diff --git a/bibliography.bib b/bibliography.bib index 9936cfc..d4722da 100644 --- a/bibliography.bib +++ b/bibliography.bib @@ -1623,3 +1623,21 @@ archivePrefix = {arXiv}, (CMS Public Pages)", doi = "10.1088/1748-0221/12/10/P10003", } +@ARTICLE{ASYMPTOTIC_LIMIT, + author = {{Cowan}, Glen and {Cranmer}, Kyle and {Gross}, Eilam and {Vitells}, Ofer}, + title = "{Asymptotic formulae for likelihood-based tests of new physics}", + journal = {European Physical Journal C}, + keywords = {Physics - Data Analysis, Statistics and Probability, High Energy Physics - Experiment}, + year = "2011", + month = "Feb", + volume = {71}, + eid = {1554}, + pages = {1554}, + doi = {10.1140/epjc/s10052-011-1554-0}, +archivePrefix = {arXiv}, + eprint = {1007.1727}, + primaryClass = {physics.data-an}, + adsurl = {https://ui.adsabs.harvard.edu/abs/2011EPJC...71.1554C}, + adsnote = {Provided by the SAO/NASA Astrophysics Data System} +} + diff --git a/thesis.aux b/thesis.aux index d9d008a..dc79d0a 100644 --- 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{{hash=63095f782c12657f0556f148e399c606}{% + family={{Vitells}}, + familyi={V\bibinitperiod}, + given={Ofer}, + giveni={O\bibinitperiod}}}% + } + \strng{namehash}{22db102a3f181de2baabd3c2fb244138} + \strng{fullhash}{01410fa503312f8756583d42dcefa458} + \strng{bibnamehash}{22db102a3f181de2baabd3c2fb244138} + \strng{authorbibnamehash}{22db102a3f181de2baabd3c2fb244138} + \strng{authornamehash}{22db102a3f181de2baabd3c2fb244138} + \strng{authorfullhash}{01410fa503312f8756583d42dcefa458} + \field{sortinit}{C} + \field{sortinithash}{4c244ceae61406cdc0cc2ce1cb1ff703} + \field{labelnamesource}{author} + \field{labeltitlesource}{title} + \field{eid}{1554} + \field{eprintclass}{physics.data-an} + \field{eprinttype}{arXiv} + \field{journaltitle}{European Physical Journal C} + \field{month}{2} + \field{title}{{Asymptotic formulae for likelihood-based tests of new physics}} + \field{volume}{71} + \field{year}{2011} + \true{nocite} + \field{pages}{1554} + \range{pages}{1} + \verb{doi} + \verb 10.1140/epjc/s10052-011-1554-0 + \endverb + \verb{eprint} + \verb 1007.1727 + \endverb + \keyw{Physics - Data Analysis,Statistics and Probability,High Energy Physics - Experiment} + \endentry \entry{SUC_COMBINATION}{article}{} \name{author}{2}{}{% {{hash=1cf847720f5b264c36c2bad0b73da94b}{% diff --git a/thesis.bcf b/thesis.bcf index 48c14b8..449439c 100644 --- a/thesis.bcf +++ b/thesis.bcf @@ -1999,24 +1999,29 @@ DEEP_BOOSTED TAU21 PREV_RESEARCH - QSTAR_THEORY - PREV_RESEARCH - website - CMS_PLOT - CMS_PLOT - ANTIKT - ANTIKT - PREV_RESEARCH - PREV_RESEARCH - QSTAR_THEORY - TAU21 - DEEP_BOOSTED - DEEP_BOOSTED - DEEP_BOOSTED - PREV_RESEARCH - PREV_RESEARCH - PREV_RESEARCH - PREV_RESEARCH + DEEP_BOOSTED + TAU21 + PREV_RESEARCH + QSTAR_THEORY + PREV_RESEARCH + website + CMS_PLOT + CMS_PLOT + ANTIKT + ANTIKT + PREV_RESEARCH + PREV_RESEARCH + QSTAR_THEORY + TAU21 + DEEP_BOOSTED + DEEP_BOOSTED + DEEP_BOOSTED + ASYMPTOTIC_LIMIT + QSTAR_THEORY + PREV_RESEARCH + PREV_RESEARCH + PREV_RESEARCH + PREV_RESEARCH * diff --git a/thesis.blg b/thesis.blg index b85f209..fee831a 100644 --- a/thesis.blg +++ b/thesis.blg @@ -1,29 +1,30 @@ [0] Config.pm:304> INFO - This is Biber 2.12 [0] Config.pm:307> INFO - Logfile is 'thesis.blg' -[22] biber:315> INFO - === Sa Okt 26, 2019, 11:19:55 -[40] Biber.pm:371> INFO - Reading 'thesis.bcf' -[97] Biber.pm:886> INFO - Using all citekeys in bib section 0 -[108] Biber.pm:4093> INFO - Processing section 0 -[118] Biber.pm:4254> INFO - Looking for bibtex format file 'bibliography.bib' for section 0 -[127] bibtex.pm:1523> INFO - LaTeX decoding ... -[240] bibtex.pm:1340> INFO - Found BibTeX data source 'bibliography.bib' -[249] Utils.pm:193> WARN - month field 'May' in entry 'LHC' is not an integer - this will probably not sort properly. -[254] Utils.pm:193> WARN - month field 'Mar' in entry 'TAU21' is not an integer - this will probably not sort properly. -[257] Utils.pm:193> WARN - month field 'Jan' in entry 'PARTICLE_FLOW' is not an integer - this will probably not sort properly. -[263] Utils.pm:193> WARN - month field 'May' in entry 'SDM' is not an integer - this will probably not sort properly. -[270] Utils.pm:193> WARN - month field 'Apr' in entry 'ANTIKT' is not an integer - this will probably not sort properly. -[273] Utils.pm:193> WARN - month field 'Oct' in entry 'CMS_TRIGGER' is not an integer - this will probably not sort properly. -[277] Utils.pm:193> WARN - month field 'Aug' in entry 'PREV_RESEARCH' is not an integer - this will probably not sort properly. -[2922] Utils.pm:193> WARN - month field 'Jun' in entry 'CMS_PLOT' is not an integer - this will probably not sort properly. -[2925] Utils.pm:193> WARN - month field 'Apr' in entry 'MONTECARLO' is not an integer - this will probably not sort properly. -[2926] Utils.pm:193> WARN - month field 'aug' in entry 'LHC_MACHINE' is not an integer - this will probably not sort properly. -[3207] Utils.pm:193> WARN - month field 'Aug' in entry 'PARTICLE_PHYSICS' is not an integer - this will probably not sort properly. -[3211] Utils.pm:193> WARN - month field 'Nov' in entry 'HADRONIZATION' is not an integer - this will probably not sort properly. -[3215] Utils.pm:193> WARN - month field 'Oct' in entry 'SUC_COMBINATION' is not an integer - this will probably not sort properly. -[5724] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'normalization = NFD' with 'normalization = prenormalized' -[5724] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'variable = shifted' with 'variable = non-ignorable' -[5724] Biber.pm:3921> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'en-GB' -[5724] Biber.pm:3927> INFO - No sort tailoring available for locale 'en-GB' -[5873] bbl.pm:636> INFO - Writing 'thesis.bbl' with encoding 'UTF-8' -[13899] bbl.pm:739> INFO - Output to thesis.bbl -[13901] Biber.pm:110> INFO - WARNINGS: 13 +[21] biber:315> INFO - === Mo Okt 28, 2019, 07:32:14 +[39] Biber.pm:371> INFO - Reading 'thesis.bcf' +[95] Biber.pm:886> INFO - Using all citekeys in bib section 0 +[105] Biber.pm:4093> INFO - Processing section 0 +[114] Biber.pm:4254> INFO - Looking for bibtex format file 'bibliography.bib' for section 0 +[123] bibtex.pm:1523> INFO - LaTeX decoding ... +[238] bibtex.pm:1340> INFO - Found BibTeX data source 'bibliography.bib' +[248] Utils.pm:193> WARN - month field 'Feb' in entry 'ASYMPTOTIC_LIMIT' is not an integer - this will probably not sort properly. +[251] Utils.pm:193> WARN - month field 'Oct' in entry 'CMS_TRIGGER' is not an integer - this will probably not sort properly. +[2583] Utils.pm:193> WARN - month field 'aug' in entry 'LHC_MACHINE' is not an integer - this will probably not sort properly. +[2593] Utils.pm:193> WARN - month field 'Apr' in entry 'ANTIKT' is not an integer - this will probably not sort properly. +[2600] Utils.pm:193> WARN - month field 'May' in entry 'SDM' is not an integer - this will probably not sort properly. +[2606] Utils.pm:193> WARN - month field 'May' in entry 'LHC' is not an integer - this will probably not sort properly. +[2923] Utils.pm:193> WARN - month field 'Aug' in entry 'PARTICLE_PHYSICS' is not an integer - this will probably not sort properly. +[2927] Utils.pm:193> WARN - month field 'Oct' in entry 'SUC_COMBINATION' is not an integer - this will probably not sort properly. +[2931] Utils.pm:193> WARN - month field 'Aug' in entry 'PREV_RESEARCH' is not an integer - this will probably not sort properly. +[2935] Utils.pm:193> WARN - month field 'Mar' in entry 'TAU21' is not an integer - this will probably not sort properly. +[2938] Utils.pm:193> WARN - month field 'Apr' in entry 'MONTECARLO' is not an integer - this will probably not sort