a deep
|
||||
neural network. By using more data and new tagging techniques, it aims to either confirm the existence of the q\*
|
||||
particle or improve the previously set lower limit of 5 TeV respectively 4.7 TeV for the decay to qW respectively qZ on
|
||||
its mass to even higher values. It will also directly compare the performance of this new tagging technique to an older
|
||||
tagger based on jet substructure studies used in the previous research.
|
||||
|
||||
First, a theoretical background will be presented explaining in short the Standard Model, its shortcomings and the
|
||||
theory of excited quarks. Then the Large Hadron Collider and the Compact Muon Solenoid, the detector that collected the
|
||||
data for this analysis, will be described. After that, the main analysis part follows, describing how the data was used
|
||||
to extract limits on the mass of the excited quark particle. At the very end, the results are presented and compared to
|
||||
previous research.
|
||||
In chapter 2, a theoretical background will be presented explaining in short the Standard Model, its shortcomings and
|
||||
the theory of excited quarks. Then, in chapter 3, the Large Hadron Collider and the Compact Muon Solenoid, the detector
|
||||
that collected the data for this analysis, will be described. After that, in chapters 4-7, the main analysis part
|
||||
follows, describing how the data was used to extract limits on the mass of the excited quark particle. At the very end,
|
||||
in chapter 8, the results are presented and compared to previous research.
|
||||
|
||||
\newpage
|
||||
|
||||
# Theoretical background
|
||||
# Theoretical motivation
|
||||
|
||||
This chapter presents a short summary of the theoretical background relevant to this thesis. It first gives an
|
||||
introduction to the standard model itself and some of the issues it raises. It then goes on to explain the background
|
||||
processes of quantum chromodynamics and the theory of q*, which will be the main topic of this thesis.
|
||||
|
||||
## Standard model
|
||||
## Standard model {#sec:sm}
|
||||
|
||||
The Standard Model of physics proofed very successful in describing three of the four fundamental interactions currently
|
||||
known: the electromagnetic, weak and strong interaction. The fourth, gravity, could not yet be successfully included in
|
||||
this theory.
|
||||
The Standard Model of physics proved to be very successful in describing three of the four fundamental interactions
|
||||
currently known: the electromagnetic, weak and strong interaction. The fourth, gravity, could not yet be successfully
|
||||
included in this theory.
|
||||
|
||||
The Standard Model divides all particles into spin-$\frac{n}{2}$ fermions and spin-n bosons, where n could be any
|
||||
integer but so far is only known to be one for fermions and either one (gauge bosons) or zero (scalar bosons) for
|
||||
bosons. The fermions are further divided into quarks and leptons. Each of those exists in six so called flavours.
|
||||
Furthermore, quarks and leptons can also be divided into three generations, each of which contains two particles.
|
||||
In the lepton category, each generation has one charged lepton and one neutrino, that has no charge. Also, the mass of
|
||||
the neutrinos is not yet known, only an upper bound has been established. A full list of particles known to the
|
||||
standard model can be found in [@fig:sm]. Furthermore, all fermions have an associated anti particle with reversed
|
||||
charge. Multiple quarks can form bound states called hadrons (e.g. proton and neutron).
|
||||
bosons. Fermions are further classified into quarks and leptons.
|
||||
Quarks and leptons can also be categorized into three generations, each of which contains two particles, also called
|
||||
flavours. For leptons, the three generations each consist of a lepton and its corresponding neutrino, namely first the
|
||||
electron, then the muon and third, the tau. The three quark generations consist of first, the up and down, second, the
|
||||
charm and strange, and third, the top and bottom quark. So overall, their exists a total of six quark and six lepton
|
||||
flavours. A full list of particles known to the standard model can be found in [@fig:sm]. Furthermore, all fermions have
|
||||
an associated anti particle with reversed charge.
|
||||
|
||||
{width=50% #fig:sm}
|
||||
|
||||
The gauge bosons, namely the photon, $W^\pm$ bosons, $Z^0$ boson, and gluon, are mediators of the different
|
||||
|
|
@ -116,15 +125,94 @@ The probability of a quark changing its flavour from $i$ to $j$ is given by the
|
|||
matrix element $V_{ij}$. It is easy to see, that the change of flavour in the same generation is way more likely than
|
||||
any other flavour change.
|
||||
|
||||
The quantum chromodynamics (QCD) describe the strong interaction of particles. It applies to all
|
||||
particles carrying colour (e.g. quarks). The force is mediated by the gluon. This boson carries colour as well,
|
||||
although it doesn't carry only one colour but rather a combination of a colour and an anticolour, and can therefore
|
||||
interact with itself and exists in eight different variant. As a result of this, processes, where a gluon decays into
|
||||
two gluons are possible. Furthermore the strong force, binding to colour carrying particles, increases with their
|
||||
distance r making it at a certain point more energetically efficient to form a new quark - antiquark pair than
|
||||
separating the two particles even further. This effect is known as colour confinement. Due to this effect, colour
|
||||
carrying particles can't be observed directly, but rather form so called jets that cause hadronic showers in the
|
||||
detector. An effect called Hadronisation.
|
||||
Due to their high masses of 80.39 GeV resp. 91.19 GeV, the $W^\pm$ and $Z^0$ bosons themselves decay very quickly.
|
||||
Either in the leptonic or hadronic decay channel. In the leptonic channel, the $W^\pm$ decays to a lepton and the
|
||||
corresponding anti-lepton neutrino, in the hadronic channel it decays to a quark and an anti-quark of a different
|
||||
flavour. Due to the $Z^0$ boson having no charge, it always decays to a fermion and its anti-particle, in the leptonic
|
||||
channel this might be for example a electron - positron pair, in the hadronic channel an up and anti-up quark pair. This
|
||||
thesis examines the hadronic decay channel, where both vector bosons essentially decay to to quarks.
|
||||
|
||||
The quantum chromodynamics (QCD) describes the strong interaction of particles. It applies to all
|
||||
particles carrying colour (e.g. quarks). The force is mediated by gluons. These bosons carry colour as well,
|
||||
although they don't carry only one colour but rather a combination of a colour and an anticolour, and can therefore
|
||||
interact with themselves and exist in eight different variants. As a result of this, processes, where a gluon decays
|
||||
into two gluons are possible. Furthermore the strength of the strong force, binding to colour carrying particles,
|
||||
increases with their distance making it at a certain point more energetically efficient to form a new quark - antiquark
|
||||
pair than separating the two particles even further. This effect is known as colour confinement. Due to this effect,
|
||||
colour carrying particles can't be observed directly, but rather form so called jets that cause hadronic showers in the
|
||||
detector. Those jets are cone like structures made of hadrons and other particles. The effect is called Hadronisation.
|
||||
|
||||
### Shortcomings of the Standard Model
|
||||
|
||||
While being very successful in describing the effects observed in particle colliders or the particles reaching earth
|
||||
from cosmological sources, the Standard Model still has several shortcomings.
|
||||
|
||||
- **Gravity**: as already noted, the standard model doesn't include gravity as a force.
|
||||
- **Dark Matter**: observations of the rotational velocity of galaxies can't be explained by the known matter. Dark
|
||||
matter currently is our best theory to explain those.
|
||||
- **Matter-antimatter asymmetry**: The amount of matter vastly outweights the amount of antimatter in the observable
|
||||
universe. This can't be explained by the standard model, which predicts a similar amount of matter and antimatter.
|
||||
- **Symmetries between particles**: Why do exactly three generations of fermions exist? Why is the charge of a quark
|
||||
exactly one third of the charge of a lepton? How are the masses of the particles related? Those and more questions
|
||||
cannot be answered by the standard model.
|
||||
- **Hierarchy problem**: The weak force is approximately $10^{24}$ times stronger than gravity and so far, there's no
|
||||
satisfactory explanation as to why that is.
|
||||
|
||||
## Excited quark states {#sec:qs}
|
||||
|
||||
One category of theories that try to explain the symmetries between particles of the standard model are the composite
|
||||
quark models. Those state, that quarks consist of some particles unknown to us so far. This could explain the symmetries
|
||||
between the different fermions. A common prediction of those models are excited quark states (q\*, q\*\*, q\*\*\*...).
|
||||
Similar to atoms, that can be excited by the absorption of a photon and can then decay again under emission of a photon
|
||||
with an energy corresponding to the excited state, those excited quark states could decay under the emission of any
|
||||
boson. Quarks are smaller than $10^{-18}$ m. This corresponds to an energy scale of approximately 1 TeV. Therefore the
|
||||
excited quark states are expected to be in that region. That will cause the emitted boson to be highly boosted.
