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Address some of the comments by Irene and Andreas

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# Appendix
: 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 |
: 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 |

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\newpage
\hypertarget{appendix}{%
\section*{Appendix}\label{appendix}}
\begin{longtable}[]{@{}lllll@{}}
\caption{Cross Section limits using 2016 data and the N-subjettiness
tagger for the decay to qW}\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 & 0.10406 & 0.14720 & 0.07371 & 0.08165\tabularnewline
1.8 & 0.07656 & 0.10800 & 0.05441 & 0.04114\tabularnewline
2.0 & 0.05422 & 0.07605 & 0.03879 & 0.04043\tabularnewline
2.5 & 0.02430 & 0.03408 & 0.01747 & 0.04052\tabularnewline
3.0 & 0.01262 & 0.01775 & 0.00904 & 0.02109\tabularnewline
3.5 & 0.00703 & 0.00992 & 0.00502 & 0.00399\tabularnewline
4.0 & 0.00424 & 0.00603 & 0.00300 & 0.00172\tabularnewline
4.5 & 0.00355 & 0.00478 & 0.00273 & 0.00249\tabularnewline
5.0 & 0.00269 & 0.00357 & 0.00211 & 0.00240\tabularnewline
6.0 & 0.00103 & 0.00160 & 0.00068 & 0.00062\tabularnewline
7.0 & 0.00063 & 0.00105 & 0.00039 & 0.00086\tabularnewline
\bottomrule
\end{longtable}
\begin{longtable}[]{@{}lllll@{}}
\caption{Cross Section limits using 2016 data and the deep boosted
tagger for the decay to qW}\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 & 0.17750 & 0.25179 & 0.12572 & 0.38242\tabularnewline
1.8 & 0.11125 & 0.15870 & 0.07826 & 0.11692\tabularnewline
2.0 & 0.08188 & 0.11549 & 0.05799 & 0.09528\tabularnewline
2.5 & 0.03328 & 0.04668 & 0.02373 & 0.03653\tabularnewline
3.0 & 0.01648 & 0.02338 & 0.01181 & 0.01108\tabularnewline
3.5 & 0.00840 & 0.01195 & 0.00593 & 0.00683\tabularnewline
4.0 & 0.00459 & 0.00666 & 0.00322 & 0.00342\tabularnewline
4.5 & 0.00276 & 0.00412 & 0.00190 & 0.00366\tabularnewline
5.0 & 0.00177 & 0.00271 & 0.00118 & 0.00401\tabularnewline
6.0 & 0.00110 & 0.00175 & 0.00071 & 0.00155\tabularnewline
7.0 & 0.00065 & 0.00108 & 0.00041 & 0.00108\tabularnewline
\bottomrule
\end{longtable}
\begin{longtable}[]{@{}lllll@{}}
\caption{Cross Section limits using 2016 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 & 0.08687 & 0.12254 & 0.06174 & 0.06987\tabularnewline
1.8 & 0.06719 & 0.09477 & 0.04832 & 0.03424\tabularnewline
2.0 & 0.04734 & 0.06640 & 0.03405 & 0.03310\tabularnewline
2.5 & 0.01867 & 0.02619 & 0.01343 & 0.03214\tabularnewline
3.0 & 0.01043 & 0.01463 & 0.00744 & 0.01773\tabularnewline
3.5 & 0.00596 & 0.00840 & 0.00426 & 0.00347\tabularnewline
4.0 & 0.00353 & 0.00500 & 0.00250 & 0.00140\tabularnewline
4.5 & 0.00233 & 0.00335 & 0.00164 & 0.00181\tabularnewline
5.0 & 0.00157 & 0.00231 & 0.00110 & 0.00188\tabularnewline
6.0 & 0.00082 & 0.00126 & 0.00054 & 0.00049\tabularnewline
7.0 & 0.00050 & 0.00083 & 0.00031 & 0.00066\tabularnewline
\bottomrule
\end{longtable}
\begin{longtable}[]{@{}lllll@{}}
\caption{Cross Section limits using 2016 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 & 0.16687 & 0.23805 & 0.11699 & 0.35999\tabularnewline
1.8 & 0.12750 & 0.17934 & 0.09138 & 0.12891\tabularnewline
2.0 & 0.09062 & 0.12783 & 0.06474 & 0.09977\tabularnewline
2.5 & 0.03391 & 0.04783 & 0.02422 & 0.03754\tabularnewline
3.0 & 0.01781 & 0.02513 & 0.01277 & 0.01159\tabularnewline
3.5 & 0.00949 & 0.01346 & 0.00678 & 0.00741\tabularnewline
4.0 & 0.00494 & 0.00711 & 0.00349 & 0.00362\tabularnewline
4.5 & 0.00293 & 0.00429 & 0.00203 & 0.00368\tabularnewline
5.0 & 0.00188 & 0.00284 & 0.00127 & 0.00426\tabularnewline
6.0 & 0.00102 & 0.00161 & 0.00066 & 0.00155\tabularnewline
7.0 & 0.00053 & 0.00085 & 0.00034 & 0.00085\tabularnewline
\bottomrule
\end{longtable}
\begin{longtable}[]{@{}lllll@{}}
\caption{Cross Section limits using the combined data and the
N-subjettiness tagger for the decay to qW}\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 & 0.05703 & 0.07999 & 0.04088 & 0.03366\tabularnewline
1.8 & 0.03953 & 0.05576 & 0.02833 & 0.04319\tabularnewline
2.0 & 0.02844 & 0.03989 & 0.02045 & 0.04755\tabularnewline
2.5 & 0.01270 & 0.01781 & 0.00913 & 0.01519\tabularnewline
3.0 & 0.00658 & 0.00923 & 0.00473 & 0.01218\tabularnewline
3.5 & 0.00376 & 0.00529 & 0.00269 & 0.00474\tabularnewline
4.0 & 0.00218 & 0.00309 & 0.00156 & 0.00114\tabularnewline
4.5 & 0.00132 & 0.00188 & 0.00094 & 0.00068\tabularnewline
