Study of Inclusive Jet Production and Jet Shapes in proton-proton collisions at s = 7 TeV using the ATLAS Detector 1

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1 axiv:.4497v [hep-ex] 22 Oct 20 Study of Inclusive Jet Poduction and Jet Shapes in poton-poton collisions at s = 7 ev using the ALAS Detecto Fancesc Vives Vaqué Institut de Física d Altes Enegies Univesitat Autònoma de Bacelona Depatament de Física Edifici Cn, Campus UAB E-0893 Bellatea (Bacelona) Bacelona, July 20 supevised by Pof. Maio Matínez Péez ICREA / Institut de Física d Altes Enegies / Univesitat Autònoma de Bacelona Ph.D. Dissetation

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3 he studies pesented in this thesis ae pat of the following publications: he ALAS Collaboation, Study of shapes in inclusive poduction in pp collisions at s = 7 ev using the ALAS detecto, Physical Review D 83, (20) he ALAS Collaboation, Measuement of inclusive and di coss sections in poton-poton collisions at 7 ev cente-of-mass enegy with the ALAS detecto, Euopean Physical Jounal C7 52 (20) and of the following public ALAS notes: he ALAS Collaboation, Jet Shapes in ALAS and Monte Calo modeling, AL-PUB (20) he ALAS Collaboation, Measuement of inclusive and di coss sections in poton-poton collision data at 7 ev cente-of-mass enegy using the ALAS detecto, ALAS-CONF (20) he ALAS Collaboation, Popeties and intenal stuctue of s poduced in soft poton-poton collisions at s = 900 GeV, ALAS-CONF (200)

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5 Acknowledgments Fist of all, I would like to thank my supeviso Maio Matínez. His boad knowledge of physics, involvement in the analysis I was pefoming and love fo igoous wok have played a cucial ole in this thesis. I am gateful to Enique Fénandez, Matteo Cavalli and Matine Bosman, who welcomed me at IFAE, and fom whom I admie thei passion fo physics. I also want to thank the ALAS collaboation. In paticula, I want to mention Fabiola Gianotti, the spokespeson, Kevin Einsweile and Jon Buttewoth, the Standad Model goup convenes, and ancedi Cali and Richad eusche, convenes of the Jet/EtMiss goup. Istated the shapes analysis with Monica D Onofio. Iwould like to thank he fo this collaboation, but mainly fo he multiple advises and fiendship. Othe postdocs have helped me duing my Ph.D., and I am gateful to all of them: Bilge Demiköz, with whom I analyzed the fist ALAS data, Chistophe Ochando, Ilya Koolkov, Luca Fioini and Sebastian Ginstein. Estel, Evelin and Valeio have been excellent office-mates, and actually moe thanthat. Justtoputanexample, theyweethefistfiendstovisitmydaughte Gemma when she was bon! I also want to thank my othe colleagues at IFAE, in paticula Machi, Jodi and Volke. I am gateful to Juan and Sonia, fo thei encouagement duing the Ph.D., and to all my fiends woking at CERN: Ila, Peppe, Alessio, Ciccio, Simone, Lidia, Delo, Paola... Finally, I want to thank the most impotant people in my life: my family. I want to paticulaly mention my wife, Maia Laua, not only fo moving to life with me close to CERN, but mainly fo he daily suppot.

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7 Contents Contents List of Figues List of ables vi xviii Intoduction QCD at Hadon Collides 3. he Standad Model Quantum Chomodynamics heoy Deep inelastic scatteing Petubative QCD he factoization theoem Paton Distibution Functions Uncetainties Monte Calo simulation Paton Showe Hadonization Undelying Event Monte Calo Geneato Pogams Jet Algoithms Cone algoithms Sequential ecombination algoithms he ALAS Detecto at the Lage Hadon Collide 2 2. he Lage Hadon Collide he ALAS expeiment Inne Detecto Caloimetes ii