properly. +[2941] Utils.pm:193> WARN - month field 'Jan' in entry 'PARTICLE_FLOW' is not an integer - this will probably not sort properly. +[5592] Utils.pm:193> WARN - month field 'Jun' in entry 'CMS_PLOT' is not an integer - this will probably not sort properly. +[5596] Utils.pm:193> WARN - month field 'Nov' in entry 'HADRONIZATION' is not an integer - this will probably not sort properly. +[5732] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'variable = shifted' with 'variable = non-ignorable' +[5732] UCollate.pm:68> INFO - Overriding locale 'en-GB' defaults 'normalization = NFD' with 'normalization = prenormalized' +[5732] Biber.pm:3921> INFO - Sorting list 'nty/global//global/global' of type 'entry' with template 'nty' and locale 'en-GB' +[5732] Biber.pm:3927> INFO - No sort tailoring available for locale 'en-GB' +[5889] bbl.pm:636> INFO - Writing 'thesis.bbl' with encoding 'UTF-8' +[13861] bbl.pm:739> INFO - Output to thesis.bbl +[13863] Biber.pm:110> INFO - WARNINGS: 14 diff --git a/thesis.log b/thesis.log index bd2fde3..9ed2a86 100644 --- a/thesis.log +++ b/thesis.log @@ -1,4 +1,4 @@ -This is LuaTeX, Version 1.10.0 (TeX Live 2019/Arch Linux) (format=lualatex 2019.8.29) 26 OCT 2019 11:20 +This is LuaTeX, Version 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Package biblatex Info: ... file 'blx-unicode.def' found. @@ -1691,34 +1699,34 @@ File: english.lbx 2018/11/02 v3.12 biblatex localization (PK/MW) )) (./thesis.aux) \openout1 = thesis.aux -LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for TU/lmr/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. -LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 115. -LaTeX Font Info: ... okay on input line 115. +LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for TU/lmr/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for PD1/pdf/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. +LaTeX Font Info: Checking defaults for PU/pdf/m/n on input line 116. +LaTeX Font Info: ... okay on input line 116. 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LaTeX Font Info: Overwriting symbol font `symbols' in version `normal' (Font) OMS/lmsy/m/n --> TU/latinmodern-math.otf(2)/m/n on input - line 115. + line 116. LaTeX Font Info: Encoding `OMS' has changed to `TU' for symbol font -(Font) `symbols' in the math version `bold' on input line 115. +(Font) `symbols' in the math version `bold' on input line 116. LaTeX Font Info: Overwriting symbol font `symbols' in version `bold' (Font) OMS/lmsy/b/n --> TU/latinmodern-math.otf(2)/bx/n on inpu -t line 115. +t line 116. Package fontspec Info: latinmodern-math scale = 1.037739856970899. @@ -1978,48 +1986,48 @@ h.otf]:mode=base;script=math;language=DFLT;+ssty=0;"<-7.2>s*[1.037636082985202]" LaTeX Font Info: Encoding `OMX' has changed to `TU' for symbol font (Font) `largesymbols' in the math version `normal' on input line 11 -5. +6. LaTeX Font Info: Overwriting symbol font `largesymbols' in version `normal' (Font) OMX/lmex/m/n --> TU/latinmodern-math.otf(3)/m/n on input - line 115. + line 116. 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Package microtype Info: Using protrusion set `basicmath'. @@ -2065,7 +2073,7 @@ File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live )) \AtBeginShipoutBox=\box80 -Package hyperref Info: Link coloring OFF on input line 115. +Package hyperref Info: Link coloring OFF on input line 116. (/usr/share/texmf-dist/tex/latex/hyperref/nameref.sty Package: nameref 2016/05/21 v2.44 Cross-referencing by name of section @@ -2075,9 +2083,9 @@ Package: gettitlestring 2016/05/16 v1.5 Cleanup title references (HO) ) \c@section@level=\count481 ) -LaTeX Info: Redefining \ref on input line 115. -LaTeX Info: Redefining \pageref on input line 115. -LaTeX Info: Redefining \nameref on input line 115. +LaTeX Info: Redefining \ref on input line 116. +LaTeX Info: Redefining \pageref on input line 116. +LaTeX Info: Redefining \nameref on input line 116. *geometry* driver: auto-detecting *geometry* detected driver: luatex @@ -2124,7 +2132,7 @@ ABD: EveryShipout initializing macros Package tikz-feynman Warning: Consider loading TikZ-Feynman with \usepackage[com pat=1.1.0]{tikz-feynman} so that you can be warned if TikZ-Feynman changes. on i -nput line 115. +nput line 116. Package caption Info: Begin \AtBeginDocument code. Package caption Info: subfig package v1.3 is loaded. @@ -2139,34 +2147,34 @@ Package biblatex Info: Automatic encoding selection. Package biblatex Info: Trying to load bibliographic data... Package biblatex Info: ... file 'thesis.bbl' found. (./thesis.bbl) -Package biblatex Info: Reference section=0 on input line 115. -Package biblatex Info: Reference segment=0 on input line 115. +Package biblatex Info: Reference section=0 on input line 116. +Package biblatex Info: Reference segment=0 on input line 116. Package microtype Info: Loading generic protrusion settings for font family (microtype) `lmss' (encoding: TU). (microtype) For optimal results, create family-specific settings. (microtype) See the microtype manual for details. LaTeX Font Info: Font shape `TU/TimesNewRoman(0)/m/n' will be -(Font) scaled to size 20.74pt on input line 117. +(Font) scaled to size 20.74pt on input line 118. 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[13<./figures/cb_fit.pdf>] Package epstopdf Info: Source file: <./figures/2016/v1_Cleaner_N_jets_stack.eps> @@ -2251,15 +2279,15 @@ converted-to.pdf> (epstopdf) size: 8841 bytes (epstopdf) Command: -(epstopdf) \includegraphics on input line 828. +(epstopdf) \includegraphics on input line 858. Package epstopdf Info: Output file is already uptodate. -<./figures/2016/v1_Cleaner_N_jets_stack-eps-converted-to.pdf, id=469, 569.12625p +<./figures/2016/v1_Cleaner_N_jets_stack-eps-converted-to.pdf, id=472, 569.12625p t x 534.99875pt> File: ./figures/2016/v1_Cleaner_N_jets_stack-eps-converted-to.pdf Graphic file ( type pdf) Package luatex.def Info: ./figures/2016/v1_Cleaner_N_jets_stack-eps-converted-to -.pdf used on input line 828. +.pdf used on input line 858. (luatex.def) Requested size: 227.6204pt x 213.9712pt. 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Package epstopdf Info: Source file: <./figures/combined/v1_Njet_deta_stack.eps> (epstopdf) date: 2019-10-14 10:24:56 @@ -2378,15 +2406,15 @@ onverted-to.pdf> (epstopdf) size: 96978 bytes (epstopdf) Command: -(epstopdf) \includegraphics on input line 867. +(epstopdf) \includegraphics on input line 897. Package epstopdf Info: Output file is already uptodate. -<./figures/combined/v1_Njet_deta_stack-eps-converted-to.pdf, id=476, 569.12625pt +<./figures/combined/v1_Njet_deta_stack-eps-converted-to.pdf, id=479, 569.12625pt x 534.99875pt> File: ./figures/combined/v1_Njet_deta_stack-eps-converted-to.pdf Graphic file (t ype pdf) Package luatex.def Info: ./figures/combined/v1_Njet_deta_stack-eps-converted-to. -pdf used on input line 867. +pdf used on input line 897. (luatex.def) Requested size: 227.6204pt x 213.9712pt. Package epstopdf Info: Source file: <./figures/combined/v1_Eta_deta_stack.eps> (epstopdf) date: 2019-10-14 10:25:01 @@ -2397,23 +2425,23 @@ nverted-to.pdf> (epstopdf) size: 94537 bytes (epstopdf) Command: -(epstopdf) \includegraphics on input line 870. +(epstopdf) \includegraphics on input line 900. Package epstopdf Info: Output file is already uptodate. -<./figures/combined/v1_Eta_deta_stack-eps-converted-to.pdf, id=477, 569.12625pt +<./figures/combined/v1_Eta_deta_stack-eps-converted-to.pdf, id=480, 569.12625pt x 534.99875pt> File: ./figures/combined/v1_Eta_deta_stack-eps-converted-to.pdf Graphic file (ty pe pdf) Package luatex.def Info: ./figures/combined/v1_Eta_deta_stack-eps-converted-to.p -df used on input line 870. +df used on input line 900. 