5.0 & 0.00084 & 0.00122 & 0.00060 & 0.00059\tabularnewline
6.0 & 0.00044 & 0.00066 & 0.00030 & 0.00041\tabularnewline
7.0 & 0.00022 & 0.00036 & 0.00014 & 0.00043\tabularnewline
\bottomrule
\end{longtable}
\begin{longtable}[]{@{}lllll@{}}
\caption{Cross Section limits using the combined data and the deep
boosted tagger for the decay to qW}\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 & 0.06656 & 0.09495 & 0.04698 & 0.12374\tabularnewline
1.8 & 0.04281 & 0.06141 & 0.03001 & 0.05422\tabularnewline
2.0 & 0.03297 & 0.04650 & 0.02363 & 0.04658\tabularnewline
2.5 & 0.01328 & 0.01868 & 0.00950 & 0.01109\tabularnewline
3.0 & 0.00650 & 0.00917 & 0.00464 & 0.00502\tabularnewline
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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</bcf:bibdata> </bcf:bibdata>
<bcf:section number="0"> <bcf:section number="0">
<bcf:citekey order="1">website</bcf:citekey> <bcf:citekey order="1">PREV_RESEARCH</bcf:citekey>
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<bcf:citekey order="3">PREV_RESEARCH</bcf:citekey> <bcf:citekey order="3">PREV_RESEARCH</bcf:citekey>
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<bcf:citekey order="0" nocite="1">*</bcf:citekey> <bcf:citekey order="0" nocite="1">*</bcf:citekey>
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@ -8,7 +8,6 @@ header-includes: |
\usepackage{tikz-feynman} \usepackage{tikz-feynman}
\usepackage{csquotes} \usepackage{csquotes}
\pagenumbering{gobble} \pagenumbering{gobble}
\setlength{\parindent}{1.0em}
\setlength{\parskip}{0.5em} \setlength{\parskip}{0.5em}
\bibliographystyle{lucas_unsrt} \bibliographystyle{lucas_unsrt}
abstract: | 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 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. 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 One category of such theories is based on a composite quark model. Quarks are currently considered elementary particles
to us so far or can bind to other particles using unknown forces. This could explain some symmetries between 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 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 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 In a previous research [@PREV_RESEARCH], a lower limit for the mass of an excited quark has already been set using data
of the Large Hadron Collider with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$. Since then, a lot more data from the 2016 run of the Large Hadron Collider with an integrated luminosity of $\SI{35.92}{\per\femto\barn}$. Since
has been collected, totalling to $\SI{137.19}{\per\femto\barn}$. This thesis uses this new data as well as a new then, a lot more data has been collected, totalling to $\SI{137.19}{\per\femto\barn}$ of data usable for research. This
technique to identify decays of highly boosted particles based on a deep neural network to further improve this limit thesis uses this new data as well as a new technique to identify decays of highly boosted particles based on a deep
and therefore exclude the excited quark particle to even higher masses. It will also compare this new tagging technique neural network. By using more data and new tagging techniques, it aims to either confirm the existence of the q\*
to an older tagger based on jet substructure studies used in the previous research. 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 In chapter 2, a theoretical background will be presented explaining in short the Standard Model, its shortcomings and
theory of excited quarks. Then the Large Hadron Collider and the Compact Muon Solenoid, the detector that collected the the theory of excited quarks. Then, in chapter 3, the Large Hadron Collider and the Compact Muon Solenoid, the detector
data for this analysis, will be described. After that, the main analysis part follows, describing how the data was used that collected the data for this analysis, will be described. After that, in chapters 4-7, the main analysis part
to extract limits on the mass of the excited quark particle. At the very end, the results are presented and compared to follows, describing how the data was used to extract limits on the mass of the excited quark particle. At the very end,
previous research. in chapter 8, the results are presented and compared to previous research.