8 Contents 2.4. Liquid Agon Caloimete Hadonic caloimetes Caloimete opological Clustes Muon System Luminosity measuement igge Inclusive Jet Coss Section 3 3. Monte Calo simulation Jet econstuction and calibation Jet and event selection Unfolding to the paticle level Systematic Uncetainties JES uncetainty Othe souces of systematic uncetainties Results Jet Shapes Jet shape definition Event selection Monte Calo simulation Jet shapes at caloimete level Coection fo detecto effects Systematic uncetainties Coss-checks using othe detecto objects Results Jet Shapes in ALAS and Monte Calo modeling 0 5. Monte Calo samples Results Compaison with PYHIA Compaison with Hewig++ and HERWIG/JIMMY Compaison with ALPGEN and Shepa Compaison with POWHEG χ 2 statistical tests Conclusions 29 iii

9 Contents A Sensitivity of the shapes to the undelying event and to the pile-up using MC simulated events 3 B Jet shapes and enegy flow in pp collisions at s = 900 GeV 39 B. Event Selection and Monte Calo Simulation B.. Jet Shapes using Caloimete owes B..2 Jet Shapes using acks B.2 Enegy Flow B.2. Enegy flow in the azimuthal diection B.2.2 Enegy Flow in apidity B.2.3 Enegy Pofiles beyond the cone of the C Enegy Flow 59 Bibliogaphy 63 iv

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11 List of Figues List of Figues. Summay of measuements of α s as a function of the enegy scale Q 5.2 Electon scatteing fom a poton Electon-poton deep inelastic scatteing Example of PDFs of the valence quaks of the poton, the gluon, and the sea quaks as a function of x Diagams at LO of the diffeent paton inteactions StuctuefunctionF 2 ofthepotonasmeasuedbyzeus,bcdms, E665 and NMC expeiments Leading ode diagams fo 2 2 paton inteactions PDF of the gluon as a function of x accoding to diffeent PDF goups at q 2 = 2 GeV Illustation of the paton showe fom the outgoing patons of the had inteaction A sample paton-level event clusteed with the algoithm Maximum instantaneous and integated luminosity vesus day deliveed by the LHC View of the full ALAS detecto View of the caloimete system Sketch of a module of the LA caloimete Bael and extended bael sections of the ile Caloimete Kinematic ange of the inclusive coss section measuements Jet enegy esponse at the EM scale as a function of the η det Aveage JES coection as a function of calibated p Jet offset at the EM scale shown as a function of pseudoapidity and the numbe of econstucted pimay vetices Efficiency fo identification as a function of p vi

12 List of Figues 3.6 Jet tigge efficiency as a function of econstucted p Factional JES uncetainty as a function of p Relative pile-up uncetainty in the case of two measued pimay vetices Inclusive coss section as a function of p in diffeent egions of y Ratio of the inclusive coss section as a function of p in diffeent egions of y of the data to the theoetical pedictions Ratio of the inclusive coss section as a function of p in diffeent egions of y of the data to the theoetical pedictions (inclusion of esults with othe PDFs) Ratio of the inclusive coss section as a function of p in diffeent egions of y of the data to the theoetical pedictions (inclusion of Powheg esults) he measued diffeential shape using caloimete clustes fo s with y < 2.8 and 30 GeV < p < 20 GeV he measued diffeential shape using caloimete clustes fo s with y < 2.8 and 20 GeV < p < 600 GeV he measued integated shape using caloimete clustes fo s with y < 2.8 and 30 GeV < p < 20 GeV he measued integated shape using caloimete clustes fo s with y < 2.8 and 20 GeV < p < 600 GeV Coection factos applied to the measued diffeential shapes to coect the measuements fo detecto effects fo s with y < 2.8 and 30 GeV < p < 20 GeV Coection factos applied to the measued diffeential shapes to coect the measuements fo detecto effects fo s with y < 2.8 and 20 GeV < p < 600 GeV Coection factos applied to the measued integated shapes to coect the measuements fo detecto effects fo s with y < 2.8 and 30 GeV < p < 20 GeV Coection factos applied to the measued integated shapes to coect the measuements fo detecto effects fo s with y < 2.8 and 20 GeV < p < 600 GeV vii