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(luatex.def) Requested size: 150.2272pt x 141.21887pt. Package epstopdf Info: Source file: <./figures/2016/DATA/v1_invmass_deta.eps> (epstopdf) date: 2019-10-08 10:32:27 @@ -2545,15 +2573,15 @@ verted-to.pdf> (epstopdf) size: 12591 bytes (epstopdf) Command: -(epstopdf) \includegraphics on input line 943. +(epstopdf) \includegraphics on input line 975. Package epstopdf Info: Output file is already uptodate. -<./figures/2016/DATA/v1_invmass_deta-eps-converted-to.pdf, id=696, 569.12625pt x +<./figures/2016/DATA/v1_invmass_deta-eps-converted-to.pdf, id=698, 569.12625pt x 534.99875pt> File: ./figures/2016/DATA/v1_invmass_deta-eps-converted-to.pdf Graphic file (typ e pdf) Package luatex.def Info: ./figures/2016/DATA/v1_invmass_deta-eps-converted-to.pd -f used on input line 943. +f used on input line 975. (luatex.def) Requested size: 150.2272pt x 141.21887pt. 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(luatex.def) Requested size: 273.16013pt x 184.99733pt. -[28<./figures/limit_comp_w.pdf><./figures/limit_comp_z.pdf>] [29<./figures/limit -_comp_2018.pdf>] [30 +[27<./figures/results/brazilianFlag_QtoqW_Combinedtau_13TeV.pdf><./figures/resul +ts/brazilianFlag_QtoqW_Combineddb_13TeV.pdf><./figures/results/brazilianFlag_Qto +qZ_Combinedtau_13TeV.pdf><./figures/results/brazilianFlag_QtoqZ_Combineddb_13TeV +.pdf>] [28<./figures/limit_comp_w.pdf><./figures/limit_comp_z.pdf><./figures/lim +it_comp_2018.pdf>] [29 ] LaTeX Font Info: Font shape `TU/TimesNewRoman(0)/m/it' will be -(Font) scaled to size 12.0pt on input line 1488. +(Font) scaled to size 12.0pt on input line 1528. -Underfull \hbox (badness 10000) in paragraph at lines 1489--1489 +Underfull \hbox (badness 10000) in paragraph at lines 1529--1529 []\TU/TimesNewRoman(0)/m/n/12 Florian Beau-dette. ‘ The CMS Particle Flow Al -gorithm’. In: \TU/TimesNewRoman(0)/m/it/12 arXiv e-prints\TU/TimesNewRoman(0 )/m/n/12 , [] -[31] [32] [33] [34] [35] [36] -Package atveryend Info: Empty hook `BeforeClearDocument' on input line 1710. -Package atveryend Info: Empty hook `AfterLastShipout' on input line 1710. +[30] [31] [32] [33] [34] [35] +Package atveryend Info: Empty hook `BeforeClearDocument' on input line 1750. +Package atveryend Info: Empty hook `AfterLastShipout' on input line 1750. (./thesis.aux) -Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 1710. -Package atveryend Info: Empty hook `AtEndAfterFileList' on input line 1710. +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 1750. +Package atveryend Info: Empty hook `AtEndAfterFileList' on input line 1750. LaTeX Warning: There were undefined references. @@ -2927,24 +2952,24 @@ Package logreq Info: Writing requests to 'thesis.run.xml'. ) Here is how much of LuaTeX's memory you used: - 55005 strings out of 494300 + 55166 strings out of 494300 125171,2848258 words of node,token memory allocated - 747 words of node memory still in use: - 7 hlist, 2 vlist, 2 rule, 5 glue, 4 kern, 1 glyph, 26 attribute, 73 glue_spec -, 26 attribute_list, 1 write, 8 pdf_action nodes - avail lists: 1:5,2:3008,3:619,4:64,5:111,6:38,7:5245,8:77,9:526,10:25,11:290 - 57032 multiletter control sequences out of 65536+600000 - 186 fonts using 56483563 bytes - 74i,13n,118p,1009b,2406s stack positions out of 5000i,500n,10000p,200000b,100000s + 782 words of node memory still in use: + 7 hlist, 2 vlist, 2 rule, 5 glue, 4 kern, 1 glyph, 27 attribute, 78 glue_spec +, 27 attribute_list, 1 write, 9 pdf_action nodes + avail lists: 1:5,2:3010,3:619,4:68,5:158,6:57,7:5432,8:80,9:526,10:25,11:312 + 57139 multiletter control sequences out of 65536+600000 + 215 fonts using 65844759 bytes + 74i,13n,118p,1009b,2404s stack positions out of 5000i,500n,10000p,200000b,100000s -Output written on thesis.pdf (38 pages, 1992379 bytes). +otf> +Output written on thesis.pdf (37 pages, 1996122 bytes). -PDF statistics: 1802 PDF objects out of 2073 (max. 8388607) - 1194 compressed objects within 12 object streams +PDF statistics: 1806 PDF objects out of 2073 (max. 8388607) + 1199 compressed objects within 12 object streams 173 named destinations out of 1000 (max. 131072) 304 words of extra memory for PDF output out of 10000 (max. 100000000) diff --git a/thesis.md b/thesis.md index 8921142..cfc9175 100644 --- a/thesis.md +++ b/thesis.md @@ -7,25 +7,40 @@ header-includes: | \usepackage{siunitx} \usepackage{tikz-feynman} \usepackage{csquotes} + \usepackage{abstract} \pagenumbering{gobble} \setlength{\parskip}{0.5em} \bibliographystyle{lucas_unsrt} abstract: | - A search for an excited quark state, called q\*, is presented using data recorded by CMS during the years 2016, 2017 - and 2018. By analysing its decay channels to qW and qZ, a minimum mass of 6.1 TeV resp. 5.5 TeV is established. This - limit is about 1 TeV higher than the limits found by a previous research of data collected by CMS in 2016 - [@PREV_RESEARCH], excluding the q\* particle up to a mass of 5.0 TeV resp. 4.7 TeV. Also a comparison of the new - DeepAK8 [@DEEP_BOOSTED] and the older N-subjettiness [@TAU21] tagger is conducted, showing that the newer DeepAK8 - tagger is currently approximately at the same level as the N-subjettiness tagger, but has the potential to further - improve in performance. + A search for an excited quark state, called q\*, is presented using data recorded by the CMS experiment during the + years 2016, 2017 and 2018 with a centre-of-mass energy of $\sqrt{s} = \SI{13}{\tera\eV}$ and a total integrated + luminosity of $\SI{137.19}{\per\femto\barn}$. By analysing its decay channels to q + W and q + Z that further decay + to $q + q\bar{q}$, resulting in two jets in the final state, the q\* can be excluded up to a mass of 6.1 (qW) TeV + resp. 5.5 TeV (qZ) with a confidence level of 95 %. This limit is about 1 TeV higher than the limits found by a + previous research of data collected by CMS in 2016 [@PREV_RESEARCH], excluding the q\* particle up to a mass of 5.0 + TeV resp. 4.7 TeV. Also a comparison of the new DeepAK8 [@DEEP_BOOSTED] and the older N-subjettiness [@TAU21] tagger + is conducted, showing that the newer DeepAK8 tagger, based on a deep neural network, is currently approximately at + the same level as the N-subjettiness tagger, but has the potential to further improve in performance, between others + because of an improved training that was just published. ```{=tex} \end{abstract} + \renewcommand{\abstractname}{Zusammenfassung} \begin{abstract} - Abstract 2. ``` + In dieser Arbeit wird eine Suche nach angeregten Quarkzuständen, genannt q\*, durchgeführt. Dafür werden Daten mit + einer gesamten integrierten Luminosität von $\SI{137.19}{\per\femto\barn}$ analysiert, welche über die Jahre 2016, + 2017 und 2018 bei einer Schwerpunktsenergie von $\sqrt{s} = \SI{13}{\tera\eV}$ vom CMS Experiment aufgenommen + wurden. Indem der Zerfall des q\* Teilchens zu q + W und q + Z untersucht wird, kann dieses mit einem + Konfidenzniveau von 95 % bis zu einer Masse von 6.1 TeV (qW) bzw. 5.5 TeV (qZ) ausgeschlossen werden. Dieses Limit + liegt etwa 1 TeV höher, als das von vorhergegangener Forschung [@PREV_RESEARCH] gesetzte von 5.0 TeV bzw. 4.7 TeV. + Dabei wird der neue DeepAK8 Tagger [@DEEP_BOOSTED], welcher auf einem neuronalen Netzwerk basiert, mit dem älteren + N-Subjetiness Tagger [@TAU21] verglichen. Das Endergebnis der beiden Tagger unterscheidet sich kaum, jedoch gibt es + beim DeepAK8 Tagger noch potential zur Verbesserung, unter anderem durch ein verbessertes Traininig, welches vor + kurzem veröffentlicht wurde. + documentclass: article geometry: - top=2.5cm @@ -280,6 +295,8 @@ $f_{rev} = \SI{11.2}{\kilo\Hz}$, $\beta^* = \SI{0.55}{\m}$, $\epsilon_n = \SI{3. To quantify the amount of data collected by one of the experiments at LHC, the integrated luminosity is introduced as $L_{int} = \int L dt$. +explain pdf -> not all 13 TeV available for collision + ## Compact Muon Solenoid @@ -382,7 +399,7 @@ changed according to its hardness in regards to the transverse momentum. A softe 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 soft-drop mass can be used. It is calculated by removing wide angle soft particles from the jet to counter the effects of contamination from initial state radiation, underlying event and multiple hadron scattering. It therefore is more accurate in determining the mass of a particle causing a jet than taking the mass of all constituent particles of the jet combined. @@ -452,7 +469,9 @@ The signal is fitted using a double sided crystal ball function. It has six para A gaussian and a poisson function have also been studied but found to be not able to reproduce the signal shape as they couldn't model the tails on both sides of the peak. -An example of a fit of these functions to a toy dataset with gaussian errors can be seen in [@fig:cb_fit]. In this +A linear combination of the signal and background function is then fitted to a toy dataset with gaussian errors and a +simulated signal cross section of $\SI{1}{\per\pico\barn}$. The resulting coefficients of said combination then show the +expected signal rate for the simulated cross section. An example of such a fit 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. 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 @@ -468,10 +487,10 @@ Combined fit of signal and background on a toy dataset with gaussian errors and To reduce the background and increase the signal sensitivity, a selection of events by different variables is introduced. It is divided into two stages. The first one (the preselection) adds some general physics motivated -selection using kinematic variables and is also used to make sure a good trigger efficiency is achieved. In the second -part, different taggers will be used as a discriminator between QCD background and signal events. After the -preselection, it is made sure, that the simulated samples represent the real data well by comparing the data with the -simulation in the signal as well as a sideband region, where no signal events are expected. +selection using kinematic variables and is also used to ensure a high trigger efficiency. In the second part, different +taggers will be used as a discriminator between QCD background and signal events. After the preselection, it is made +sure, that the simulated samples represent the real data well by comparing the data with the simulation in the signal as +well as a sideband region, where no signal events are expected. ## Preselection @@ -481,10 +500,10 @@ reconstruction. Furthermore, all events with one of the two highest $p_t$ jets h than 0.8 from any electron or muon are discarded to allow future use of the results in studies of the semi or all-leptonic decay channels. -From a decaying q\* particle, we expect two jets in the endstate. The dijet invariant mass of those two jets will be -used to reconstruct the mass of the q\* particle. Therefore a cut is added to have at least 2 jets. -More jets are also possible, for example caused by gluon radiation of a quark causing another jet. If this is the case, -the two jets with the highest $p_t$ are used for the reconstruction of the q\* mass. +From a decaying q\* particle, two jets are expected in the final state. The dijet invariant mass of those two jets will +be used to reconstruct the mass of the q\* particle. Therefore a cut is added to have at least 2 jets, accounting for +the possibility of more jets, for example caused by gluon radiation of a quark or other QCD effects. 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} @@ -500,16 +519,17 @@ The distributions of the number of jets before and after the selection can be se \begin{minipage}{0.5\textwidth} \includegraphics{./figures/combined/v1_Njet_N_jets_stack.eps} \end{minipage} -\caption{Number of jet distribution showing the cut at number of jets $\ge$ 2. Left: distribution before the cut. Right: +\caption{Comparison of the number of jet distribution before and after the cut at number of jets $\ge$ 2. Left: +distribution before the cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018. The signal curves are amplified by a factor of 10,000, to be visible.} \label{fig:njets} \end{figure} The next selection is done using $\Delta\eta = |\eta_1 - \eta_2|$, with $\eta_1$ and $\eta_2$ being the $\eta$ of the -first two jets in regards to their transverse momentum. The q\* particle is expected to be very heavy in regards to the -center of mass energy of the collision and will therefore be almost stationary. Its decay products should therefore be -close to back to back, which means the $\Delta\eta$ distribution is expected to peak at 0. At the same time, particles +two jets with the highest transverse momentum. The q\* particle is expected to be very heavy in regards to the center of +mass energy of the collision and will therefore be almost stationary. Its decay products should therefore be close to +back to back, which means the $\Delta\eta$ distribution is expected to peak at 0. At the same time, particles originating from QCD effects are expected to have a higher $\Delta\eta$ as they mainly form from less heavy resonances. To maintain comparability, the same selection as in previous research of $\Delta\eta \le 1.3$ is used. A comparison of the $\Delta\eta$ distribution before and after the selection can be seen in [@fig:deta]. @@ -527,17 +547,19 @@ the $\Delta\eta$ distribution before and after the selection can be seen in [@fi \begin{minipage}{0.5\textwidth} \includegraphics{./figures/combined/v1_Eta_deta_stack.eps} \end{minipage} -\caption{$\Delta\eta$ distribution showing the cut at $\Delta\eta \le 1.3$. Left: distribution before the cut. Right: -distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018. The signal curves -are amplified by a factor of 10,000, to be visible.} +\caption{Comparison of the $\Delta\eta$ distribution before and after the cut at $\Delta\eta \le 1.3$. Left: +distribution before the cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from +2016, 2017 and 2018. The signal curves are amplified by a factor of 10,000, to be visible.} \label{fig:deta} \end{figure} The last selection in the preselection is on the dijet invariant mass: $m_{jj} \ge \SI{1050}{\giga\eV}$. It is important -for a high trigger efficiency and can be seen in [@fig:invmass]. Also, it has a huge impact on the background because it -usually consists of way lighter particles. The q\* on the other hand is expected to have a very high invariant mass of -more than 1 TeV. The $m_{jj}$ distribution should be a smoothly falling function for the QCD background and peak at the -simulated resonance mass for the signal events. +for a trigger efficiency higher than 99 % with a soft-drop mass cut of $m_{SDM} > \SI{65}{\giga\eV}$ applied to the jet +with the highest transverse momentum. A comparison of its distribution before and after the selection can be seen in +[@fig:invmass]. Also, it has a huge impact on the background because it usually consists of way lighter particles. The +q\* on the other hand is expected to have a very high invariant mass of more than 1 TeV. The $m_{jj}$ distribution +should be a smoothly falling function for the QCD background and peak at the simulated resonance mass for the signal +events. \begin{figure} \begin{minipage}{0.5\textwidth} @@ -552,8 +574,8 @@ simulated resonance mass for the signal events. \begin{minipage}{0.5\textwidth} \includegraphics{./figures/combined/v1_invmass_invMass_stack.eps} \end{minipage} -\caption{Invariant mass distribution showing the cut at $m_{jj} \ge \SI{1050}{\giga\eV}$. It shows the expected smooth -falling functions of the background whereas the signal peaks at the simulated resonance mass. +\caption{Comparison of the invariant mass distribution before and after the cut at $m_{jj} \ge \SI{1050}{\giga\eV}$. It +shows the expected smooth falling functions of the background whereas the signal peaks at the simulated resonance mass. Left: distribution before the cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018.