\newpage \newpage
# Theoretical background # Theoretical motivation
This chapter presents a short summary of the theoretical background relevant to this thesis. It first gives an 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 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. 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 The Standard Model of physics proved to be very successful in describing three of the four fundamental interactions
known: the electromagnetic, weak and strong interaction. The fourth, gravity, could not yet be successfully included in currently known: the electromagnetic, weak and strong interaction. The fourth, gravity, could not yet be successfully
this theory. 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 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 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. bosons. Fermions are further classified into quarks and leptons.
Furthermore, quarks and leptons can also be divided into three generations, each of which contains two particles. Quarks and leptons can also be categorized into three generations, each of which contains two particles, also called
In the lepton category, each generation has one charged lepton and one neutrino, that has no charge. Also, the mass of flavours. For leptons, the three generations each consist of a lepton and its corresponding neutrino, namely first the
the neutrinos is not yet known, only an upper bound has been established. A full list of particles known to the electron, then the muon and third, the tau. The three quark generations consist of first, the up and down, second, the
standard model can be found in [@fig:sm]. Furthermore, all fermions have an associated anti particle with reversed charm and strange, and third, the top and bottom quark. So overall, their exists a total of six quark and six lepton
charge. Multiple quarks can form bound states called hadrons (e.g. proton and neutron). 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.
![Elementary particles of the Standard Model and their mass charge and spin. The matter around us, is built from so called hadrons, that are bound states of quarks, for example protons and
neutrons. Long lived hadrons consist of up and down quarks, as the heavier ones over time decay to those.
![
Elementary particles of the Standard Model and their mass charge and spin.
](./figures/sm_wikipedia.pdf){width=50% #fig:sm} ](./figures/sm_wikipedia.pdf){width=50% #fig:sm}
The gauge bosons, namely the photon, $W^\pm$ bosons, $Z^0$ boson, and gluon, are mediators of the different 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 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. any other flavour change.
The quantum chromodynamics (QCD) describe the strong interaction of particles. It applies to all Due to their high masses of 80.39 GeV resp. 91.19 GeV, the $W^\pm$ and $Z^0$ bosons themselves decay very quickly.
particles carrying colour (e.g. quarks). The force is mediated by the gluon. This boson carries colour as well, Either in the leptonic or hadronic decay channel. In the leptonic channel, the $W^\pm$ decays to a lepton and the
although it doesn't carry only one colour but rather a combination of a colour and an anticolour, and can therefore corresponding anti-lepton neutrino, in the hadronic channel it decays to a quark and an anti-quark of a different
interact with itself and exists in eight different variant. As a result of this, processes, where a gluon decays into flavour. Due to the $Z^0$ boson having no charge, it always decays to a fermion and its anti-particle, in the leptonic
two gluons are possible. Furthermore the strong force, binding to colour carrying particles, increases with their channel this might be for example a electron - positron pair, in the hadronic channel an up and anti-up quark pair. This
distance r making it at a certain point more energetically efficient to form a new quark - antiquark pair than thesis examines the hadronic decay channel, where both vector bosons essentially decay to to quarks.