13 List of Figues 4.9 Systematic uncetainty on the diffeential shape elated to the absolute enegy scale uncetainties on clustes and s, fo s with y < 2.8 and 30 GeV < p < 20 GeV Systematic uncetainty on the diffeential shape elated to the absolute enegy scale uncetainties on clustes and s, fo s with y < 2.8 and 20 GeV < p < 600 GeV Systematic uncetainty on the diffeential shape elated to the caloimete showeing model, fo s with y < 2.8 and 30 GeV < p < 20 GeV Systematic uncetainty on the diffeential shape elated to the caloimete showeing model, fo s with y < 2.8 and 20 GeV < p < 600 GeV Systematic uncetainty on the diffeential shape elated to the p esolution, fo s with y < 2.8 and 30 GeV < p < 20 GeV Systematic uncetainty on the diffeential shape elated to the p esolution, fo s with y < 2.8 and 20 GeV < p < 600 GeV Systematic uncetainty on the diffeential shape elated to the coection fo detecto effects with diffeent physics models assumptions, fo s with y < 2.8 and 30 GeV < p < 20 GeV Systematic uncetainty on the diffeential shape elated to the coection fo detecto effects with diffeent physics models assumptions, fo s with y < 2.8 and 20 GeV < p < 600 GeV Systematic uncetainty on the diffeential shape elated to the nonclosue of the coection fo detecto effects pocedue, fo s with y < 2.8 and 30 GeV < p < 20 GeV Systematic uncetainty on the diffeential shape elated to the nonclosue of the coection fo detecto effects pocedue, fo s with y < 2.8 and 20 GeV < p < 600 GeV Summay of systematic uncetainties fo the diffeential shape measuements fo s with y < 2.8 and 30 GeV < p < 20 GeV Summay of systematic uncetainties fo the diffeential shape measuements fo s with y < 2.8 and 20 GeV < p < 600 GeV Summay of systematic uncetainties fo the integated shape measuements fo s with y < 2.8 and 30 GeV < p < 20 GeV Summay of systematic uncetainties fo the integated shape measuements fo s with y < 2.8 and 20 GeV < p < 600 GeV viii

14 List of Figues 4.23 Measued diffeential shapes using tacks inside s fo s with y <.9 and 30 GeV < p < 20 GeV Measued diffeential shapes using caloimete clustes fo s with y <.9 and 30 GeV < p < 20 GeV Double-atio of the diffeential shapes deived by compaing caloimete and tacking atios of esults in data and Monte Calo simulations fo s with y <.9 and 30 GeV < p < 20 GeV Compaison of diffeential shapes with caloimete clustes and topo-towes befoe coecting fo detecto effects fo s with y <.9 and 30 GeV < p < 20 GeV Compaison of diffeential shapes with caloimete clustes and topo-towes afte coecting fo detecto effects fo s with y <.9 and 30 GeV < p < 20 GeV he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 30 GeV < p < 0 GeV he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 0 GeV < p < 30 GeV he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 30 GeV < p < 600 GeV he measued integated shape, Ψ(), in inclusive poduction fo s with y < 2.8 and 30 GeV < p < 0 GeV he measued integated shape, Ψ(), in inclusive poduction fo s with y < 2.8 and 0 GeV < p < 30 GeV he measued integated shape, Ψ(), in inclusive poduction fo s with y < 2.8 and 30 GeV < p < 600 GeV he measued integated shape, Ψ( = 0.3), as a function of p fo s with y < 2.8 and 30 GeV < p < 600 GeV he measued integated shape, Ψ( = 0.3), as a function of y fo s with y < 2.8 and 30 GeV < p < 20 GeV in diffeent y bins he measued integated shape, Ψ( = 0.3), as a function of y fo s with y < 2.8 and 20 GeV < p < 500 GeV in diffeent y bins he measued integated shape, Ψ( = 0.3), as a function of p fo s with y < 2.8 and 30 GeV < p < 600 GeV (compaed to a diffeent set of MCs) ix