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\feynmandiagram [large, horizontal=qs to v] {
|
||||
a -- qs -- b,
|
||||
qs -- [fermion, edge label=\(q*\)] v,
|
||||
q1 [particle=\(q\)] -- v -- w [particle=\(W\)],
|
||||
q2 [particle=\(q\)] -- w -- q3 [particle=\(q\)],
|
||||
};
|
||||
\caption{Feynman diagram showing a possible decay of a q* particle to a W boson and a quark with the W boson also
|
||||
decaying to two quarks.} \label{fig:qsfeynman}
|
||||
\end{figure}
|
||||
This thesis will search data collected by the CMS in the years 2016, 2017 and 2018 for the single excited quark state
|
||||
q\* which can decay to a quark and any boson. An example of a q\* decaying to a quark and a W boson can be seen in
|
||||
[@fig:qsfeynman]. As explained in [@sec:sm], the vector boson can then decay either in the hadronic or leptonic decay
|
||||
channel. This research investigates only the hadronic channel with two quarks in the endstate. Because the boson is
|
||||
highly boosted, those will be very close together and therefore appear to the detector as only one jet. This means that
|
||||
the decay of a q\* particle will have two jets in the endstate (assuming the W/Z boson decays to two quarks) and will
|
||||
therefore be hard to distinguish from the QCD background described in [@sec:qcdbg].
|
||||
|
||||
The choice of only examining the decay of the q\* particle to the vector bosons is motivated by the branching ratios
|
||||
calculated for the decay [@QSTAR_THEORY]:
|
||||
|
||||
|
||||
: Branching ratios of the decaying q\* particle.
|
||||
|
||||
| decay mode | br. ratio [%] | decay mode | br. ratio [%] |
|
||||
|---------------------------|---------------|---------------------------|---------------|
|
||||
| $U^* \rightarrow ug$ | 83.4 | $D^* \rightarrow dg$ | 83.4 |
|
||||
| $U^* \rightarrow dW$ | 10.9 | $D^* \rightarrow uW$ | 10.9 |
|
||||
| $U^* \rightarrow u\gamma$ | 2.2 | $D^* \rightarrow d\gamma$ | 0.5 |
|
||||
| $U^* \rightarrow uZ$ | 3.5 | $D^* \rightarrow dZ$ | 5.1 |
|
||||
|
||||
The decay to the vector bosons have the second highest branching ratio. The decay to a gluon and a quark is the dominant
|
||||
decay, but virtually impossible to distinguish from the QCD background described in the next section. This makes the
|
||||
decay to the vector bosons the obvious choice.
|
||||
|
||||
To reconstruct the mass of the q\* particle from an event successfully recognized to be the decay of such a particle,
|
||||
the dijet invariant mass has to be calculated. This can be achieved by adding their four momenta, vectors consisting of
|
||||
the energy and momentum of a particle, together. From the four momentum it's easy to derive the mass by solving
|
||||
$E=\sqrt{p^2 + m^2}$ for m.
|
||||
|
||||
This theory has already been investigated in [@PREV_RESEARCH] analysing data recorded by CMS in 2016, excluding the q\*
|
||||
particle up to a mass of 5 TeV resp. 4.7 TeV for the decay to qW resp. qZ analysing the hadronic decay of the vector
|
||||
boson. This thesis aims to either exclude the particle to higher masses or find a resonance showing its existence using
|
||||
the higher center of mass energy of the LHC as well as more data that is available now.
|
||||
|
||||
### Quantum Chromodynamic background {#sec:qcdbg}
|
||||
|
||||
|
|
@ -133,8 +221,8 @@ signal processes from QCD effects. Those can also produce two jets in the endsta
|
|||
They are also happening very often in a proton proton collision, as it is happening in the Large Hadron Collider. This
|
||||
is caused by the structure of the proton. It not only consists of three quarks, called valence quarks, but also of a lot
|
||||
of quark-antiquark pairs connected by gluons, called the sea quarks, that exist due to the self interaction of the
|
||||
gluons binding the three valence quarks. Therefore in a proton - proton collision, interactions of gluons and quarks are
|
||||
the main processes causing a very strong QCD background.
|
||||
gluons binding the three valence quarks. Therefore the QCD multijet backgroubd is the dominant background of the signal
|
||||
described in [@sec:qs].
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
|
|
@ -151,56 +239,6 @@ the main processes causing a very strong QCD background.
|
|||
\caption{Two examples of QCD processes resulting in two jets.} \label{fig:qcdfeynman}
|
||||
\end{figure}
|
||||
|
||||
### Shortcomings of the Standard Model
|
||||
|
||||
While being very successful in describing mostly all of the effects we can observe in particle colliders so far, the
|
||||
Standard Model still has several shortcomings.
|
||||
|
||||
- **Gravity**: as already noted, the standard model doesn't include gravity as a force.
|
||||
- **Dark Matter**: observations of the rotational velocity of galaxies can't be explained by the known matter. Dark
|
||||
matter currently is our best theory to explain those.
|
||||
- **Matter-antimatter assymetry**: The amount of matter vastly outweights the amount of
|
||||
antimatter in the observable universe. This can't be explained by the standard model, which predicts a similar amount
|
||||
of matter and antimatter.
|
||||
- **Symmetries between particles**: Why do exactly three generations of fermions exist? Why is the charge of a quark
|
||||
exactly one third of the charge of a lepton? How are the masses of the particles related? Those and more questions
|
||||
cannot be answered by the standard model.
|
||||
- **Hierarchy problem**: The weak force is approximately $10^{24}$ times stronger than gravity and so far, there's no
|
||||
satisfactory explanation as to why that is.
|
||||
|
||||
## Excited quark states {#sec:qs}
|
||||
|
||||
One category of theories that try to solve some of the shortcomings of the standard model are the composite quark
|
||||
models. Those state, that quarks consist of some particles unknown to us so far. This could explain the symmetries
|
||||
between the different fermions. A common prediction of those models are excited quark states (q\*, q\*\*, q\*\*\*...).
|
||||
Similar to atoms, that can be excited by the absorption of a photon and can then decay again under emission of a photon
|
||||
with an energy corresponding to the excited state, those excited quark states could decay under the emission of some
|
||||
boson. Quarks are smaller than $10^{-18}$ m, due to that, excited states have to be of very high energy. That will cause
|
||||
the emitted boson to be highly boosted.
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\feynmandiagram [large, horizontal=qs to v] {
|
||||
a -- qs -- b,
|
||||
qs -- [fermion, edge label=\(q*\)] v,
|
||||
q1 [particle=\(q\)] -- v -- w [particle=\(W\)],
|
||||
q2 [particle=\(q\)] -- w -- q3 [particle=\(q\)],
|
||||
};
|
||||
\caption{Feynman diagram showing a possible decay of a q* particle to a W boson and a quark with the W boson also
|
||||
decaying to two quarks.} \label{fig:qsfeynman}
|
||||
\end{figure}
|
||||
This thesis will search data collected by the CMS in the years 2016, 2017 and 2018 for the single excited quark state
|
||||
q\* which can decay to a quark and any boson. An example of a q\* decaying to a quark and a W boson can be seen in
|
||||
[@fig:qsfeynman]. The boson quickly further decays into for example two quarks. Because the boson is highly boosted,
|
||||
those will be very close together and therefore appear to the detector as only one jet. This means that the decay of a
|
||||
q\* particle will have two jets in the endstate (assuming the W/Z boson decays to two quarks) and will therefore be hard
|
||||
to distinguish from the QCD background described in [@sec:qcdbg].
|
||||
|
||||
To reconstruct the mass of the q\* particle from an event successfully recognized to be the decay of such a particle,
|
||||
the dijet invariant mass, the mass of the two jets in the final state, can be calculated by adding their four momenta,
|
||||
vectors consisting of the energy and momentum of a particle, together. From the four momentum it's easy to derive the
|
||||
mass by solving $E=\sqrt{p^2 + m^2}$ for m.
|
||||
|
||||
\newpage
|
||||
|
||||
# Experimental Setup
|
||||
|
|
@ -210,9 +248,9 @@ Following on, the experimental setup used to gather the data analysed in this th
|
|||
## Large Hadron Collider
|
||||
|
||||
The Large Hadron Collider is the world's largest and most powerful particle accelerator [@website]. It has a perimeter
|
||||
of 27 km and can collide protons at a centre of mass energy of 13 TeV. It is home to several experiments, the biggest of
|
||||
those are ATLAS and the Compact Muon Solenoid (CMS). Both are general-purpose detectors to investigate the particles
|
||||
that form during particle collisions.
|
||||
of 27 km and can accelerate two beams of protons to an energy of 6.5 TeV resulting in a collision with a centre of mass
|
||||
energy of 13 TeV. It is home to several experiments, the biggest of those are ATLAS and the Compact Muon Solenoid (CMS).
|
||||
Both are general-purpose detectors to investigate the particles that form during particle collisions.
|
||||
|
||||
Particle colliders are characterized by their luminosity L. It is a quantity to be able to calculate the number of
|
||||
events per second generated in a collision by $N_{event} = L\sigma_{event}$ with $\sigma_{event}$ being the cross
|
||||
|
|
@ -237,7 +275,7 @@ $L_{int} = \int L dt$.
|
|||
|
||||
## Compact Muon Solenoid
|
||||
|
||||
The data used in this thesis was captured by the Compact Muon Solenoid (CMS). It is one of the biggest experiments at
|
||||
The data used in this thesis was recorded by the Compact Muon Solenoid (CMS). It is one of the four main experiments at
|
||||
the Large Hadron Collider. It can detect all elementary particles of the standard model except neutrinos. For that, it
|
||||
has an onion like setup. The particles produced in a collision first go through a tracking system. They then pass an
|
||||
electromegnetic as well as a hadronic calorimeter. This part is surrounded by a superconducting solenoid that generates
|
||||
|
|
@ -249,13 +287,15 @@ $\SI{137.19}{\per\femto\barn}$.