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 The quantum chromodynamics (QCD) describes the strong interaction of particles. It applies to all
detector. An effect called Hadronisation. 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} ### 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 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 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 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 gluons binding the three valence quarks. Therefore the QCD multijet backgroubd is the dominant background of the signal
the main processes causing a very strong QCD background. described in [@sec:qs].
\begin{figure} \begin{figure}
\centering \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} \caption{Two examples of QCD processes resulting in two jets.} \label{fig:qcdfeynman}
\end{figure} \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 \newpage
# Experimental Setup # Experimental Setup
@ -210,9 +248,9 @@ Following on, the experimental setup used to gather the data analysed in this th
## Large Hadron Collider ## Large Hadron Collider
The Large Hadron Collider is the world's largest and most powerful particle accelerator [@website]. It has a perimeter 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 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
those are ATLAS and the Compact Muon Solenoid (CMS). Both are general-purpose detectors to investigate the particles energy of 13 TeV. It is home to several experiments, the biggest of those are ATLAS and the Compact Muon Solenoid (CMS).
that form during particle collisions. 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 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 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 ## 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 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 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 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 ### Coordinate conventions
Per convention, the z axis points along the beam axis, the y axis upwards and the x axis horizontal towards the LHC Per convention, the z axis points along the beam axis in the direction of the magnetic fields of the solenoid, the y
centre. Furthermore, the azimuthal angle $\phi$, which describes the angle in the x - y plane, the polar angle $\theta$, axis upwards and the x axis horizontal towards the LHC centre. The azimuthal angle $\phi$, which describes the angle in
which describes the angle in the y - z plane and the pseudorapidity $\eta$, which is defined as $\eta = the x - y plane, the polar angle $\theta$, which describes the angle in the y - z plane and the pseudorapidity $\eta$,
-ln\left(tan\frac{\theta}{2}\right)$ are introduced. The coordinates are visualised in [@fig:cmscoords]. Furthermore, which is defined as $\eta = -ln\left(tan\frac{\theta}{2}\right)$ are also introduced. The coordinates are visualised in
to describe a particles momentum, often the transverse momentum, $p_t$ is used. It is the component of the momentum [@fig:cmscoords]. Furthermore, to describe a particle's momentum, often the transverse momentum, $p_t$ is used. It is
transversal to the beam axis. It is a useful quantity, because the sum of all transverse momenta has to be zero. the component of the momentum transversal to the beam axis. Before the collision, the transverse momentum obviously has
Missing transverse momentum implies particles that weren't detected such as neutrinos. 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 ![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 $\phi$. 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
The tracking system is built of two parts, first a pixel detector and then silicon strip sensors. It is used to The tracking system is built of two parts, closest to the collision is a pixel detector and around that silicon strip
reconstruct the tracks of charged particles, measuring their charge sign, direction and momentum. It is as close to the sensors. They are used to reconstruct the tracks of charged particles, measuring their charge sign, direction and
collision as possible to be able to identify secondary vertices. momentum. They are as close to the collision as possible to be able to identify secondary vertices.
### The electromagnetic calorimeter ### The electromagnetic calorimeter
The electromagnetic calorimeter measures the energy of photons and electrons. It is made of tungstate crystal. The electromagnetic calorimeter measures the energy of photons and electrons. It is made of tungstate crystal and
When passed by particles, it produces light in proportion to the particle's energy. This light is measured by photodetectors. When passed by particles, the crystal produces light in proportion to the particle's energy. This light
photodetectors that convert this scintillation light to an electrical signal. To measure a particles energy, it has to is measured by the photodetectors that convert this scintillation light to an electrical signal. To measure a particles
leave its whole energy in the ECAL, which is true for photons and electrons, but not for other particles such as energy, it has to leave its whole energy in the ECAL, which is true for photons and electrons, but not for other
hadrons and muons. They too leave some energy in the ECAL. 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 ### The hadronic calorimeter
@ -322,9 +363,10 @@ algorithm. It arises from a generalization of several other clustering algorithm
and SISCone clustering algorithms. and SISCone clustering algorithms.
The anti-$k_t$ clustering algorithm associates hard particles with their soft particles surrounding them within a radius 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 $R = \sqrt{\eta^2 - \phi^2}$ in the $\eta$ - $\phi$ plane forming cone like jets. If two jets overlap, the jets shape is
hardness. A softer particles jet will change its shape more than a harder particles. A visual comparison of four changed according to its hardness in regards to the transverse momentum. A softer particles jet will change its shape
different clustering algorithms can be seen in [@fig:antiktcomparision]. For this analysis, a radius of 0.8 is used. 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 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 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. particle causing a jet than taking the mass of all constituent particles of the jet combined.
![ ![
Comparision of the $k_t$, Cambridge/Aachen, SISCone and anti-$k_t$ algorithms clustering a sample parton-level event 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 with many random soft "ghosts". Taken from [@ANTIKT]
](./figures/antikt-comparision.png){#fig:antiktcomparision} ](./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 \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 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. 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 As described in [@sec:qs], the decay of the q\* particle to a quark and a vector boson with the vector boson then
to be as follows [@QSTAR_THEORY]: 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.