15 List of Figues 4.38 he measued integated shape, Ψ( = 0.3), as a function of p in diffeent apidity egions fo s with y < 2.8 and 30 GeV < p < 500 GeV he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 30 GeV < p < 0 GeV is shown in diffeent p egions. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of PYHIA- Peugia20 (solid lines), PYHIA-AUE2 (dotted lines), PYHIA- AMB (dashed lines), and Pythia 8-4C (dashed-dotted lines) ae shown fo compaison he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 0 GeV < p < 30 GeV is shown in diffeent p egions. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of PYHIA- Peugia20 (solid lines), PYHIA-AUE2 (dotted lines), PYHIA- AMB (dashed lines), and Pythia 8-4C (dashed-dotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of y in diffeent p egions fo s with y < 2.8 and 30 GeV < p < 0 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of PYHIA-Peugia20 (solid lines), PYHIA-AUE2(dotted lines), PYHIA-AMB(dashed lines), and Pythia 8-4C (dashed-dotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of y in diffeent p egions fo s with y < 2.8 and 0 GeV < p < 30 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of PYHIA-Peugia20 (solid lines), PYHIA-AUE2(dotted lines), PYHIA-AMB(dashed lines), and Pythia 8-4C (dashed-dotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of p in diffeent apidity egions fo s with y < 2.8 and 30 GeV < p < 500GeV. Eobasindicatethestatistical andsystematicuncetainties added in quadatue. he pedictions of PYHIA-Peugia20 (solid lines), PYHIA-AUE2(dotted lines), PYHIA-AMB(dashed lines), and Pythia 8-4C (dashed-dotted lines) ae shown fo compaison. 09 x

16 List of Figues 5.6 he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 30 GeV < p < 0 GeV is shown in diffeent p egions. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Hewig (solid lines), Hewig bug (dotted lines), Hewig (dasheddotted lines), and HERWIG/JIMMY-AUE2 (dashed lines) ae shown fo compaison he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 0 GeV < p < 30 GeV is shown in diffeent p egions. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Hewig (solid lines), Hewig bug (dotted lines), Hewig (dasheddotted lines), and HERWIG/JIMMY-AUE2 (dashed lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of y in diffeent p egions fo s with y < 2.8 and 30 GeV < p < 0 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Hewig (solid lines), Hewig bug (dotted lines), Hewig (dasheddotted lines), and HERWIG/JIMMY-AUE2 (dashed lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of y in diffeent p egions fo s with y < 2.8 and 0 GeV < p < 30 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Hewig (solid lines), Hewig bug (dotted lines), Hewig (dasheddotted lines), and HERWIG/JIMMY-AUE2 (dashed lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of p in diffeent apidity egions fo s with y < 2.8 and 30 GeV < p < 500 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Hewig (solid lines), Hewig bug(dotted lines), Hewig (dashed-dotted lines), and HERWIG/JIMMY-AUE2 (dashed lines) ae shown fo compaison xi

17 List of Figues 5. he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 30 GeV < p < 0 GeV is shown in diffeent p egions. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Shepa.3.0 (2 2)(solid lines), Shepa.2.3 (2 2) (dotted lines), Shepa (up to 2 6) (dashed lines), and ALPGEN intefaced to PYHIA (dasheddotted lines) ae shown fo compaison he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 0 GeV < p < 30 GeV is shown in diffeent p egions. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Shepa.3.0 (2 2)(solid lines), Shepa.2.3 (2 2) (dotted lines), Shepa (up to 2 6) (dashed lines), and ALPGEN intefaced to PYHIA (dasheddotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of y in diffeent p egions fo s with y < 2.8 and 30 GeV < p < 0 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Shepa.3.0 (2 2)(solid lines), Shepa.2.3 (2 2) (dotted lines), Shepa (up to 2 6) (dashed lines), and ALPGEN intefaced to PYHIA (dasheddotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of y in diffeent p egions fo s with y < 2.8 and 0 GeV < p < 30 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Shepa.3.0 (2 2)(solid lines), Shepa.2.3 (2 2) (dotted lines), Shepa (up to 2 6) (dashed lines), and ALPGEN intefaced to PYHIA (dasheddotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of p in diffeent apidity egions fo s with y < 2.8 and 30 GeV < p < 500 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of Shepa.3.0 (2 2)(solid lines), Shepa.2.3 (2 2) (dotted lines), Shepa (up to 2 6) (dashed lines), and ALPGEN intefaced to PYHIA (dasheddotted lines) ae shown fo compaison xii