} \label{fig:invmass} @@ -565,18 +587,18 @@ preselection is reduced to 5 % of the original events. For the combined data of similar. Decaying to qW signal efficiencies between 49 % (1.6 TeV) and 56 % (7 TeV) are reached, wheres the efficiencies when decaying to qZ are in the range of 46 % (1.6 TeV) to 50 % (7 TeV). Here, the background could be reduced to 8 % of the original events. So while keeping around 50 % of the signal, the background was already reduced to less than a -tenth. Still, as can be seen in [@fig:njets] to [@fig:invmass], the amount of signal is very low. +tenth. ## Data - Monte Carlo Comparison -To ensure high data quality, the simulated QCD background sample is now being compared to the actual data of the -corresponding year collected by the CMS detector. This is done for the year 2016 and for the combined data of years -2016, 2017 and 2018. The distributions are rescaled so the integral over the invariant mass distribution of data and -simulation are the same. In [@fig:data-mc], the three distributions of the variables that were used for the preselection -can be seen for year 2016 and the combined data of years 2016 to 2018. -For analysing the real data from the CMS, jet energy corrections have to be applied. Those are to calibrate the ECAL and -HCAL parts of the CMS, so the energy of the detected particles can be measured correctly. The corrections used were -published by the CMS group. [source needed, but not sure where to find it] +To ensure high data quality, the simulated QCD background sample is now being compared to the data of the corresponding +year collected by the CMS detector. This is done for the year 2016 and for the combined data of years 2016, 2017 and +2018. The distributions are rescaled so the integral over the invariant mass distribution of data and simulation are the +same. In [@fig:data-mc], the three distributions of the variables that were used for the preselection can be seen for +year 2016 and the combined data of years 2016 to 2018. +For analysing the data from the CMS, jet energy corrections have to be applied. Those are to calibrate the ECAL and HCAL +parts of the CMS, so the energy of the detected particles can be measured correctly. The corrections used were published +by the CMS group. [source needed, but not sure where to find it] \begin{figure} \begin{minipage}{0.33\textwidth} @@ -610,10 +632,10 @@ and simulation. The sideband is introduced to make sure no bias in the data and Monte Carlo simulation is introduced. It is a region in which no signal event is expected. Again, data and the Monte Carlo simulation are compared. For this analysis, the -region where the softdropmass of both of the two jets with the highest transverse momentum ($p_t$) is more than 105 GeV -was chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, the heavier vector boson. Therefore it is very -unlikely that a particle heavier than t -In [@fig:sideband], the comparison of data with simulation in the sideband region can be seen for the softdropmass +region where the soft-drop mass of both of the two jets with the highest transverse momentum is more than 105 GeV is +chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, the heavier vector boson. Therefore it is very +unlikely, that an event with a particle than the 105 GeV originates from the decay of a vector boson. +In [@fig:sideband], the comparison of data with simulation in the sideband region can be seen for the soft-drop mass 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. It can be seen, that in the sideband region data and simulation match very well. @@ -640,14 +662,14 @@ combined data from 2016, 2017 and 2018.} # Jet substructure selection -So far it was made sure, that the actual data and the simulation are in good agreement after the preselection and no -unwanted side effects are introduced in the data by the used cuts. Now another selection has to be introduced, to -further reduce the background to be able to extract the hypothetical signal events from the actual data. +So far it was made sure, that the data collected by the CMS and the simulation are in good agreement after the +preselection and no unwanted side effects are introduced in the data by the used cuts. Now another selection has to be +introduced, to further reduce the background to be able to look for the hypothetical signal events in the data. This is done by distinguishing between QCD and signal events using a tagger to identify jets coming from a vector boson. Two different taggers will be used to later compare their performance. The decay analysed includes either a W or Z boson, which are, compared to the particles in QCD effects, very heavy. This can be used by adding a cut -on the softdropmass of a jet. The softdropmass of at least one of the two leading jets is expected to be within +on the soft-drop mass of a jet. The soft-drop mass of at least one of the two leading jets is expected to be within $\SI{35}{\giga\eV}$ and $\SI{105}{\giga\eV}$. This cut already provides a good separation of QCD and signal events, on which the two taggers presented next can build. @@ -675,7 +697,7 @@ discriminator between QCD events and events originating from the decay of a boos The lower the $\tau_{21}$ is, the more likely a jet is caused by the decay of a vector boson. Therefore a selection will be introduced, so that $\tau_{21}$ of one candidate jet is smaller then some value that will be determined by an optimization process described in the next chapter. As candidate jet the one of the two highest $p_t$ jets passing the -softdropmass window is used. If both of them pass, the one with higher $p_t$ is chosen. +soft-drop mass window is used. If both of them pass, the one with higher $p_t$ is chosen. ## DeepAK8 @@ -686,7 +708,7 @@ comparision of background and signal efficiency of the DeepAK8 tagger, with, bet used in this analysis. ![Comparison of tagger efficiencies, showing, between others, the DeepAK8 and $\tau_{21}$ tagger used in this analysis. -Taken from [@DEEP_BOOSTED]](./figures/deep_ak8.pdf){#fig:ak8_eff width=80%} +Taken from [@DEEP_BOOSTED]](./figures/deep_ak8.pdf){#fig:ak8_eff width=60%} The DNN has two input lists for each jet. The first is a list of up to 100 constituent particles of the jet, sorted by decreasing $p_t$. A total of 42 properties of the particles such es $p_t$, energy deposit, charge and the @@ -701,7 +723,7 @@ In this thesis, the mass decorrelated version of the DeepAK8 tagger is used. It that is trained to quantify how strongly the output of the non-decorrelated tagger is correlated to the mass of a particle. Its output is fed back to the network as a penalty so it avoids using features of the particles correlated to their mass. The result is a largely mass decorrelated tagger of heavy resonances. -As the mass variable is already in use for the softdropmass selection, this version of the tagger is to be preferred. +As the mass variable is already in use for the soft-drop mass selection, this version of the tagger is to be preferred. The higher the discriminator value of the deep