: 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.
The data studied was collected by the CMS experiment in the years 2016, 2017 and 2018. It is analysed with the Particle 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 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 using the anti-$k_t$ algorithm with the distance parameter R being 0.8.
detector have to be calibrated. For that, jet energy corrections published by the CMS working group are applied to the
data.
To find signal events in the data, this thesis looks at the dijet invariant mass distribution. The data is assumed to To find the signal events, described in [@sec:qs], in the data, this thesis looks at the dijet invariant mass
only consist of QCD background and signal events, other backgrounds are neglected. Cuts on several distributions are distribution. The only background considered is the QCD background described in [@sec:qcdbg]. A selection using
introduced to reduce the background and improve the sensitivity for the signal. If the q\* particle exists, the dijet different kinematic variables as well as a tagger to identify jets from the decay of a vector boson is introduced to
invariant mass distribution should show a resonance at its invariant mass. This resonance will be looked for with reduce the background and increase the sensitivity for the signal. After that, it will be looked for a peak in the dijet
statistical methods explained later on. 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 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 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 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. One based on the N-subjettiness variable used in the previous research, the other being a novel mechanisms will be used to compare their performance. One based on the N-subjettiness variable used in the previous
approach using a deep neural network. 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 ## 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 - 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 - 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 A gaussian and a poisson function have also been studied but found to be not able to reproduce the signal shape as they
fit the tail on both sides of the peak. 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 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. 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 # Preselection and data quality
To separate the background from the signal, cuts on several distributions have to be introduced. The selection of events To reduce the background and increase the signal sensitivity, a selection of events by different variables is
is divided into introduced. It is divided into two stages. The first one (the preselection) adds some general physics motivated
two parts. The first one (the preselection) adds some general physics motivated cuts and is also used to make sure a selection using kinematic variables and is also used to make sure a good trigger efficiency is achieved. In the second
good trigger efficiency is achieved. It is not expected to already provide a good separation of background and signal. part, different taggers will be used as a discriminator between QCD background and signal events. After the
In the second part, different taggers will be used as a discriminator between QCD background and signal events. After preselection, it is made sure, that the simulated samples represent the real data well by comparing the data with the
the preselection, it is made sure, that the simulated samples represent the real data well. simulation in the signal as well as a sideband region, where no signal events are expected.
## Preselection ## 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 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 discard soft background and to make sure the particles are in the barrel region of the detector for an optimal track
resolution. Furthermore, all events with one of the two highest $p_t$ jets having an angular separation smaller 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 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. 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. From a decaying q\* particle, we expect two jets in the endstate. The dijet invariant mass of those two jets will be
More jets are also possible, for example caused by gluon radiation of a quark causing another jet. The cut can be seen used to reconstruct the mass of the q\* particle. Therefore a cut is added to have at least 2 jets.
in [@fig:njets]. 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{figure}
\begin{minipage}{0.5\textwidth} \begin{minipage}{0.5\textwidth}
@ -457,11 +491,13 @@ are amplified by a factor of 10,000, to be visible.}
\label{fig:njets} \label{fig:njets}
\end{figure} \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 next selection is done using $\Delta\eta = |\eta_1 - \eta_2|$, with $\eta_1$ and $\eta_2$ being the $\eta$ of the
the collision and will therefore be almost stationary. Its decay products should therefore be close to back to back, first two jets in regards to their transverse momentum. The q\* particle is expected to be very heavy in regards to the
which means the $\Delta\eta$ distribution is expected to peak at 0. At the same time, particles originating from QCD center of mass energy of the collision and will therefore be almost stationary. Its decay products should therefore be
effects are expected to have a higher $\Delta\eta$ as they mainly form from less heavy resonances. To maintain close to back to back, which means the $\Delta\eta$ distribution is expected to peak at 0. At the same time, particles
comparability, the same cut as in previous research of $\Delta\eta \le 1.3$ is used as can be seen in [@fig:deta]. 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{figure}
\begin{minipage}{0.5\textwidth} \begin{minipage}{0.5\textwidth}
@ -482,11 +518,11 @@ are amplified by a factor of 10,000, to be visible.}
\label{fig:deta} \label{fig:deta}
\end{figure} \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 The last selection in the preselection is on the dijet invariant mass: $m_{jj} \ge \SI{1050}{\giga\eV}$. It is important
high trigger efficiency and can be seen in [@fig:invmass]. Also, it has a huge impact on the background because it 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 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 more than 1 TeV. The $m_{jj}$ distribution should be a smoothly falling function for the QCD background and peak at the
resonance mass for the signal events. simulated resonance mass for the signal events.
\begin{figure} \begin{figure}
\begin{minipage}{0.5\textwidth} \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 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 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 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 tenth. Still, as can be seen in [@fig:njets] to [@fig:invmass], the amount of signal is very low.
logarithmic scale, even has to be amplified to be visible.