18 List of Figues 5.6 he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 30 GeV < p < 0 GeV is shown in diffeent p egions. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of POWHEG intefaced with PYHIA-AMB (dashed lines), POWHEG intefaced with HERWIG/JIMMY-AUE (solid lines), PYHIA-AMB (dotted lines), and HERWIG/JIMMY-AUE (dashed-dotted lines) ae shown fo compaison he measued diffeential shape, ρ(), in inclusive poduction fo s with y < 2.8 and 0 GeV < p < 30 GeV is shown in diffeent p egions. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of POWHEG intefaced with PYHIA-AMB (dashed lines), POWHEG intefaced with HERWIG/JIMMY-AUE (solid lines), PYHIA-AMB (dotted lines), and HERWIG/JIMMY-AUE (dashed-dotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of y in diffeent p egions fo s with y < 2.8 and 30 GeV < p < 0 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of POWHEG intefaced with PYHIA-AMB (dashed lines), POWHEG intefaced with HERWIG/JIMMY-AUE (solid lines), PYHIA-AMB (dotted lines), and HERWIG/JIMMY-AUE (dashed-dotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of y in diffeent p egions fo s with y < 2.8 and 0 GeV < p < 30 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of POWHEG intefaced with PYHIA-AMB (dashed lines), POWHEG intefaced with HERWIG/JIMMY-AUE (solid lines), PYHIA-AMB (dotted lines), and HERWIG/JIMMY-AUE (dashed-dotted lines) ae shown fo compaison xiii

19 List of Figues 5.20 he measued integated shape, Ψ( = 0.3), as a function of p in diffeent apidity egions fo s with y < 2.8 and 30 GeV < p < 500 GeV. Eo bas indicate the statistical and systematic uncetainties added in quadatue. he pedictions of POWHEG intefaced with PYHIA-AMB (dashed lines), POWHEG intefaced with HERWIG/JIMMY-AUE (solid lines), PYHIA-AMB (dotted lines), and HERWIG/JIMMY-AUE (dashed-dotted lines) ae shown fo compaison he measued integated shape, Ψ( = 0.3), as a function of p foswith y < 2.8and30GeV < p < 600GeV. Eobasindicate the statistical and systematic uncetainties added in quadatue. he measuements ae compaed to the diffeent MC pedictions consideed. 25 A. Diffeential shapes fo s with 37 GeV < p < 48 GeV and 0. < η < 0.7 fo events with and without UE A.2 Diffeential shapes fo s with 48 GeV < p < 380 GeV and 0. < η < 0.7 fo events with and without UE A.3 Integated shapes fo s with 37 GeV < p < 380 GeV and 0. < η < 0.7 fo events with and without UE A.4 Diffeential shapes fo the leading with 37 GeV < p < 380 GeV and η <.2 events with (open tiangles) and without (full tiangles) pile-up A.5 Integated shapes fo the leading with 37 GeV < p < 380 GeV and η <.2 events with (open tiangles) and without (full tiangles) pile-up A.6 Ψ(0.3) fo the leading with 37 GeV < p < 380 GeV and η <.2 events with (open tiangles) and without (full tiangles) pileup B. Measued basic kinematic distibutions compaed to Monte Calo pedictions (pythia tune ALAS MC09), nomalized to the numbe of s obseved in data B.2 Measued diffeential and integated shapes using caloimete towes fo s with p > 7 GeV and y < 2.6. he data ae compaed to vaious Monte Calo simulations B.3 Measued diffeential shapes using caloimete towes fo s with p > 7 GeV as a function of y. he data ae compaed to vaious Monte Calo simulations xiv