|
|||
|
||||
### Coordinate conventions
|
||||
|
||||
Per convention, the z axis points along the beam axis, the y axis upwards and the x axis horizontal towards the LHC
|
||||
centre. Furthermore, the azimuthal angle $\phi$, which describes the angle in the x - y plane, the polar angle $\theta$,
|
||||
which describes the angle in the y - z plane and the pseudorapidity $\eta$, which is defined as $\eta =
|
||||
-ln\left(tan\frac{\theta}{2}\right)$ are introduced. The coordinates are visualised in [@fig:cmscoords]. Furthermore,
|
||||
to describe a particles momentum, often the transverse momentum, $p_t$ is used. It is the component of the momentum
|
||||
transversal to the beam axis. It is a useful quantity, because the sum of all transverse momenta has to be zero.
|
||||
Missing transverse momentum implies particles that weren't detected such as neutrinos.
|
||||
Per convention, the z axis points along the beam axis in the direction of the magnetic fields of the solenoid, the y
|
||||
axis upwards and the x axis horizontal towards the LHC centre. The azimuthal angle $\phi$, which describes the angle in
|
||||
the x - y plane, the polar angle $\theta$, which describes the angle in the y - z plane and the pseudorapidity $\eta$,
|
||||
which is defined as $\eta = -ln\left(tan\frac{\theta}{2}\right)$ are also introduced. The coordinates are visualised in
|
||||
[@fig:cmscoords]. Furthermore, to describe a particle's momentum, often the transverse momentum, $p_t$ is used. It is
|
||||
the component of the momentum transversal to the beam axis. Before the collision, the transverse momentum obviously has
|
||||
to be zero, therefore, due to conservation of energy, the sum of all transverse momenta after the collision has to be
|
||||
zero, too. If this is not the case for the detected events, it implies particles that weren't detected such as
|
||||
neutrinos.
|
||||
|
||||
![Coordinate conventions of the CMS illustrating the use of $\eta$ and
|
||||
$\phi$. The Z axis is in beam direction. Taken from https://inspirehep.net/record/1236817/plots
|
||||
|
|
@ -263,17 +303,18 @@ $\phi$. The Z axis is in beam direction. Taken from https://inspirehep.net/recor
|
|||
|
||||
### The tracking system
|
||||
|
||||
The tracking system is built of two parts, first a pixel detector and then silicon strip sensors. It is used to
|
||||
reconstruct the tracks of charged particles, measuring their charge sign, direction and momentum. It is as close to the
|
||||
collision as possible to be able to identify secondary vertices.
|
||||
The tracking system is built of two parts, closest to the collision is a pixel detector and around that silicon strip
|
||||
sensors. They are used to reconstruct the tracks of charged particles, measuring their charge sign, direction and
|
||||
momentum. They are as close to the collision as possible to be able to identify secondary vertices.
|
||||
|
||||
### The electromagnetic calorimeter
|
||||
|
||||
The electromagnetic calorimeter measures the energy of photons and electrons. It is made of tungstate crystal.
|
||||
When passed by particles, it produces light in proportion to the particle's energy. This light is measured by
|
||||
photodetectors that convert this scintillation light to an electrical signal. To measure a particles energy, it has to
|
||||
leave its whole energy in the ECAL, which is true for photons and electrons, but not for other particles such as
|
||||
hadrons and muons. They too leave some energy in the ECAL.
|
||||
The electromagnetic calorimeter measures the energy of photons and electrons. It is made of tungstate crystal and
|
||||
photodetectors. When passed by particles, the crystal produces light in proportion to the particle's energy. This light
|
||||
is measured by the photodetectors that convert this scintillation light to an electrical signal. To measure a particles
|
||||
energy, it has to leave its whole energy in the ECAL, which is true for photons and electrons, but not for other
|
||||
particles such as hadrons and muons. Those have are of higher energy and therefore only leave some energy in the ECAL
|
||||
but are not stopped by it.
|
||||
|
||||
### The hadronic calorimeter
|
||||
|
||||
|
|
@ -322,9 +363,10 @@ algorithm. It arises from a generalization of several other clustering algorithm
|
|||
and SISCone clustering algorithms.
|
||||
|
||||
The anti-$k_t$ clustering algorithm associates hard particles with their soft particles surrounding them within a radius
|
||||
R in the $\eta$ - $\phi$ plane forming cone like jets. If two jets overlap, the jets shape is changed according to its
|
||||
hardness. A softer particles jet will change its shape more than a harder particles. A visual comparison of four
|
||||
different clustering algorithms can be seen in [@fig:antiktcomparision]. For this analysis, a radius of 0.8 is used.
|
||||
$R = \sqrt{\eta^2 - \phi^2}$ in the $\eta$ - $\phi$ plane forming cone like jets. If two jets overlap, the jets shape is
|
||||
changed according to its hardness in regards to the transverse momentum. A softer particles jet will change its shape
|
||||
more than a harder particles. A visual comparison of four different clustering algorithms can be seen in
|
||||
[@fig:antiktcomparison]. For this analysis, a radius of 0.8 is used.
|
||||
|
||||
Furthermore, to approximate the mass of a heavy particle that caused a jet, the softdropmass can be used. It is
|
||||
calculated by removing wide angle soft particles from the jet to counter the effects of contamination from initial state
|
||||
|
|
@ -332,53 +374,40 @@ radiation, underlying event and multiple hadron scattering. It therefore is more
|
|||
particle causing a jet than taking the mass of all constituent particles of the jet combined.
|
||||
|
||||
{#fig:antiktcomparision}
|
||||
Comparison of the $k_t$, Cambridge/Aachen, SISCone and anti-$k_t$ algorithms clustering a sample parton-level event
|
||||
with many random soft "ghosts". Taken from [@ANTIKT]
|
||||
](./figures/antikt-comparision.png){#fig:antiktcomparison}
|
||||
|
||||
[@fig:antiktcomparison] clearly shows, that the jets reconstructed using the anti-$k_t$ algorithm are closest to having
|
||||
a cone like shape and are so fucking beautiful.
|
||||
|
||||
\newpage
|
||||
|
||||
# Method of analysis
|
||||
# Method of analysis {#sec:moa}
|
||||
|
||||
This section gives an overview over how the data gathered by the LHC and CMS is going to be analysed to be able to
|
||||
either exclude the q\* particle to even higher masses than already done or maybe confirm its existence.
|
||||
|
||||
As described in [@sec:qs], an excited quark q\* can decay to a quark and any boson. The branching ratios are calculated
|
||||
to be as follows [@QSTAR_THEORY]:
|
||||
|
||||
|
||||
: Branching ratios of the decaying q\* particle.
|
||||
|
||||
| decay mode | br. ratio [%] | decay mode | br. ratio [%] |
|
||||
|---------------------------|---------------|---------------------------|---------------|
|
||||
| $U^* \rightarrow ug$ | 83.4 | $D^* \rightarrow dg$ | 83.4 |
|
||||
| $U^* \rightarrow dW$ | 10.9 | $D^* \rightarrow uW$ | 10.9 |
|
||||
| $U^* \rightarrow u\gamma$ | 2.2 | $D^* \rightarrow d\gamma$ | 0.5 |
|
||||
| $U^* \rightarrow uZ$ | 3.5 | $D^* \rightarrow dZ$ | 5.1 |
|
||||
|
||||
The majority of excited quarks will decay to a quark and a gluon, but as this is virtually impossible to distinguish
|
||||
from QCD effects (for example from the qg $\rightarrow$ qg processes), this analysis will focus on the processes q\*
|
||||
$\rightarrow$ qW and q\* $\rightarrow$ qZ. In this case, due to jet substructure studies, it is possible to establish a
|
||||
discriminator between QCD background and jets originating in a W/Z decay. They still make up roughly 20 % of the signal
|
||||
events to study and therefore seem like a good choice.
|
||||
As described in [@sec:qs], the decay of the q\* particle to a quark and a vector boson with the vector boson then
|
||||
decaying hadronically will be investigated. This is the second most probable decay of the q\* particle and easier to
|
||||
analyse than the dominant decay to a quark and a gluon. Therefore it is a good choice for this research.
|
||||
|
||||
The data studied was collected by the CMS experiment in the years 2016, 2017 and 2018. It is analysed with the Particle
|
||||
Flow algorithm to reconstruct jets and all the other particles forming during the collision. The jets are then clustered
|
||||
using the anti-$k_t$ algorithm with the distance parameter R being 0.8. Furthermore, the calorimeters of the CMS
|
||||
detector have to be calibrated. For that, jet energy corrections published by the CMS working group are applied to the
|
||||
data.
|
||||
using the anti-$k_t$ algorithm with the distance parameter R being 0.8.
|
||||
|
||||
To find signal events in the data, this thesis looks at the dijet invariant mass distribution. The data is assumed to
|
||||
only consist of QCD background and signal events, other backgrounds are neglected. Cuts on several distributions are
|
||||
introduced to reduce the background and improve the sensitivity for the signal. If the q\* particle exists, the dijet
|
||||
invariant mass distribution should show a resonance at its invariant mass. This resonance will be looked for with
|
||||
statistical methods explained later on.
|
||||
To find the signal events, described in [@sec:qs], in the data, this thesis looks at the dijet invariant mass
|
||||
distribution. The only background considered is the QCD background described in [@sec:qcdbg]. A selection using
|
||||
different kinematic variables as well as a tagger to identify jets from the decay of a vector boson is introduced to
|
||||
reduce the background and increase the sensitivity for the signal. After that, it will be looked for a peak in the dijet
|
||||
invariant mass distribution at the resonance mass of the q\* particle.