## Data - Monte Carlo Comparison ## Data - Monte Carlo Comparison
To ensure high data quality, the simulated QCD background sample is now being compared to the actual data of the 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 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 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 simulation are the same. In [@fig:data-mc], the three distributions of the variables that were used for the preselection
and the combined data of years 2016 to 2018. 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{figure}
\begin{minipage}{0.33\textwidth} \begin{minipage}{0.33\textwidth}
@ -555,13 +593,11 @@ and simulation.
### Sideband ### 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 The sideband is introduced to make sure no bias in the data and Monte Carlo simulation is introduced. It is a region in
data is used for the actual analysis. Again, data and the Monte Carlo simulation are compared. For this analysis, the 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 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 was chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, the heavier vector boson. Therefore it is very
one of those particles has to have a mass between 105 GeV and 35 GeV. Therefore events with jets with a softdropmass unlikely that a particle heavier than t
higher than 105 GeV will not be used for this analysis which makes them a good sideband to use.
In [@fig:sideband], the comparison of data with simulation in the sideband region can be seen for the softdropmass 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 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. 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 # 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 So far it was made sure, that the actual data and the simulation are in good agreement after the preselection and no
effects are introduced in the data by the used cuts. Now another selection has to be introduced, to further reduce the unwanted side effects are introduced in the data by the used cuts. Now another selection has to be introduced, to
background to be able to extract the hypothetical signal events from the actual data. 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 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 from a vector boson. Two different taggers will be used to later compare their performance. The decay analysed includes
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 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
softdropmass of a jet. The softdropmass of at least one of the two leading jets is expected to be within 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 $\SI{35}{\giga\eV}$ 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. 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 ## 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 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 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 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 applied so that this candidate jet has a WvsQCD/ZvsQCD value greater than some value determined by the optimization
presented next. 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 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 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, 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 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 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{figure}
\begin{minipage}{0.5\textwidth} \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 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 left to calculate the cross section limits, especially at higher resonance masses, the slightly less strict cut is
chosen. 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, 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, 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 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: $VvsQCD < 0.95$. 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 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 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 ## 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 %. First, the uncertainty of the Jet Energy Corrections. When measuring a particle's energy with the ECAL or HCAL part of
- *Jet Energy Corrections*: for the Jet Energy Corrections, an uncertainty of 2 % is assumed. the CMS, the electronic signals send by the photodetectors in the calorimeters have to be converted to actual energy
- *Tagger Efficiency(?)*: 6 % (TODO!) values. Therefore an error in this calibration causes the energy measured to be shifted to higher or lower values
- *Parameter Uncertainty of the fit*: The CombinedLimit program used for determining the cross section varies the causing also the position of the signal peak in the $m_{jj}$ distribution to vary. The uncertainty is approximated to be
parameters used for the fit and therefore includes their uncertainties to calculate the final result. 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 # Results
In this chapter the results and a comparison to previous research will be shown as well as a comparison between the two This chapter will start by presenting the results for the data of year 2016 using both taggers and comparing it to the
different taggers used. previous research [@PREV_RESEARCH]. It will then go on showing the results for the combined dataset, again using both
taggers comparing their performances.