20 List of Figues B.4 Measued integated shapes using caloimete towes fo s with p > 7 GeV as a function of y. he data ae compaed to vaious Monte Calo simulations B.5 Measued integated shapes Ψ( = 0.3) using caloimete towes fo s with p > 7 GeV as a function of y. he data ae compaed to vaious Monte Calo simulations B.6 Measued total numbe of tacks inside the befoe and afte final tack quality cuts, fo s with p > 7 GeV and y <.9. he data ae compaed to vaious Monte Calo simulations B.7 Measued diffeential shapes using tacks fo s with p > 7 GeV and y <.9. he data ae compaed to vaious Monte Calo simulations B.8 Measued diffeential shapes using tacks fo s with p > 7 GeV as a function of y. he data ae compaed to vaious Monte Calo simulations B.9 Sketch of the paticle flow as a function of the distance in azimuth to the axis B.0 Measued enegy flow using caloimete towes as a function of φ with espect to the diection. he measuements ae compaed to minimum bias Monte Calo simulations B. Measued enegy flow using caloimete towes as a function of φ with espect to the diection, in diffeent apidity egions. he measuements ae compaed to minimum bias Monte Calo simulations B.2 Measued enegy flow using tacks as a function of φ with espect to the diection. he measuements ae compaed to minimum bias Monte Calo simulations B.3 Measued enegy flow using tacks as a function of φ with espect to the diection, in diffeent apidity egions. he measuements ae compaed to minimum bias Monte Calo simulations B.4 Measued enegy flow using caloimete topotowes in di events and s with p > 7 GeV and y < 2.6, as a function of φ with espect to the diection and the apidity sepaation between the two s. he measuements ae compaed to minimum bias Monte Calo simulations xv

21 List of Figues B.5 Measued enegy flow using caloimete topotowes in di events and s with p > 7 GeV and y <.9, as a function of φ with espect to the diection and the apidity sepaation between the two s. he measuements ae compaed to minimum bias Monte Calo simulations B.6 Sketch of the paticle flow as a function of the distance in apidity to the axis B.7 Measued enegy flow using caloimete topotowes fo s with p > 7 GeV as a function of y in diffeent apidity egions. he measuements ae compaed to minimum bias Monte Calo simulations B.8 Measued enegy flow using caloimete topotowes fo s with p > 7 GeV as a function of y in diffeent apidity egions. he measuements ae compaed to minimum bias Monte Calo simulations B.9 Measued enegy flow using caloimete topotowes fo s with p > 7 GeV as a function of y in diffeent apidity egions. he measuements ae compaed to minimum bias Monte Calo simulations B.20 Sketch of the paticle flow as a function of the distance in adius to the axis B.2 Measued enegy flow using tacks fo s with p > 7 GeV as a function of fo s with y < 0.3 and y < 0.6. he measuements ae compaed to minimum bias Monte Calo simulations.. 58 C. Enegy flow using tacks as a function φ with espect to the diection fo s with y <.9 and 30 GeV < p < 20 GeV C.2 Enegy flow using caloimete clustes as a function φ with espect to the diection fo s with y <.9 and 30 GeV < p < 20 GeV. 6 C.3 Enegy flow using caloimete clustes as a function φ with espect to the diection fo s with.9 < y < 2.8 and 30 GeV < p < 20 GeV xvi

22 xvii List of Figues

23 List of ables List of ables 3. igges used in the cental egion, y < igges used in the fowad egion, 2.8 < y < Results of χ 2 tests to the data in Figues 4.38, 5.5, 5.0, 5.5, and 5.20 with espect to the diffeent MC pedictions xviii