boosted tagger, the more likely is the jet to be caused by decay of a vector boson. Therefore, using the same way to choose a candidate jet as for the N-subjettiness tagger, a selection is @@ -751,14 +773,19 @@ the deep boosted tagger the opposite cut from the high purity category is used: 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 -for all masspoints of the decay to qW and qZ and for both datasets used, the one from 2016 und the combined one of 2016, -2017 and 2018. +for all masspoints of the decay to qW and qZ and for both datasets used, the one from 2016 und the combined one of years +2016, 2017 and 2018. -To extract the signal from the background, its cross section limit is calculated using a frequentist asymptotic limit -calculator. It performs a shape analysis of the dijet invariant mass spectrum to determine an expected and an observed -limit. If there's no resonance of the q\* particle in the data, the observed limit should lie within the $2\sigma$ -environment of the expected limit. After that, the crossing of the theory line, representing the cross section limits -expected, if the q\* particle would exist, and the observed data is calculated, to have a limit of mass up to which the +To test for the presence of a resonance in the data, the cross section limits of the signal event are calculated using a +frequentist asymptotic limit calculator described in [@ASYMPTOTIC_LIMIT]. Using the parameters and signal rate obtained +using the method described in [@sec:moa] as well as a shape analysis on the data recorded by the CMS, it determines an +expected and an observed cross section limit by doing a signal + background versus background-only hypothesis test. It +also calculates upper and lower limits of the expected cross section corresponding to a confidence level of 95 %. + +If there's no resonance of the q\* particle in the data, the observed limit should lie within the $2\sigma$ environment, +meaning a 95 % confidence level, of the expected limit. This observed limit is plotted together with a theory line, +representing the cross section limits expected, if the q\* predicted by [@QSTAR_THEORY] would exist. +The crossing of the theory line with the observed limit is then calculated, to have a limit of mass up to which the existence of the q\* particle can be excluded. To find the uncertainty of this result, the crossing of the theory line plus, respectively minus, its uncertainty with the observed limit is also calculated. diff --git a/thesis.pdf b/thesis.pdf index 6f5b36a..a9ba0a6 100644 Binary files a/thesis.pdf and b/thesis.pdf differ diff --git a/thesis.tex b/thesis.tex index fabdcc1..7a5a3df 100644 --- a/thesis.tex +++ b/thesis.tex @@ -77,6 +77,7 @@ \usepackage{siunitx} \usepackage{tikz-feynman} \usepackage{csquotes} +\usepackage{abstract} \pagenumbering{gobble} \setlength{\parskip}{0.5em} \bibliographystyle{lucas_unsrt} @@ -116,20 +117,43 @@ \maketitle \begin{abstract} A search for an excited quark state, called q*, is presented using data -recorded by CMS during the years 2016, 2017 and 2018. By analysing its -decay channels to qW and qZ, a minimum mass of 6.1 TeV resp. 5.5 TeV is -established. This limit is about 1 TeV higher than the limits found by a -previous research of data collected by CMS in 2016 +recorded by the CMS experiment during the years 2016, 2017 and 2018 with +a centre-of-mass energy of \(\sqrt{s} = \SI{13}{\tera\eV}\) and a total +integrated luminosity of \(\SI{137.19}{\per\femto\barn}\). By analysing +its decay channels to q + W and q + Z that further decay to +\(q + q\bar{q}\), resulting in two jets in the final state, the q* can +be excluded up to a mass of 6.1 (qW) TeV resp. 5.5 TeV (qZ) with a +confidence level of 95 \%. This limit is about 1 TeV higher than the +limits found by a previous research of data collected by CMS in 2016 \autocite{PREV_RESEARCH}, excluding the q* particle up to a mass of 5.0 TeV resp. 4.7 TeV. Also a comparison of the new DeepAK8 \autocite{DEEP_BOOSTED} and the older N-subjettiness \autocite{TAU21} -tagger is conducted, showing that the newer DeepAK8 tagger is currently -approximately at the same level as the N-subjettiness tagger, but has -the potential to further improve in performance. +tagger is conducted, showing that the newer DeepAK8 tagger, based on a +deep neural network, is currently approximately at the same level as the +N-subjettiness tagger, but has the potential to further improve in +performance, between others because of an improved training that was +just published. \end{abstract} +\renewcommand{\abstractname}{Zusammenfassung} \begin{abstract} -Abstract 2. + +In dieser Arbeit wird eine Suche nach angeregten Quarkzuständen, genannt +q*, durchgeführt. Dafür werden Daten mit einer gesamten integrierten +Luminosität von \(\SI{137.19}{\per\femto\barn}\) analysiert, welche über +die Jahre 2016, 2017 und 2018 bei einer Schwerpunktsenergie von +\(\sqrt{s} = \SI{13}{\tera\eV}\) vom CMS Experiment aufgenommen wurden. +Indem der Zerfall des q* Teilchens zu q + W und q + Z untersucht wird, +kann dieses mit einem Konfidenzniveau von 95 \% bis zu einer Masse von +6.1 TeV (qW) bzw. 5.5 TeV (qZ) ausgeschlossen werden. Dieses Limit liegt +etwa 1 TeV höher, als das von vorhergegangener Forschung +\autocite{PREV_RESEARCH} gesetzte von 5.0 TeV bzw. 4.7 TeV. Dabei wird +der neue DeepAK8 Tagger \autocite{DEEP_BOOSTED}, welcher auf einem +neuronalen Netzwerk basiert, mit dem älteren N-Subjetiness Tagger +\autocite{TAU21} verglichen. Das Endergebnis der beiden Tagger +unterscheidet sich kaum, jedoch gibt es beim DeepAK8 Tagger noch +potential zur Verbesserung, unter anderem durch ein verbessertes +Traininig, welches vor kurzem veröffentlicht wurde. \end{abstract} { @@ -490,6 +514,8 @@ due to the crossing angle at the interaction point: \begin{equation} To quantify the amount of data collected by one of the experiments at LHC, the integrated luminosity is introduced as \(L_{int} = \int L dt\). +explain pdf -\textgreater{} not all 13 TeV available for collision + \hypertarget{compact-muon-solenoid}{% \subsection{Compact Muon Solenoid}\label{compact-muon-solenoid}} @@ -654,7 +680,7 @@ fig.~\ref{fig:antiktcomparison}. For this analysis, a radius of 0.8 is used. Furthermore, to approximate the mass of a heavy particle that caused a -jet, the softdropmass can be used. It is calculated by removing wide +jet, the soft-drop mass can be used. It is calculated by removing wide angle soft particles from the jet to counter the effects of contamination from initial state radiation, underlying event and multiple hadron scattering. It therefore is more accurate in determining @@ -765,15 +791,19 @@ A gaussian and a poisson function have also been studied but found to be not able to reproduce the signal shape as they couldn't model the tails on both sides of the peak. -An example of a fit of these functions to a toy dataset with gaussian -errors can be seen in fig.~\ref{fig:cb_fit}. In this 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. +A linear combination of the signal and background function is then +fitted to a toy dataset with gaussian errors and a simulated signal +cross section of \(\SI{1}{\per\pico\barn}\). The resulting coefficients +of said combination then show the expected signal rate for the simulated +cross section. An example of such a fit can be seen in +fig.