## 2016 ## 2016
Using the data collected by the CMS experiment on 2016, the cross section limits seen in [@fig:res2016] were obtained. 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:
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 limits found using the data collected in 2016 {#tbl:res2016}
| 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
| Decay | Tagger | Limit [TeV] | Upper Limit [TeV] | Lower Limit [TeV] | | 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 ### 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 The limit established by using the N-subjettiness tagger on the 2016 data is already slightly higher than the one from
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 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
intersection point happens to be in the lower region of the expected limit interval and therefore causing a very late to the fact, that in our data, the observed limit at the intersection point happens to be in the lower region of the
crossing with the theory line when using the N-subjettiness tagger (as can be seen in [@fig:res2016]. This could be expected limit interval and therefore causing a very late crossing with the theory line when using the N-subjettiness
caused by small differences of the setup used or slightly differently processed data. In general, the results appear to tagger (as can be seen in [@fig:res2016]). This could be caused by small differences of the setup used or slightly
be very similar to the previous research, seen in [@fig:prev]. 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{figure}
\begin{minipage}{0.5\textwidth} \begin{minipage}{0.5\textwidth}
@ -844,81 +832,11 @@ Taken from \cite{PREV_RESEARCH}.}
\label{fig:prev} \label{fig:prev}
\end{figure} \end{figure}
## 2016 + 2017 + 2018 ## Combined dataset
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 |
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: 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 | | 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{figure}
\begin{minipage}{0.5\textwidth} \begin{minipage}{0.5\textwidth}
@ -952,8 +873,6 @@ deep boosted tagger (right).}
\label{fig:resCombined} \label{fig:resCombined}
\end{figure} \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 ## 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. 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 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 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 N-subjettiness tagger. This was not the expected result, as the deep neural network was already found to provide a
separation between signal and background events than the older N-subjettiness tagger. Recently, some issues with the higher significance in the optimisation done in [@sec:opt]. The higher significance should also result in lower cross
training of the deep boosted tagger used in this analysis were found, so those might explain the bad performance. 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.
![Comparision of deep boosted and N-subjettiness tagger in the high purity category using the data from year 2018.
](./figures/limit_comp_2018.pdf){#fig:comp_2018}
\begin{figure} \begin{figure}
\begin{minipage}{0.5\textwidth} \begin{minipage}{0.5\textwidth}
@ -977,25 +906,47 @@ decay to qZ}
\label{fig:limit_comp} \label{fig:limit_comp}
\end{figure} \end{figure}
\clearpage
\newpage \newpage
# Summary # Summary
In this thesis, a limit on the mass of the q\* particle has been successfully established. By combining the data from 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 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 improved.
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 For the data analysis, the following selection was applied:
issues identified lately, there is still a good chance, that, with that issue fixed, it will be able to further improve
the results. - #jets >= 2
Also previously research of the 2016 data was repeated and the results compared. The previous research arrived at a - $\Delta\eta < 1.4$
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 - $m_{jj} >= \SI{1050}{\giga\eV}$
difference can be explained by small differences in the data used and the setup itself. After that, using the combined - $\SI{35}{\giga\eV} < m_{SDM} < \SI{105}{\giga\eV}$
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 For the deep boosted tagger, a high purity category of $VvsQCD > 0.95$ and a low purity category of $VvsQCD <= 0.95$ was
predict its existence at lower masses, than the one used, by overlaying the different theory curves in the plots shown used. For the N-subjettiness tagger the high purity category was $\tau_{21} < 0.35$ and the low purity category $0.35 <
in [@fig:res2016] and [@fig:resCombined]. \tau_{21} < 0.75$. 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 \newpage
\nocite{*} \nocite{*}

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@ -1,38 +1,38 @@
\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax \boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax
\babel@toc {british}{} \babel@toc {british}{}