|
||||
|
||||
The analysis will be conducted with two different sets of data. First, only the data collected by CMS in 2016 will be
|
||||
used to compare the results to the previous analysis [@PREV_RESEARCH]. Then the combined data from 2016, 2017 and 2018
|
||||
will be used to improve the previously set limits for the mass of the q\* particle. Also, two different tagging
|
||||
mechanisms will be used. One based on the N-subjettiness variable used in the previous research, the other being a novel
|
||||
approach using a deep neural network.
|
||||
will be used to improve the previously set limits for the mass of the q\* particle. Also, two different V-tagging
|
||||
mechanisms will be used to compare their performance. One based on the N-subjettiness variable used in the previous
|
||||
research [@PREV_RESEARCH], the other being a novel approach using a deep neural network, that will be explained in the
|
||||
following.
|
||||
|
||||
## Signal and Background modelling
|
||||
|
||||
|
|
@ -405,11 +434,14 @@ The signal is fitted using a double sided crystal ball function. It has six para
|
|||
- sigma: the functions width, in this case the resolution of the detector
|
||||
- n1, n2, alpha1, alpha2: parameters influencing the shape of the left and right tail
|
||||
|
||||
A gaussian and a poisson have also been studied but found to not fit the signal sample very well as they aren't able to
|
||||
fit the tail on both sides of the peak.
|
||||
A gaussian and a poisson function have also been studied but found to be not able to reproduce the signal shape as they
|
||||
couldn't model the tails on both sides of the peak.
|
||||
|
||||
An example of a fit of these functions to a toy dataset with gaussian errors can be seen in [@fig:cb_fit]. In this
|
||||
figure, a binning of 200 GeV is used. For the actual analysis a 1 GeV binning will be used.
|
||||
figure, a binning of 200 GeV is used. For the actual analysis a 1 GeV binning will be used. It can be seen that the fit
|
||||
works very well and therefore confirms the functions chosen to model signal and background. This is supported by a
|
||||
$\chi^2 /$ ndof of 0.5 and a found mean for the signal at 2999 $\pm$ 23 $\si{\giga\eV}$ which is extremely close to the
|
||||
expected 3000 GeV mean. Those numbers clearly show that the method in use is able to successfully describe the data.
|
||||
|
||||
![
|
||||
Combined fit of signal and background on a toy dataset with gaussian errors and a simulated resonance mass of 3 TeV.
|
||||
|
|
@ -419,24 +451,26 @@ Combined fit of signal and background on a toy dataset with gaussian errors and
|
|||
|
||||
# Preselection and data quality
|
||||
|
||||
To separate the background from the signal, cuts on several distributions have to be introduced. The selection of events
|
||||
is divided into
|
||||
two parts. The first one (the preselection) adds some general physics motivated cuts and is also used to make sure a
|
||||
good trigger efficiency is achieved. It is not expected to already provide a good separation of background and signal.
|
||||
In the second part, different taggers will be used as a discriminator between QCD background and signal events. After
|
||||
the preselection, it is made sure, that the simulated samples represent the real data well.
|
||||
To reduce the background and increase the signal sensitivity, a selection of events by different variables is
|
||||
introduced. It is divided into two stages. The first one (the preselection) adds some general physics motivated
|
||||
selection using kinematic variables and is also used to make sure a good trigger efficiency is achieved. In the second
|
||||
part, different taggers will be used as a discriminator between QCD background and signal events. After the
|
||||
preselection, it is made sure, that the simulated samples represent the real data well by comparing the data with the
|
||||
simulation in the signal as well as a sideband region, where no signal events are expected.
|
||||
|
||||
## Preselection
|
||||
|
||||
First, all events are cleaned of jets with a $p_t < \SI{200}{\giga\eV}$ and a pseudorapidity $|\eta| > 2.4$. This is to
|
||||
discard soft background and to make sure the particles are in the barrel region of the detector for an optimal detector
|
||||
resolution. Furthermore, all events with one of the two highest $p_t$ jets having an angular separation smaller
|
||||
discard soft background and to make sure the particles are in the barrel region of the detector for an optimal track
|
||||
reconstruction. Furthermore, all events with one of the two highest $p_t$ jets having an angular separation smaller
|
||||
than 0.8 from any electron or muon are discarded to allow future use of the results in studies of the semi or
|
||||
all-leptonic decay channels.
|
||||
|
||||
From a decaying q\* particle, we expect two jets in the endstate. Therefore a cut is added to have at least 2 jets.
|
||||
More jets are also possible, for example caused by gluon radiation of a quark causing another jet. The cut can be seen
|
||||
in [@fig:njets].
|
||||
From a decaying q\* particle, we expect two jets in the endstate. The dijet invariant mass of those two jets will be
|
||||
used to reconstruct the mass of the q\* particle. Therefore a cut is added to have at least 2 jets.
|
||||
More jets are also possible, for example caused by gluon radiation of a quark causing another jet. If this is the case,
|
||||
the two jets with the highest $p_t$ are used for the reconstruction of the q\* mass.
|
||||
The distributions of the number of jets before and after the selection can be seen in [@fig:njets].
|
||||
|
||||
\begin{figure}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
|
|
@ -457,11 +491,13 @@ are amplified by a factor of 10,000, to be visible.}
|
|||
\label{fig:njets}
|
||||
\end{figure}
|
||||
|
||||
Another cut is on $\Delta\eta$. The q\* particle is expected to be very heavy in regards to the center of mass energy of
|
||||
the collision and will therefore be almost stationary. Its decay products should therefore be close to back to back,
|
||||
which means the $\Delta\eta$ distribution is expected to peak at 0. At the same time, particles originating from QCD
|
||||
effects are expected to have a higher $\Delta\eta$ as they mainly form from less heavy resonances. To maintain
|
||||
comparability, the same cut as in previous research of $\Delta\eta \le 1.3$ is used as can be seen in [@fig:deta].
|
||||
The next selection is done using $\Delta\eta = |\eta_1 - \eta_2|$, with $\eta_1$ and $\eta_2$ being the $\eta$ of the
|
||||
first two jets in regards to their transverse momentum. The q\* particle is expected to be very heavy in regards to the
|
||||
center of mass energy of the collision and will therefore be almost stationary. Its decay products should therefore be
|
||||
close to back to back, which means the $\Delta\eta$ distribution is expected to peak at 0. At the same time, particles
|
||||
originating from QCD effects are expected to have a higher $\Delta\eta$ as they mainly form from less heavy resonances.
|
||||
To maintain comparability, the same selection as in previous research of $\Delta\eta \le 1.3$ is used. A comparison of
|
||||
the $\Delta\eta$ distribution before and after the selection can be seen in [@fig:deta].
|
||||
|
||||
\begin{figure}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
|
|
@ -482,11 +518,11 @@ are amplified by a factor of 10,000, to be visible.}
|
|||
\label{fig:deta}
|
||||
\end{figure}
|
||||
|
||||
The last cut in the preselection is on the dijet invariant mass: $m_{jj} \ge \SI{1050}{\giga\eV}$. It is important for a
|
||||
high trigger efficiency and can be seen in [@fig:invmass]. Also, it has a huge impact on the background because it
|
||||
The last selection in the preselection is on the dijet invariant mass: $m_{jj} \ge \SI{1050}{\giga\eV}$. It is important
|
||||
for a high trigger efficiency and can be seen in [@fig:invmass]. Also, it has a huge impact on the background because it
|
||||
usually consists of way lighter particles. The q\* on the other hand is expected to have a very high invariant mass of
|
||||
more than 1 TeV. The distribution should be a smoothly falling function for the QCD background and peak at the simulated
|
||||
resonance mass for the signal events.
|
||||
more than 1 TeV. The $m_{jj}$ distribution should be a smoothly falling function for the QCD background and peak at the
|
||||
simulated resonance mass for the signal events.
|
||||
|
||||
\begin{figure}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
|
|
@ -514,16 +550,18 @@ preselection is reduced to 5 % of the original events. For the combined data of
|
|||
similar. Decaying to qW signal efficiencies between 49 % (1.6 TeV) and 56 % (7 TeV) are reached, wheres the efficiencies
|
||||
when decaying to qZ are in the range of 46 % (1.6 TeV) to 50 % (7 TeV). Here, the background could be reduced to 8 % of
|
||||
the original events. So while keeping around 50 % of the signal, the background was already reduced to less than a
|
||||
tenth. Still, as can be seen in [@fig:njets] to [@fig:invmass], the amount of signal is very low and, without
|
||||
logarithmic scale, even has to be amplified to be visible.
|
||||
tenth. Still, as can be seen in [@fig:njets] to [@fig:invmass], the amount of signal is very low.
|
||||
|
||||
## Data - Monte Carlo Comparison
|
||||
|
||||
To ensure high data quality, the simulated QCD background sample is now being compared to the actual data of the
|
||||
corresponding year collected by the CMS detector. This is done for the year 2016 and for the combined data of years
|
||||
2016, 2017 and 2018. The distributions are rescaled so the integral over the invariant mass distribution of data and
|
||||
simulation are the same. In [@fig:data-mc], the three distributions that cuts were applied on can be seen for year 2016
|
||||
and the combined data of years 2016 to 2018.
|
||||
simulation are the same. In [@fig:data-mc], the three distributions of the variables that were used for the preselection
|
||||
can be seen for year 2016 and the combined data of years 2016 to 2018.