~\ref{fig:cb_fit}. In this 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. \begin{figure} \hypertarget{fig:cb_fit}{% @@ -795,9 +825,9 @@ To reduce the background and increase the signal sensitivity, a selection of events by different variables is introduced. It is divided into two stages. The first one (the preselection) adds some general physics motivated selection using kinematic variables and is also used -to make sure a good trigger efficiency is achieved. In the second part, -different taggers will be used as a discriminator between QCD background -and signal events. After the preselection, it is made sure, that the +to ensure a high trigger efficiency. In the second part, different +taggers will be used as a discriminator between QCD background and +signal events. After the preselection, it is made sure, that the simulated samples represent the real data well by comparing the data with the simulation in the signal as well as a sideband region, where no signal events are expected. @@ -814,14 +844,14 @@ an angular separation smaller than 0.8 from any electron or muon are discarded to allow future use of the results in studies of the semi or all-leptonic decay channels. -From a decaying q* particle, we expect two jets in the endstate. The -dijet invariant mass of those two jets will be used to reconstruct the -mass of the q* particle. Therefore a cut is added to have at least 2 -jets. More jets are also possible, for example caused by gluon radiation -of a quark causing another jet. If this is the case, the two jets with -the highest \(p_t\) are used for the reconstruction of the q* mass. The -distributions of the number of jets before and after the selection can -be seen in fig.~\ref{fig:njets}. +From a decaying q* particle, two jets are expected in the final state. +The dijet invariant mass of those two jets will be used to reconstruct +the mass of the q* particle. Therefore a cut is added to have at least 2 +jets, accounting for the possibility of more jets, for example caused by +gluon radiation of a quark or other QCD effects. 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.~\ref{fig:njets}. \begin{figure} \begin{minipage}{0.5\textwidth} @@ -836,25 +866,25 @@ be seen in fig.~\ref{fig:njets}. \begin{minipage}{0.5\textwidth} \includegraphics{./figures/combined/v1_Njet_N_jets_stack.eps} \end{minipage} -\caption{Number of jet distribution showing the cut at number of jets $\ge$ 2. Left: distribution before the cut. Right: +\caption{Comparison of the number of jet distribution before and after the cut at number of jets $\ge$ 2. Left: +distribution before the cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018. The signal curves are amplified by a factor of 10,000, to be visible.} \label{fig:njets} \end{figure} The next selection is done using \(\Delta\eta = |\eta_1 - \eta_2|\), -with \(\eta_1\) and \(\eta_2\) being the \(\eta\) of the first two jets -in regards to their transverse momentum. The q* particle is expected to -be very heavy in regards to the center of mass energy of the collision -and will therefore be almost stationary. Its decay products should -therefore be close to back to back, which means the \(\Delta\eta\) -distribution is expected to peak at 0. At the same time, particles -originating from QCD effects are expected to have a higher -\(\Delta\eta\) as they mainly form from less heavy resonances. To -maintain comparability, the same selection as in previous research of -\(\Delta\eta \le 1.3\) is used. A comparison of the \(\Delta\eta\) -distribution before and after the selection can be seen in -fig.~\ref{fig:deta}. +with \(\eta_1\) and \(\eta_2\) being the \(\eta\) of the two jets with +the highest transverse momentum. The q* particle is expected to be very +heavy in regards to the center of mass energy of the collision and will +therefore be almost stationary. Its decay products should therefore be +close to back to back, which means the \(\Delta\eta\) distribution is +expected to peak at 0. At the same time, particles originating from QCD +effects are expected to have a higher \(\Delta\eta\) as they mainly form +from less heavy resonances. To maintain comparability, the same +selection as in previous research of \(\Delta\eta \le 1.3\) is used. A +comparison of the \(\Delta\eta\) distribution before and after the +selection can be seen in fig.~\ref{fig:deta}. \begin{figure} \begin{minipage}{0.5\textwidth} @@ -869,16 +899,19 @@ fig.~\ref{fig:deta}. \begin{minipage}{0.5\textwidth} \includegraphics{./figures/combined/v1_Eta_deta_stack.eps} \end{minipage} -\caption{$\Delta\eta$ distribution showing the cut at $\Delta\eta \le 1.3$. Left: distribution before the cut. Right: -distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018. The signal curves -are amplified by a factor of 10,000, to be visible.} +\caption{Comparison of the $\Delta\eta$ distribution before and after the cut at $\Delta\eta \le 1.3$. Left: +distribution before the cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from +2016, 2017 and 2018. The signal curves are amplified by a factor of 10,000, to be visible.} \label{fig:deta} \end{figure} The last selection in the preselection is on the dijet invariant mass: -\(m_{jj} \ge \SI{1050}{\giga\eV}\). It is important for a high trigger -efficiency and can be seen in fig.~\ref{fig:invmass}. Also, it has a -huge impact on the background because it usually consists of way lighter +\(m_{jj} \ge \SI{1050}{\giga\eV}\). It is important for a trigger +efficiency higher than 99 \% with a soft-drop mass cut of +\(m_{SDM} > \SI{65}{\giga\eV}\) applied to the jet with the highest +transverse momentum. A comparison of its distribution before and after +the selection can be seen in fig.~\ref{fig:invmass}. Also, it has a huge +impact on the background because it usually consists of way lighter particles. The q* on the other hand is expected to have a very high invariant mass of more than 1 TeV. The \(m_{jj}\) distribution should be a smoothly falling function for the QCD background and peak at the @@ -897,8 +930,8 @@ simulated resonance mass for the signal events. \begin{minipage}{0.5\textwidth} \includegraphics{./figures/combined/v1_invmass_invMass_stack.eps} \end{minipage} -\caption{Invariant mass distribution showing the cut at $m_{jj} \ge \SI{1050}{\giga\eV}$. It shows the expected smooth -falling functions of the background whereas the signal peaks at the simulated resonance mass. +\caption{Comparison of the invariant mass distribution before and after the cut at $m_{jj} \ge \SI{1050}{\giga\eV}$. It +shows the expected smooth falling functions of the background whereas the signal peaks at the simulated resonance mass. Left: distribution before the cut. Right: distribution after the cut. 1st row: data from 2016. 2nd row: combined data from 2016, 2017 and 2018.} \label{fig:invmass} @@ -914,22 +947,21 @@ and 56 \% (7 TeV) are reached, wheres the efficiencies when decaying to qZ are in the range of 46 \% (1.6 TeV) to 50 \% (7 TeV). Here, the background could be reduced to 8 \% of the original events. So while keeping around 50 \% of the signal, the background was already reduced -to less than a tenth. Still, as can be seen in fig.~\ref{fig:njets} to -fig.~\ref{fig:invmass}, the amount of signal is very low. +to less than a tenth. \hypertarget{data---monte-carlo-comparison}{% \subsection{Data - Monte Carlo Comparison}\label{data---monte-carlo-comparison}} To ensure high data quality, the simulated QCD background sample is now -being compared to the actual data of the corresponding year collected by -the CMS detector. This is done for the year 2016 and for the combined -data of years 2016, 2017 and 2018. The distributions are rescaled so the +being compared to the data of the corresponding year collected by the +CMS detector. This is done for the year 2016 and for the combined data +of years 2016, 2017 and 2018. The distributions are rescaled so the integral over the invariant mass distribution of data and simulation are the same. In fig.