\contentsline {section}{\numberline {1}Introduction}{1}{section.1}% \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 {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 {2.1.1}Shortcomings of the Standard Model}{4}{subsubsection.2.1.1}%
\contentsline {subsubsection}{\numberline {2.1.2}Shortcomings of the Standard Model}{3}{subsubsection.2.1.2}%
\contentsline {subsection}{\numberline {2.2}Excited quark states}{4}{subsection.2.2}% \contentsline {subsection}{\numberline {2.2}Excited quark states}{4}{subsection.2.2}%
\contentsline {section}{\numberline {3}Experimental Setup}{6}{section.3}% \contentsline {subsubsection}{\numberline {2.2.1}Quantum Chromodynamic background}{5}{subsubsection.2.2.1}%
\contentsline {subsection}{\numberline {3.1}Large Hadron Collider}{6}{subsection.3.1}% \contentsline {section}{\numberline {3}Experimental Setup}{7}{section.3}%
\contentsline {subsection}{\numberline {3.2}Compact Muon Solenoid}{6}{subsection.3.2}% \contentsline {subsection}{\numberline {3.1}Large Hadron Collider}{7}{subsection.3.1}%
\contentsline {subsubsection}{\numberline {3.2.1}Coordinate conventions}{7}{subsubsection.3.2.1}% \contentsline {subsection}{\numberline {3.2}Compact Muon Solenoid}{7}{subsection.3.2}%
\contentsline {subsubsection}{\numberline {3.2.2}The tracking system}{7}{subsubsection.3.2.2}% \contentsline {subsubsection}{\numberline {3.2.1}Coordinate conventions}{8}{subsubsection.3.2.1}%
\contentsline {subsubsection}{\numberline {3.2.3}The electromagnetic calorimeter}{7}{subsubsection.3.2.3}% \contentsline {subsubsection}{\numberline {3.2.2}The tracking system}{8}{subsubsection.3.2.2}%
\contentsline {subsubsection}{\numberline {3.2.4}The hadronic calorimeter}{8}{subsubsection.3.2.4}% \contentsline {subsubsection}{\numberline {3.2.3}The electromagnetic calorimeter}{9}{subsubsection.3.2.3}%
\contentsline {subsubsection}{\numberline {3.2.5}The solenoid}{8}{subsubsection.3.2.5}% \contentsline {subsubsection}{\numberline {3.2.4}The hadronic calorimeter}{9}{subsubsection.3.2.4}%
\contentsline {subsubsection}{\numberline {3.2.6}The muon system}{8}{subsubsection.3.2.6}% \contentsline {subsubsection}{\numberline {3.2.5}The solenoid}{9}{subsubsection.3.2.5}%
\contentsline {subsubsection}{\numberline {3.2.7}The Trigger system}{8}{subsubsection.3.2.7}% \contentsline {subsubsection}{\numberline {3.2.6}The muon system}{9}{subsubsection.3.2.6}%
\contentsline {subsubsection}{\numberline {3.2.8}The Particle Flow algorithm}{8}{subsubsection.3.2.8}% \contentsline {subsubsection}{\numberline {3.2.7}The Trigger system}{9}{subsubsection.3.2.7}%
\contentsline {subsection}{\numberline {3.3}Jet clustering}{9}{subsection.3.3}% \contentsline {subsubsection}{\numberline {3.2.8}The Particle Flow algorithm}{9}{subsubsection.3.2.8}%
\contentsline {section}{\numberline {4}Method of analysis}{11}{section.4}% \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 {subsection}{\numberline {4.1}Signal and Background modelling}{12}{subsection.4.1}%
\contentsline {section}{\numberline {5}Preselection and data quality}{13}{section.5}% \contentsline {section}{\numberline {5}Preselection and data quality}{14}{section.5}%
\contentsline {subsection}{\numberline {5.1}Preselection}{13}{subsection.5.1}% \contentsline {subsection}{\numberline {5.1}Preselection}{14}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Data - Monte Carlo Comparison}{17}{subsection.5.2}% \contentsline {subsection}{\numberline {5.2}Data - Monte Carlo Comparison}{18}{subsection.5.2}%
\contentsline {subsubsection}{\numberline {5.2.1}Sideband}{18}{subsubsection.5.2.1}% \contentsline {subsubsection}{\numberline {5.2.1}Sideband}{19}{subsubsection.5.2.1}%
\contentsline {section}{\numberline {6}Jet substructure selection}{20}{section.6}% \contentsline {section}{\numberline {6}Jet substructure selection}{20}{section.6}%
\contentsline {subsection}{\numberline {6.1}N-Subjettiness}{20}{subsection.6.1}% \contentsline {subsection}{\numberline {6.1}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 {subsection}{\numberline {6.3}Optimization}{21}{subsection.6.3}%
\contentsline {section}{\numberline {7}Signal extraction}{22}{section.7}% \contentsline {section}{\numberline {7}Signal extraction}{22}{section.7}%
\contentsline {subsection}{\numberline {7.1}Uncertainties}{22}{subsection.7.1}% \contentsline {subsection}{\numberline {7.1}Uncertainties}{23}{subsection.7.1}%
\contentsline {section}{\numberline {8}Results}{22}{section.8}% \contentsline {section}{\numberline {8}Results}{23}{section.8}%
\contentsline {subsection}{\numberline {8.1}2016}{23}{subsection.8.1}% \contentsline {subsection}{\numberline {8.1}2016}{23}{subsection.8.1}%
\contentsline {subsubsection}{\numberline {8.1.1}Previous research}{26}{subsubsection.8.1.1}% \contentsline {subsubsection}{\numberline {8.1.1}Previous research}{24}{subsubsection.8.1.1}%
\contentsline {subsection}{\numberline {8.2}2016 + 2017 + 2018}{26}{subsection.8.2}% \contentsline {subsection}{\numberline {8.2}Combined dataset}{25}{subsection.8.2}%
\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{28}{subsection.8.3}% \contentsline {subsection}{\numberline {8.3}Comparison of taggers}{25}{subsection.8.3}%
\contentsline {section}{\numberline {9}Summary}{30}{section.9}% \contentsline {section}{\numberline {9}Summary}{29}{section.9}%