|
||||
For analysing the real data from the CMS, jet energy corrections have to be applied. Those are to calibrate the ECAL and
|
||||
HCAL parts of the CMS, so the energy of the detected particles can be measured correctly. The corrections used were
|
||||
published by the CMS group. [source needed, but not sure where to find it]
|
||||
|
||||
\begin{figure}
|
||||
\begin{minipage}{0.33\textwidth}
|
||||
|
|
@ -555,13 +593,11 @@ and simulation.
|
|||
|
||||
### Sideband
|
||||
|
||||
The sideband is introduced to make sure there are no unwanted side effects of the used cuts. It is a region in which no
|
||||
data is used for the actual analysis. Again, data and the Monte Carlo simulation are compared. For this analysis, the
|
||||
The sideband is introduced to make sure no bias in the data and Monte Carlo simulation is introduced. It is a region in
|
||||
which no signal event is expected. Again, data and the Monte Carlo simulation are compared. For this analysis, the
|
||||
region where the softdropmass of both of the two jets with the highest transverse momentum ($p_t$) is more than 105 GeV
|
||||
was chosen. Because the decay of a q\* to a vector boson is being investigated, later on, a selection is applied that
|
||||
one of those particles has to have a mass between 105 GeV and 35 GeV. Therefore events with jets with a softdropmass
|
||||
higher than 105 GeV will not be used for this analysis which makes them a good sideband to use.
|
||||
|
||||
was chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, the heavier vector boson. Therefore it is very
|
||||
unlikely that a particle heavier than t
|
||||
In [@fig:sideband], the comparison of data with simulation in the sideband region can be seen for the softdropmass
|
||||
distribution as well as the dijet invariant mass distribution. As in [fig:data-mc], the histograms are rescaled, so that
|
||||
the dijet invariant mass distributions of data and simulation have the same integral.
|
||||
|
|
@ -589,14 +625,14 @@ combined data from 2016, 2017 and 2018.}
|
|||
|
||||
# Jet substructure selection
|
||||
|
||||
So far it was made sure, that the actual data and the simulation match well after the preselection and no unwanted side
|
||||
effects are introduced in the data by the used cuts. Now another selection has to be introduced, to further reduce the
|
||||
background to be able to extract the hypothetical signal events from the actual data.
|
||||
So far it was made sure, that the actual data and the simulation are in good agreement after the preselection and no
|
||||
unwanted side effects are introduced in the data by the used cuts. Now another selection has to be introduced, to
|
||||
further reduce the background to be able to extract the hypothetical signal events from the actual data.
|
||||
|
||||
This is done by distinguishing between QCD and signal events using a tagger to identify jets coming
|
||||
from a vector boson. Two different taggers will be used to later compare the results. The decay analysed includes either
|
||||
a W or Z boson, which are, compared to the particles in QCD effects, very heavy. This can be used by adding a cut on the
|
||||
softdropmass of a jet. The softdropmass of at least one of the two leading jets is expected to be within
|
||||
from a vector boson. Two different taggers will be used to later compare their performance. The decay analysed includes
|
||||
either a W or Z boson, which are, compared to the particles in QCD effects, very heavy. This can be used by adding a cut
|
||||
on the softdropmass of a jet. The softdropmass of at least one of the two leading jets is expected to be within
|
||||
$\SI{35}{\giga\eV}$ and $\SI{105}{\giga\eV}$. This cut already provides a good separation of QCD and signal events, on
|
||||
which the two taggers presented next can build.
|
||||
|
||||
|
|
@ -605,7 +641,7 @@ QCD effects. This value will be optimized afterwards to make sure the maximum ef
|
|||
|
||||
## N-Subjettiness
|
||||
|
||||
The N-subjettiness $\tau_n$ is a jet shape parameter designed to identify boosted hadronically-decaying objects. When a
|
||||
The N-subjettiness $\tau_N$ is a jet shape parameter designed to identify boosted hadronically-decaying objects. When a
|
||||
vector boson decays hadronically, it produces two quarks each causing a jet. But because of the high mass of the vector
|
||||
bosons, the particles are highly boosted and appear, after applying a clustering algorithm, as just one. This algorithm
|
||||
now tries to figure out, whether one jet might consist of two subjets by using the kinematics and positions of the
|
||||
|
|
@ -651,7 +687,7 @@ vector boson. Therefore, using the same way to choose a candidate jet as for the
|
|||
applied so that this candidate jet has a WvsQCD/ZvsQCD value greater than some value determined by the optimization
|
||||
presented next.
|
||||
|
||||
## Optimization
|
||||
## Optimization {#sec:opt}
|
||||
|
||||
To figure out the best value to cut on the discriminators introduced by the two taggers, a value to quantify how good a
|
||||
cut is has to be introduced. For that, the significance calculated by $\frac{S}{\sqrt{B}}$ will be used. S stands for
|
||||
|
|
@ -660,7 +696,9 @@ error on the background so it will be calculated for the 2 TeV masspoint where e
|
|||
this assumption. It follows from the central limit theorem that states, that for identical distributed random variables,
|
||||
their sum converges to a gaussian distribution. The significance therefore represents how good the signal can be
|
||||
distinguished from the background in units of the standard deviation of the background. As interval, a 10 % margin
|
||||
around the masspoint is chosen.
|
||||
around the resonance nominal mass is chosen. The significance is then calculated for different selections on the
|
||||
discriminant of the two taggers and then plotted in dependence on the minimum resp. maximum allowed value of the
|
||||
discriminant to pass the selection for the deep boosted resp. the N-subjettiness tagger.
|
||||
|
||||
\begin{figure}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
|
|
@ -678,13 +716,14 @@ boosted cut is placed at $\ge 0.95$. For the deep boosted tagger, 0.97 would giv
|
|||
it is very close to the edge where the significance drops very low and the higher the cut the less background will be
|
||||
left to calculate the cross section limits, especially at higher resonance masses, the slightly less strict cut is
|
||||
chosen.
|
||||
The significance for the $\tau_{21}$ cut is 14.08, and for the deep boosted tagger 25.61.
|
||||
The significance for the $\tau_{21}$ cut is 14, and for the deep boosted tagger 26.
|
||||
|
||||
For both taggers also a low purity category is introduced for high TeV regions. Using the cuts optimized for 2 TeV,
|
||||
there are very few background events left for higher resonance masses, but to reliably calculate cross section limits,
|
||||
those are needed. As low purity category for the N-subjettiness tagger, a cut at $0.35 < \tau_{21} < 0.75$ is used. For
|
||||
the deep boosted tagger the opposite cut from the high purity category is used: $VvsQCD < 0.95$.
|
||||
|
||||
# Signal extraction
|
||||
# Signal extraction {#sec:extr}
|
||||
|
||||
After the optimization, now the optimal selection for the N-subjettiness as well as the deep boosted tagger is found and
|
||||
applied to the simulated samples as well as the data collected by the CMS. The fit described in [@sec:moa] is performed
|
||||
|
|
@ -702,99 +741,45 @@ uncertainty with the observed limit is also calculated.
|
|||
|
||||
## Uncertainties
|
||||
|
||||
The following uncertainties are considered:
|
||||
For calculating the cross section of the signal, four sources of uncertainties are considered.
|
||||
|
||||
- *Luminosity*: the integrated luminosity of the LHC has an uncertainty of 2.5 %.
|
||||
- *Jet Energy Corrections*: for the Jet Energy Corrections, an uncertainty of 2 % is assumed.
|
||||
- *Tagger Efficiency(?)*: 6 % (TODO!)
|
||||
- *Parameter Uncertainty of the fit*: The CombinedLimit program used for determining the cross section varies the
|
||||
parameters used for the fit and therefore includes their uncertainties to calculate the final result.
|
||||
First, the uncertainty of the Jet Energy Corrections. When measuring a particle's energy with the ECAL or HCAL part of
|
||||
the CMS, the electronic signals send by the photodetectors in the calorimeters have to be converted to actual energy
|
||||
values. Therefore an error in this calibration causes the energy measured to be shifted to higher or lower values
|
||||
causing also the position of the signal peak in the $m_{jj}$ distribution to vary. The uncertainty is approximated to be
|
||||
2 %.
|
||||
|
||||
Second, the tagger is not perfect and therefore some events, that don't originate from a V boson are wrongly chosen and
|
||||
on the other hand sometimes events that do originate from one are not. It influences the events chose for analysis and
|
||||
is therefore also considered as an uncertainty, which is approximated to be 6 %.
|
||||
|
||||
Third, the uncertainty of the parameters of the background fit is also considered, as it might change the background
|
||||
shape a little and therefore influence how many signal and background events are reconstructed from the data.
|
||||
|
||||
Fourth, the uncertainty on the Luminosity of the LHC of 2.5 % is also taken into account for the final results.
|
||||
|
||||
# Results
|
||||
|
||||
In this chapter the results and a comparison to previous research will be shown as well as a comparison between the two
|
||||
different taggers used.
|
||||
This chapter will start by presenting the results for the data of year 2016 using both taggers and comparing it to the
|
||||
previous research [@PREV_RESEARCH]. It will then go on showing the results for the combined dataset, again using both
|
||||
taggers comparing their performances.
|
||||
|
||||
## 2016
|
||||
|
||||
Using the data collected by the CMS experiment on 2016, the cross section limits seen in [@fig:res2016] were obtained.
|
||||
The extracted cross section limits are:
|
||||
Using the data collected by the CMS experiment on 2016, the cross section limits seen in [@fig:res2016] were obtained.