24 xix List of ables

25 Intoduction he Standad Model (SM) is the theoy that povides the best desciption of the popeties and inteactions of elementay paticles. he stong inteaction between quaks and gluons is descibed by the Quantum Chomodynamics (QCD) field theoy. Jet poduction is the high-p pocess with the lagest coss section at hadon collides. he coss section measuement is a fundamental test of QCD and it is sensitive to the pesence of new physics. It also povides infomation on the paton distibution functions and the stong coupling. One of the fundamental elements of measuements is the pope undestanding of the enegy flow aound the coe and the validation of the QCD desciption contained in the event geneatos, such as paton showe cascades, and the fagmentation and undelying event models. Jet shapes obsevables ae sensitive to these phenomena and thus vey adequate to this pupose. he fist measuement of the inclusive coss section in pp collisions at s = 7 ev deliveed by the LHC was done using an integated luminosity of 7 nb ecoded by the ALAS expeiment. he measuement was pefomed fo s with p > 60 GeV and y < 2.8, econstucted with the algoithm with adius paametes R = 0.4 and R = 0.6. his Ph.D. hesis pesents the updated measuement of the inclusive coss section using the full 200 data set, coesponding to 37 pb collected by ALAS. Jets with p > 20 GeV and y < 4.4 ae consideed in this analysis. he measuement of the shapes using the fist 3 pb is also pesented, fo s with p > 30 GeV and y < 2.8. Both measuements ae unfolded back to the paticle level. he inclusive coss section measuement is compaed to NLO pedictions coected fo non-petubative effects, and to pedictions fom an event geneato that includes NLO matix elements. Jet shapes measuements ae compaed to the pedictions fom seveal LO matix elements event geneatos. he contents of this hesis ae oganized as follows: Chapte contains a

26 List of ables desciption of the stong inteaction theoy and phenomenology. he LHC collide and the ALAS expeiment ae descibed in Chapte 2. he inclusive coss section measuement is descibed in detail in Chapte 3, and the shapes measuements in Chapte 4. Additional compaison of the shapes measuement to Monte Calo event geneato pedictions ae shown in Chapte 5. hee ae two appendixes at the end of the document. he fist one contains additional shapes studies, and the second one is devoted to enegy flow studies at caloimete level. 2

27 Chapte QCD at Hadon Collides. he Standad Model he Standad Model (SM) [] is the most successful theoy descibing the popeties and inteactions (electomagnetic, weak and stong) of the elementay paticles. he SM is a gauge quantum field theoy based in the symmety goup SU(3) C SU(2) L U() Y, whee the electoweak secto is based in the SU(2) L U() Y goup, and the stong secto is based in the SU(3) C goup. Inteactions in the SM occu via the exchange of intege spin bosons. he mediatos of the electomagnetic and stong inteactions, the photon and eight gluons espectively, ae massless. he weak foce acts via the exchange of thee massive bosons, the W ± and the Z. he othe elementay paticles in the SM ae half-intege spin femions: six quaks and six leptons. Both inteact electoweakly, but only quaks feel the stong inteaction. Electons (e), muons(µ) and taus(τ) ae massive leptons and have electical chage Q = -. hei associated neutinos (ν e, ν µ, ν τ ) do not have electical chage. Quaks can be classified in up-type (u, s, t) and down-type (d,s,b) depending on thei electical chage (Q = 2/3 and Q = -/3 espectively). Fo each paticle in the SM, thee is an anti-paticle with opposite quantum numbes. he SM fomalism is witten fo massless paticles and the Higgs mechanism of spontaneous symmety beaking is poposed fo geneating non-zeo boson and femion masses. he symmety beaking equies the intoduction of a new field that leads to the existence of a new massive boson, the Higgs boson, that has still not been obseved. 3