~\ref{fig:data-mc}, the three distributions of the variables that were used for the preselection can be seen for year 2016 -and the combined data of years 2016 to 2018. For analysing the real data -from the CMS, jet energy corrections have to be applied. Those are to +and the combined data of years 2016 to 2018. For analysing the 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 @@ -970,12 +1002,12 @@ simulation. The sideband is introduced to make sure no bias in the data and Monte Carlo simulation is introduced. It is a region in which no signal event is expected. Again, data and the Monte Carlo simulation are compared. -For this analysis, the region where the softdropmass of both of the two -jets with the highest transverse momentum (\(p_t\)) is more than 105 GeV -was chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, the -heavier vector boson. Therefore it is very unlikely that a particle +For this analysis, the region where the soft-drop mass of both of the +two jets with the highest transverse momentum (\(p_t\)) is more than 105 +GeV was chosen. 105 GeV is well above the mass of 91 GeV of the Z boson, +the heavier vector boson. Therefore it is very unlikely that a particle heavier than t In fig.~\ref{fig:sideband}, the comparison of data with -simulation in the sideband region can be seen for the softdropmass +simulation in the sideband region can be seen for the soft-drop mass 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 @@ -1005,19 +1037,19 @@ combined data from 2016, 2017 and 2018.} \hypertarget{jet-substructure-selection}{% \section{Jet substructure selection}\label{jet-substructure-selection}} -So far it was made sure, that the actual data and the simulation are in -good agreement after the preselection and no unwanted side effects are -introduced in the data by the used cuts. Now another selection has to be -introduced, to further reduce the background to be able to extract the -hypothetical signal events from the actual data. +So far it was made sure, that the data collected by the CMS and the +simulation are in good agreement after the preselection and no unwanted +side effects are introduced in the data by the used cuts. Now another +selection has to be introduced, to further reduce the background to be +able to look for the hypothetical signal events in the data. This is done by distinguishing between QCD and signal events using a tagger to identify jets coming from a vector boson. Two different taggers will be used to later compare their performance. The decay analysed includes either a W or Z boson, which are, compared to the particles in QCD effects, very heavy. This can be used by adding a cut -on the softdropmass of a jet. The softdropmass of at least one of the -two leading jets is expected to be within \(\SI{35}{\giga\eV}\) and +on the soft-drop mass of a jet. The soft-drop mass of at least one of +the two leading jets is expected to be within \(\SI{35}{\giga\eV}\) and \(\SI{105}{\giga\eV}\). This cut already provides a good separation of QCD and signal events, on which the two taggers presented next can build. @@ -1057,7 +1089,7 @@ decay of a vector boson. Therefore a selection will be introduced, so that \(\tau_{21}\) of one candidate jet is smaller then some value that will be determined by an optimization process described in the next chapter. As candidate jet the one of the two highest \(p_t\) jets -passing the softdropmass window is used. If both of them pass, the one +passing the soft-drop mass window is used. If both of them pass, the one with higher \(p_t\) is chosen. \hypertarget{deepak8}{% @@ -1075,7 +1107,7 @@ efficiency of the DeepAK8 tagger, with, between others, the \begin{figure} \hypertarget{fig:ak8_eff}{% \centering -\includegraphics[width=0.8\textwidth,height=\textheight]{./figures/deep_ak8.pdf} +\includegraphics[width=0.6\textwidth,height=\textheight]{./figures/deep_ak8.pdf} \caption{Comparison of tagger efficiencies, showing, between others, the DeepAK8 and \(\tau_{21}\) tagger used in this analysis. Taken from \autocite{DEEP_BOOSTED}}\label{fig:ak8_eff} @@ -1103,7 +1135,7 @@ correlated to the mass of a particle. Its output is fed back to the network as a penalty so it avoids using features of the particles correlated to their mass. The result is a largely mass decorrelated tagger of heavy resonances. As the mass variable is already in use for -the softdropmass selection, this version of the tagger is to be +the soft-drop mass selection, this version of the tagger is to be preferred. The higher the discriminator value of the deep boosted tagger, the more @@ -1175,20 +1207,28 @@ 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.~\ref{sec:moa} is performed for all masspoints of the decay to qW and qZ and for both datasets used, the one from 2016 und the combined -one of 2016, 2017 and 2018. +one of years 2016, 2017 and 2018. -To extract the signal from the background, its cross section limit is -calculated using a frequentist asymptotic limit calculator. It performs -a shape analysis of the dijet invariant mass spectrum to determine an -expected and an observed limit. If there's no resonance of the q* -particle in the data, the observed limit should lie within the -\(2\sigma\) environment of the expected limit. After that, the crossing -of the theory line, representing the cross section limits expected, if -the q* particle would exist, and the observed data is calculated, to -have a limit of mass up to which the existence of the q* particle can be -excluded. To find the uncertainty of this result, the crossing of the -theory line plus, respectively minus, its uncertainty with the observed -limit is also calculated. +To test for the presence of a resonance in the data, the cross section +limits of the signal event are calculated using a frequentist asymptotic +limit calculator described in \autocite{ASYMPTOTIC_LIMIT}. Using the +parameters and signal rate obtained using the method described in +sec.~\ref{sec:moa} as well as a shape analysis on the data recorded by +the CMS, it determines an expected and an observed cross section limit +by doing a signal + background versus background-only hypothesis test. +It also calculates upper and lower limits of the expected cross section +corresponding to a confidence level of 95 \%. + +If there's no resonance of the q* particle in the data, the observed +limit should lie within the \(2\sigma\) environment, meaning a 95 \% +confidence level, of the expected limit. This observed limit is plotted +together with a theory line, representing the cross section limits +expected, if the q* predicted by \autocite{QSTAR_THEORY} would exist. +The crossing of the theory line with the observed limit is then +calculated, to have a limit of mass up to which the existence of the q* +particle can be excluded. To find the uncertainty of this result, the +crossing of the theory line plus, respectively minus, its uncertainty +with the observed limit is also calculated. \hypertarget{uncertainties}{% \subsection{Uncertainties}\label{uncertainties}} diff --git a/thesis.toc b/thesis.toc index 74934ce..2cde5ea 100644 --- a/thesis.toc +++ b/thesis.toc @@ -34,5 +34,5 @@ \contentsline {subsection}{\numberline {8.1}2016}{24}{subsection.8.1}% \contentsline {subsubsection}{\numberline {8.1.1}Previous research}{24}{subsubsection.8.1.1}% \contentsline {subsection}{\numberline {8.2}Combined dataset}{26}{subsection.8.2}% -\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{28}{subsection.8.3}% -\contentsline {section}{\numberline {9}Summary}{30}{section.9}% +\contentsline {subsection}{\numberline {8.3}Comparison of taggers}{27}{subsection.8.3}% +\contentsline {section}{\numberline {9}Summary}{29}{section.9}%