|
||||
|
||||
As described in [@sec:extr], the calculated cross section limits are used to then calculate a mass limit, meaning the
|
||||
lowest possible mass of the q\* particle, by finding the crossing of the theory line with the observed cross section
|
||||
limit. In [@fig:res2016] it can be seen, that the observed limit in the region where theory and observed limit cross is
|
||||
very high compared to when using the N-subjettiness tagger. Therefore the two lines cross earlier, which results in
|
||||
lower exclusion limits on the mass of the q\* particle causing the deep boosted tagger to perform worse than the
|
||||
N-subjettiness tagger in regards of establishing those limits as can be seen in {@tbl:res2016}. The table also shows the
|
||||
upper and lower limits on the mass found by calculating the crossing of the theory plus resp. minus its uncertainty. Due
|
||||
to the theory and the observed limits line being very flat in the high TeV region, even a small uncertainty of the
|
||||
theory can cause a high difference of the mass limit.
|
||||
|
||||
|
||||
: Cross Section limits using 2016 data and the N-subjettiness tagger for the decay to qW
|
||||
|
||||
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
||||
|------------|-----------------|------------------|------------------|-----------------|
|
||||
| 1.6 | 0.10406 | 0.14720 | 0.07371 | 0.08165 |
|
||||
| 1.8 | 0.07656 | 0.10800 | 0.05441 | 0.04114 |
|
||||
| 2.0 | 0.05422 | 0.07605 | 0.03879 | 0.04043 |
|
||||
| 2.5 | 0.02430 | 0.03408 | 0.01747 | 0.04052 |
|
||||
| 3.0 | 0.01262 | 0.01775 | 0.00904 | 0.02109 |
|
||||
| 3.5 | 0.00703 | 0.00992 | 0.00502 | 0.00399 |
|
||||
| 4.0 | 0.00424 | 0.00603 | 0.00300 | 0.00172 |
|
||||
| 4.5 | 0.00355 | 0.00478 | 0.00273 | 0.00249 |
|
||||
| 5.0 | 0.00269 | 0.00357 | 0.00211 | 0.00240 |
|
||||
| 6.0 | 0.00103 | 0.00160 | 0.00068 | 0.00062 |
|
||||
| 7.0 | 0.00063 | 0.00105 | 0.00039 | 0.00086 |
|
||||
|
||||
|
||||
: Cross Section limits using 2016 data and the deep boosted tagger for the decay to qW
|
||||
|
||||
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
||||
|------------|-----------------|------------------|------------------|-----------------|
|
||||
| 1.6 | 0.17750 | 0.25179 | 0.12572 | 0.38242 |
|
||||
| 1.8 | 0.11125 | 0.15870 | 0.07826 | 0.11692 |
|
||||
| 2.0 | 0.08188 | 0.11549 | 0.05799 | 0.09528 |
|
||||
| 2.5 | 0.03328 | 0.04668 | 0.02373 | 0.03653 |
|
||||
| 3.0 | 0.01648 | 0.02338 | 0.01181 | 0.01108 |
|
||||
| 3.5 | 0.00840 | 0.01195 | 0.00593 | 0.00683 |
|
||||
| 4.0 | 0.00459 | 0.00666 | 0.00322 | 0.00342 |
|
||||
| 4.5 | 0.00276 | 0.00412 | 0.00190 | 0.00366 |
|
||||
| 5.0 | 0.00177 | 0.00271 | 0.00118 | 0.00401 |
|
||||
| 6.0 | 0.00110 | 0.00175 | 0.00071 | 0.00155 |
|
||||
| 7.0 | 0.00065 | 0.00108 | 0.00041 | 0.00108 |
|
||||
|
||||
|
||||
: Cross Section limits using 2016 data and the N-subjettiness tagger for the decay to qZ
|
||||
|
||||
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
||||
|------------|-----------------|------------------|------------------|-----------------|
|
||||
| 1.6 | 0.08687 | 0.12254 | 0.06174 | 0.06987 |
|
||||
| 1.8 | 0.06719 | 0.09477 | 0.04832 | 0.03424 |
|
||||
| 2.0 | 0.04734 | 0.06640 | 0.03405 | 0.03310 |
|
||||
| 2.5 | 0.01867 | 0.02619 | 0.01343 | 0.03214 |
|
||||
| 3.0 | 0.01043 | 0.01463 | 0.00744 | 0.01773 |
|
||||
| 3.5 | 0.00596 | 0.00840 | 0.00426 | 0.00347 |
|
||||
| 4.0 | 0.00353 | 0.00500 | 0.00250 | 0.00140 |
|
||||
| 4.5 | 0.00233 | 0.00335 | 0.00164 | 0.00181 |
|
||||
| 5.0 | 0.00157 | 0.00231 | 0.00110 | 0.00188 |
|
||||
| 6.0 | 0.00082 | 0.00126 | 0.00054 | 0.00049 |
|
||||
| 7.0 | 0.00050 | 0.00083 | 0.00031 | 0.00066 |
|
||||
|
||||
|
||||
: Cross Section limits using 2016 data and deep boosted tagger for the decay to qZ
|
||||
|
||||
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
||||
|------------|-----------------|------------------|------------------|-----------------|
|
||||
| 1.6 | 0.16687 | 0.23805 | 0.11699 | 0.35999 |
|
||||
| 1.8 | 0.12750 | 0.17934 | 0.09138 | 0.12891 |
|
||||
| 2.0 | 0.09062 | 0.12783 | 0.06474 | 0.09977 |
|
||||
| 2.5 | 0.03391 | 0.04783 | 0.02422 | 0.03754 |
|
||||
| 3.0 | 0.01781 | 0.02513 | 0.01277 | 0.01159 |
|
||||
| 3.5 | 0.00949 | 0.01346 | 0.00678 | 0.00741 |
|
||||
| 4.0 | 0.00494 | 0.00711 | 0.00349 | 0.00362 |
|
||||
| 4.5 | 0.00293 | 0.00429 | 0.00203 | 0.00368 |
|
||||
| 5.0 | 0.00188 | 0.00284 | 0.00127 | 0.00426 |
|
||||
| 6.0 | 0.00102 | 0.00161 | 0.00066 | 0.00155 |
|
||||
| 7.0 | 0.00053 | 0.00085 | 0.00034 | 0.00085 |
|
||||
|
||||
|
||||
As can be seen in [@fig:res2016], the observed limit in the region where theory and observed limit cross is very high
|
||||
compared to when using the N-subjettiness tagger. Therefore the two lines cross earlier, which results in lower
|
||||
exclusion limits on the mass of the q\* particle.
|
||||
|
||||
|
||||
: Mass limits found using the data collected in 2016
|
||||
: Mass limits found using the data collected in 2016 {#tbl:res2016}
|
||||
|
||||
| Decay | Tagger | Limit [TeV] | Upper Limit [TeV] | Lower Limit [TeV] |
|
||||
|-------|--------------|-------------|-------------------|-------------------|
|
||||
|
|
@ -825,12 +810,15 @@ exclusion limits on the mass of the q\* particle.
|
|||
|
||||
### Previous research
|
||||
|
||||
The limit is already slightly higher than the one from previous research, which was found to be 5 TeV for the decay to
|
||||
qW and 4.7 TeV for the decay to qZ. This is mainly due to the fact, that in our data, the observed limit at the
|
||||
intersection point happens to be in the lower region of the expected limit interval and therefore causing a very late
|
||||
crossing with the theory line when using the N-subjettiness tagger (as can be seen in [@fig:res2016]. This could be
|
||||
caused by small differences of the setup used or slightly differently processed data. In general, the results appear to
|
||||
be very similar to the previous research, seen in [@fig:prev].
|
||||
The limit established by using the N-subjettiness tagger on the 2016 data is already slightly higher than the one from
|
||||
previous research, which was found to be 5 TeV for the decay to qW and 4.7 TeV for the decay to qZ. This is mainly due
|
||||
to the fact, that in our data, the observed limit at the intersection point happens to be in the lower region of the
|
||||
expected limit interval and therefore causing a very late crossing with the theory line when using the N-subjettiness
|
||||
tagger (as can be seen in [@fig:res2016]). This could be caused by small differences of the setup used or slightly
|
||||
differently processed data. Comparing the expected limits, there is a difference between 3 % and 30 %, between the
|
||||
values calculated by this thesis compared to the previous research. It is not, however, that one of the two results was
|
||||
constantly lower or higher but rather fluctuating. Therefore it can be said, that the results are in good agreement. The
|
||||
cross section limits of the previous research can be seen in [@fig:prev].
|
||||
|
||||
\begin{figure}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
|
|
@ -844,81 +832,11 @@ Taken from \cite{PREV_RESEARCH}.}
|
|||
\label{fig:prev}
|
||||
\end{figure}
|
||||
|
||||
## 2016 + 2017 + 2018
|
||||
|
||||
Using the combined data, the cross section limits seen in [@fig:resCombined] were obtained. It is quite obvious, that
|
||||
the limits are already significantly lower than when only using the data of 2016. The extracted cross section limits are
|
||||
the following:
|
||||
|
||||
|
||||
: Cross Section limits using the combined data and the N-subjettiness tagger for the decay to qW
|
||||
|
||||
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
||||
|------------|-----------------|------------------|------------------|-----------------|
|
||||
| 1.6 | 0.05703 | 0.07999 | 0.04088 | 0.03366 |
|
||||
| 1.8 | 0.03953 | 0.05576 | 0.02833 | 0.04319 |
|
||||
| 2.0 | 0.02844 | 0.03989 | 0.02045 | 0.04755 |
|
||||
| 2.5 | 0.01270 | 0.01781 | 0.00913 | 0.01519 |
|
||||
| 3.0 | 0.00658 | 0.00923 | 0.00473 | 0.01218 |
|
||||
| 3.5 | 0.00376 | 0.00529 | 0.00269 | 0.00474 |
|
||||
| 4.0 | 0.00218 | 0.00309 | 0.00156 | 0.00114 |
|
||||
| 4.5 | 0.00132 | 0.00188 | 0.00094 | 0.00068 |
|
||||
| 5.0 | 0.00084 | 0.00122 | 0.00060 | 0.00059 |
|
||||
| 6.0 | 0.00044 | 0.00066 | 0.00030 | 0.00041 |
|
||||
| 7.0 | 0.00022 | 0.00036 | 0.00014 | 0.00043 |
|
||||
|
||||
|
||||
: Cross Section limits using the combined data and the deep boosted tagger for the decay to qW
|
||||
|
||||
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
||||
|------------|-----------------|------------------|------------------|-----------------|
|
||||
| 1.6 | 0.06656 | 0.09495 | 0.04698 | 0.12374 |
|
||||
| 1.8 | 0.04281 | 0.06141 | 0.03001 | 0.05422 |
|
||||
| 2.0 | 0.03297 | 0.04650 | 0.02363 | 0.04658 |
|
||||
| 2.5 | 0.01328 | 0.01868 | 0.00950 | 0.01109 |
|
||||
| 3.0 | 0.00650 | 0.00917 | 0.00464 | 0.00502 |
|
||||
| 3.5 | 0.00338 | 0.00479 | 0.00241 | 0.00408 |
|
||||
| 4.0 | 0.00182 | 0.00261 | 0.00129 | 0.00127 |
|
||||
| 4.5 | 0.00107 | 0.00156 | 0.00074 | 0.00123 |
|
||||
| 5.0 | 0.00068 | 0.00102 | 0.00046 | 0.00149 |
|
||||
| 6.0 | 0.00038 | 0.00060 | 0.00024 | 0.00034 |
|
||||
| 7.0 | 0.00021 | 0.00035 | 0.00013 | 0.00046 |
|
||||
|
||||
|
||||
|
||||
: Cross Section limits using the combined data and the N-subjettiness tagger for the decay to qZ
|
||||
|
||||
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
||||
|------------|-----------------|------------------|------------------|-----------------|
|
||||
| 1.6 | 0.05125 | 0.07188 | 0.03667 | 0.02993 |
|
||||
| 1.8 | 0.03547 | 0.04989 | 0.02551 | 0.03614 |
|
||||
| 2.0 | 0.02523 | 0.03539 | 0.01815 | 0.04177 |
|
||||
| 2.5 | 0.01059 | 0.01485 | 0.00761 | 0.01230 |
|
||||
| 3.0 | 0.00576 | 0.00808 | 0.00412 | 0.01087 |
|
||||
| 3.5 | 0.00327 | 0.00460 | 0.00234 | 0.00425 |
|
||||
| 4.0 | 0.00190 | 0.00269 | 0.00136 | 0.00097 |
|
||||
| 4.5 | 0.00119 | 0.00168 | 0.00084 | 0.00059 |
|
||||
| 5.0 | 0.00077 | 0.00110 | 0.00054 | 0.00051 |
|
||||
| 6.0 | 0.00039 | 0.00057 | 0.00026 | 0.00036 |
|
||||
| 7.0 | 0.00019 | 0.00031 | 0.00013 | 0.00036 |
|
||||
|
||||
|
||||
: Cross Section limits using the combined data and deep boosted tagger for the decay to qZ
|
||||
|
||||
| Mass [TeV] | Exp. limit [pb] | Upper limit [pb] | Lower limit [pb] | Obs. limit [pb] |
|
||||
|------------|-----------------|------------------|------------------|-----------------|
|
||||
| 1.6 | 0.07719 | 0.10949 | 0.05467 | 0.14090 |
|
||||
| 1.8 | 0.05297 | 0.07493 | 0.03752 | 0.06690 |
|
||||
| 2.0 | 0.03875 | 0.05466 | 0.02768 | 0.05855 |
|
||||
| 2.5 | 0.01512 | 0.02126 | 0.01080 | 0.01160 |
|
||||
| 3.0 | 0.00773 | 0.01088 | 0.00554 | 0.00548 |
|
||||
| 3.5 | 0.00400 | 0.00565 | 0.00285 | 0.00465 |
|
||||
| 4.0 | 0.00211 | 0.00301 | 0.00149 | 0.00152 |
|
||||
| 4.5 | 0.00118 | 0.00172 | 0.00082 | 0.00128 |
|
||||
| 5.0 | 0.00073 | 0.00108 | 0.00050 | 0.00161 |
|
||||
| 6.0 | 0.00039 | 0.00060 | 0.00025 | 0.00036 |
|
||||
| 7.0 | 0.00021 | 0.00034 | 0.00013 | 0.00045 |
|
||||
## Combined dataset
|
||||
|
||||
Using the combined data, the cross section limits seen in [@fig:resCombined] were obtained. The cross section limits
|
||||
are, compared to only using the 2016 dataset, almost cut in half. This shows the big improvement achieved by using more
|
||||
than three times the amount of data.
|
||||
|
||||
The results for the mass limits of the combined years are as follows:
|
||||
|
||||
|
|
@ -933,6 +851,9 @@ The results for the mass limits of the combined years are as follows:
|
|||
| qZ | deep boosted | 4.92 | 5.02 | 4.80 |
|
||||
|
||||
|
||||
The combination of the three years not just improved the cross section limits, but also the limit for the mass of the
|
||||
q\* particle. The final result is 1 TeV higher for the decay to qW and almost 0.8 TeV higher for the decay to qZ than
|
||||
what was concluded by the previous research [@PREV_RESEARCH].
|
||||
|
||||
\begin{figure}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
|
|
@ -952,8 +873,6 @@ deep boosted tagger (right).}
|
|||
\label{fig:resCombined}
|
||||
\end{figure}
|
||||
|
||||
The combination of the three years has a big impact on the result. The final limit is 1 TeV higher than what could
|
||||
previously be concluded.
|
||||
|
||||
## Comparison of taggers
|
||||
|
||||
|
|
@ -961,9 +880,19 @@ The previously shown results already show, that the deep boosted tagger was not
|
|||
results compared to the N-subjettiness tagger.
|
||||
For further comparison, in [@fig:limit_comp] the expected limits of the different taggers for the q\* $\rightarrow$ qW
|
||||
and the q\* $\rightarrow$ qZ decay are shown. It can be seen, that the deep boosted is at best as good as the
|
||||
N-subjettiness tagger. This was not the expected result, as the deep neural network was supposed to provide better
|
||||
separation between signal and background events than the older N-subjettiness tagger. Recently, some issues with the
|
||||
training of the deep boosted tagger used in this analysis were found, so those might explain the bad performance.
|
||||
N-subjettiness tagger. This was not the expected result, as the deep neural network was already found to provide a
|
||||
higher significance in the optimisation done in [@sec:opt]. The higher significance should also result in lower cross
|
||||
section limits. Apparently, doing the optimization only on data of the year 2018, was not the best choice. To make sure,
|
||||
there is no mistake in the setup, also the expected cross section limits using only the high purity category of the two
|
||||
taggers with 2018 data are compared in [@fig:comp_2018]. There, the cross section limits calculated using the deep
|
||||
boosted tagger are a bit lower than with the N-subjettiness tagger, showing, that the method used for optimisation was
|
||||
working but should have been applied to the combined dataset.
|
||||
|
||||
Recently, some issues with the training of the deep boosted tagger used in this analysis were also found, which might
|
||||
explain, why it didn't perform much better in general.
|
||||
|
||||
{#fig:comp_2018}
|
||||
|
||||
\begin{figure}
|
||||
\begin{minipage}{0.5\textwidth}
|
||||
|
|
@ -977,25 +906,47 @@ decay to qZ}
|
|||
\label{fig:limit_comp}
|
||||
\end{figure}
|
||||
|
||||
\clearpage
|
||||
\newpage
|
||||
|
||||
# Summary
|
||||
|
||||
In this thesis, a limit on the mass of the q\* particle has been successfully established. By combining the data from
|
||||
the years 2016, 2017 and 2018, collected by the CMS experiment, the previously set limit could be significantly
|
||||
improved. For that, a combined fit to the QCD background and signal had to be performed and the cross section limits
|
||||
extracted. Also, the new deep boosted tagger, using a deep neural network, was compared to the older N-subjettiness
|
||||
tagger and found to not significantly change the result, neither to the better nor to the worse. Due to some training
|
||||
issues identified lately, there is still a good chance, that, with that issue fixed, it will be able to further improve
|
||||
the results.
|
||||
Also previously research of the 2016 data was repeated and the results compared. The previous research arrived at a
|
||||
exclusion limit up to 5 TeV resp. 4.7 TeV for the decay to qW resp. qZ, this thesis at 5.4 TeV resp. 4.9 TeV. The
|
||||
difference can be explained by small differences in the data used and the setup itself. After that, using the combined
|
||||
data, the limit could be significantly improved to exclude the q\* particle up to a mass of 6.2 TeV resp. 5.5 TeV.
|
||||
With the research presented in this thesis, it would also be possible to test other theories of the q\* particle that
|
||||
predict its existence at lower masses, than the one used, by overlaying the different theory curves in the plots shown
|
||||
in [@fig:res2016] and [@fig:resCombined].
|
||||
improved.
|
||||
|
||||
For the data analysis, the following selection was applied:
|
||||
|
||||
- #jets >= 2
|
||||
- $\Delta\eta < 1.4$
|
||||
- $m_{jj} >= \SI{1050}{\giga\eV}$
|
||||
- $\SI{35}{\giga\eV} < m_{SDM} < \SI{105}{\giga\eV}$
|
||||
|
||||
For the deep boosted tagger, a high purity category of $VvsQCD > 0.95$ and a low purity category of $VvsQCD <= 0.95$ was
|
||||
used. For the N-subjettiness tagger the high purity category was $\tau_{21} < 0.35$ and the low purity category $0.35 <
|
||||
\tau_{21} < 0.75$. These values were found by optimizing for the highest possible significance of the signal.
|
||||
|
||||
After the selection, the cross section limits were extracted from the data and new exclusion limits for the mass of the
|
||||
q\* particles set. These are 6.1 TeV by analyzing the decay to qW, respectively 5.5 TeV for the decay to qZ. Those
|
||||
limits are about 1 TeV higher than the ones found in previous research, that found them to be 5 TeV resp. 4.7 TeV.
|
||||
|
||||
Two different taggers were used to compare the result. The newer deep boosted tagger was found to not improve the result
|
||||
over the older N-subjettiness tagger. This was rather unexpected but might be caused by some training issues, that were
|
||||
identified lately.
|
||||
|
||||
This research can also be used to test other theories of the q\* particle that predict its existence at lower masses,
|
||||
than the one used, by overlaying the different theory curves in the plots shown in [@fig:res2016] and
|
||||
[@fig:resCombined].
|
||||
|
||||
The optimization process used to find the optimal values for the discriminant provided by the taggers, was found to not
|
||||
be optimal. It was only done using 2018 data, with which the deep boosted tagger showed a higher significance than the
|
||||
N-subjettiness tagger. Apparently, the assumption, that the same optimization would apply to the data of the other years
|
||||
as well, did not hold. Using the combined dataset, the deep boosted tagger showed no better cross section limits than
|
||||
the N-subjettiness tagger, which are directly related to the significance used for the optimization. Therefore, with a
|
||||
better optimization and the fixed training issues of the deep boosted tagger, it is very likely, that the result
|
||||
presented could be further improved.
|
||||
|
||||
\newpage
|
||||
|
||||
\nocite{*}
|
||||
|
||||
|
|
|
|||
BIN
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54
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54
thesis.toc
|
|
@ -1,38 +1,38 @@
|
|||
\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax
|
||||
\babel@toc {british}{}
|
||||
\contentsline {section}{\numberline {1}Introduction}{1}{section.1}%
|
||||
\contentsline {section}{\numberline {2}Theoretical background}{2}{section.2}%
|
||||
\contentsline {section}{\numberline {2}Theoretical motivation}{2}{section.2}%
|
||||
\contentsline {subsection}{\numberline {2.1}Standard model}{2}{subsection.2.1}%
|
||||
\contentsline {subsubsection}{\numberline {2.1.1}Quantum Chromodynamic background}{3}{subsubsection.2.1.1}%
|
||||
\contentsline {subsubsection}{\numberline {2.1.2}Shortcomings of the Standard Model}{3}{subsubsection.2.1.2}%
|
||||
\contentsline {subsubsection}{\numberline {2.1.1}Shortcomings of the Standard Model}{4}{subsubsection.2.1.1}%
|
||||
\contentsline {subsection}{\numberline {2.2}Excited quark states}{4}{subsection.2.2}%
|
||||
\contentsline {section}{\numberline {3}Experimental Setup}{6}{section.3}%
|
||||
\contentsline {subsection}{\numberline {3.1}Large Hadron Collider}{6}{subsection.3.1}%
|
||||
\contentsline {subsection}{\numberline {3.2}Compact Muon Solenoid}{6}{subsection.3.2}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.1}Coordinate conventions}{7}{subsubsection.3.2.1}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.2}The tracking system}{7}{subsubsection.3.2.2}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.3}The electromagnetic calorimeter}{7}{subsubsection.3.2.3}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.4}The hadronic calorimeter}{8}{subsubsection.3.2.4}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.5}The solenoid}{8}{subsubsection.3.2.5}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.6}The muon system}{8}{subsubsection.3.2.6}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.7}The Trigger system}{8}{subsubsection.3.2.7}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.8}The Particle Flow algorithm}{8}{subsubsection.3.2.8}%
|
||||
\contentsline {subsection}{\numberline {3.3}Jet clustering}{9}{subsection.3.3}%
|
||||
\contentsline {section}{\numberline {4}Method of analysis}{11}{section.4}%
|
||||
\contentsline {subsubsection}{\numberline {2.2.1}Quantum Chromodynamic background}{5}{subsubsection.2.2.1}%
|
||||
\contentsline {section}{\numberline {3}Experimental Setup}{7}{section.3}%
|
||||
\contentsline {subsection}{\numberline {3.1}Large Hadron Collider}{7}{subsection.3.1}%
|
||||
\contentsline {subsection}{\numberline {3.2}Compact Muon Solenoid}{7}{subsection.3.2}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.1}Coordinate conventions}{8}{subsubsection.3.2.1}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.2}The tracking system}{8}{subsubsection.3.2.2}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.3}The electromagnetic calorimeter}{9}{subsubsection.3.2.3}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.4}The hadronic calorimeter}{9}{subsubsection.3.2.4}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.5}The solenoid}{9}{subsubsection.3.2.5}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.6}The muon system}{9}{subsubsection.3.2.6}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.7}The Trigger system}{9}{subsubsection.3.2.7}%
|
||||
\contentsline {subsubsection}{\numberline {3.2.8}The Particle Flow algorithm}{9}{subsubsection.3.2.8}%
|
||||
\contentsline {subsection}{\numberline {3.3}Jet clustering}{10}{subsection.3.3}%
|
||||
\contentsline {section}{\numberline {4}Method of analysis}{12}{section.4}%
|
||||
\contentsline {subsection}{\numberline {4.1}Signal and Background modelling}{12}{subsection.4.1}%
|
||||
\contentsline {section}{\numberline {5}Preselection and data quality}{13}{section.5}%
|
||||
\contentsline {subsection}{\numberline {5.1}Preselection}{13}{subsection.5.1}%
|
||||
\contentsline {subsection}{\numberline {5.2}Data - Monte Carlo Comparison}{17}{subsection.5.2}%
|
||||
\contentsline {subsubsection}{\numberline {5.2.1}Sideband}{18}{subsubsection.5.2.1}%
|
||||
\contentsline {section}{\numberline {5}Preselection and data quality}{14}{section.5}%
|
||||
\contentsline {subsection}{\numberline {5.1}Preselection}{14}{subsection.5.1}%
|
||||
\contentsline {subsection}{\numberline {5.2}Data - Monte Carlo Comparison}{18}{subsection.5.2}%
|
||||
\contentsline {subsubsection}{\numberline {5.2.1}Sideband}{19}{subsubsection.5.2.1}%
|
||||
\contentsline {section}{\numberline {6}Jet substructure selection}{20}{section.6}%
|
||||
\contentsline {subsection}{\numberline {6.1}N-Subjettiness}{20}{subsection.6.1}%
|
||||
\contentsline {subsection}{\numberline {6.2}DeepAK8}{20}{subsection.6.2}%
|
||||
\contentsline {subsection}{\numberline {6.2}DeepAK8}{21}{subsection.6.2}%
|
||||
\contentsline {subsection}{\numberline {6.3}Optimization}{21}{subsection.6.3}%
|
||||
\contentsline {section}{\numberline {7}Signal extraction}{22}{section.7}%
|
||||
\contentsline {subsection}{\numberline {7.1}Uncertainties}{22}{subsection.7.1}%
|
||||
\contentsline {section}{\numberline {8}Results}{22}{section.8}%
|
||||
\contentsline {subsection}{\numberline {7.1}Uncertainties}{23}{subsection.7.1}%
|
||||
\contentsline {section}{\numberline {8}Results}{23}{section.8}%
|
||||
\contentsline {subsection}{\numberline {8.1}2016}{23}{subsection.8.1}%
|
||||
\contentsline {subsubsection}{\numberline {8.1.1}Previous research}{26}{subsubsection.8.1.1}%
|
||||
\contentsline {subsection}{\numberline {8.2}2016 + 2017 + 2018}{26}{subsection.8.2}%
|
||||
\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{28}{subsection.8.3}%
|
||||
\contentsline {section}{\numberline {9}Summary}{30}{section.9}%
|
||||
\contentsline {subsubsection}{\numberline {8.1.1}Previous research}{24}{subsubsection.8.1.1}%
|
||||
\contentsline {subsection}{\numberline {8.2}Combined dataset}{25}{subsection.8.2}%
|
||||
\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{25}{subsection.8.3}%
|
||||
\contentsline {section}{\numberline {9}Summary}{29}{section.9}%
|
||||
|
|
|
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Loading…
Reference in New Issue
Block a user