28 Chapte. QCD at Hadon Collides.2 Quantum Chomodynamics heoy Quantum Chomodynamics (QCD) [2] is the enomalizable gauge field theoy that descibes the stong inteaction between coloed paticles in the SM. It is based in the SU(3) symmetic goup, and its lagangian eads: L QCD = 4 FA αβf αβ A + flavos q(iγ µ D µ m)q (.) whee the sum uns ove the six diffeent types of quaks, q, that have mass m. he field stength tenso, F A αβ is deived fom the gluon field AA α : F A αβ = [ αa A β βa A α gfabc A B α AC β ] (.2) f ABC ae the stuctue constants of SU(3), and the indices A, B, C un ove the eight colo degees of feedom of the gluon field. he thid tem oiginates fom the non-abelian chaacte of the SU(3) goup, and is the esponsible of the gluon self-inteaction, giving ise to tiple and quaduple gluon vetexes. his leads to a stong coupling, α s = g 2 /4π that is lage at low enegies and small at high enegies (see Figue.). wo consequences follow fom this: Confinement: he colo field potential inceases linealy with the distance, and theefoe quaks and gluons can neve be obseved as fee paticles. hey ae always inside hadons, eithe mesons (quak-antiquak) o bayons (thee quaks each with a diffeent colo). If two quaks sepaate fa enough, the field enegy inceases and new quaks ae ceated foming cololess hadons. Asymptotic feedom: At small distances the stength of the stong coupling is that low that quak and gluons behave as essentially fee. his allows to use the petubative appoach in this egime, whee α s..3 Deep inelastic scatteing he scatteing of electons fom potons, as illustated in Figue.2, has played a cucial ole in the undestanding of the poton stuctue. If the enegy of the incoming electon (E) is low enough, the poton can be consideed as a point 4

29 .3. Deep inelastic scatteing 0.5 α s (Q) 0.4 July 2009 Deep Inelastic Scatteing e + e Annihilation Heavy Quakonia QCD α s(μ Z) = 0.84 ± Q [GeV] Figue.: Summay of measuements of α s as a function of the enegy scale Q, fom [3]. chage (without stuctue). he diffeential coss section with espect to the solid angle of the scatteed electon is : ( ) 2 dσ dω = α E 2Esin 2 (θ/2) E ( cos 2 (θ/2)+ 2EE sin 4 (θ/2) M 2 ) (.3) whee α ( /37) is the fine stuctue constant, θ is the angle at which the electon is scatteed, E is the outgoing electon enegy and M the mass of the poton. E is kinematically detemined by θ. Fo highe enegies of the incoming electons, the inteaction is sensitive to the poton stuctue, and the coss section becomes: ( ) 2 dσ dω = α E 4MEsin 2 (θ/2) E [2K sin 2 (θ/2)+k 2 cos 2 (θ/2)] (.4) K and K 2 ae functions that contain infomation on the poton stuctue and should be detemined expeimentally. Given that E is kinematically detemined by θ, K and K 2 only dependent on one vaiable. he mass of the electon is neglected in all fomulas in this Section by assuming E >> m. 5

30 Chapte. QCD at Hadon Collides Figue.2: Electon scatteing fom a poton. Figue.3: Electon-poton deep inelastic scatteing. Finally, fo even highe electon enegies, the poton beaks in a multi-hadon final state as illustated in Figue.3. he coss section is then: ( ) 2 dσ de dω = α [2W 2Esin 2 sin 2 (θ/2)+w 2 cos 2 (θ/2)] (.5) (θ/2) Now p is the sum of the momenta of the hadons oiginating fom the poton, and it is not constained by p 2 = M 2. heefoe, W and W 2 ae functions of two independent vaiables, E and θ. heoetically it is moe convenient to use the Loentz-invaiant vaiables q 2 = (k k ) 2 and x = q 2 /2qp, whee p is the momenta of the incoming poton. he Paton Model descibes the poton as built out of thee point-like quaks ( valence quaks ) with spin /2, and intepets x as the faction of the poton momentum caied by the quak. Fom the idea that at high q 2 the vitual photon inteacts with a quak essentially fee, Bjoken pedicted that W and 6

31 .3. Deep inelastic scatteing W 2 depend only on x at lage q 2 (q 2 GeV): MW (q 2,x) F (x) (.6) q 2 2Mx W 2(q 2,x) F 2 (x) (.7) Accoding to the Paton Model: F (x) = Q 2 2 if i (x) (.8) i whee f i (x), called Paton Distibution Function (PDF), is the pobability that theithquakcaiesafactionofthepotonmomentumx, andq i istheelectical chage of the quak. heefoe, it is expected that x 0 i f i (x)dx = (.9) but it was found expeimentally that the esult of this integal is 0.5. he est of the poton momentum is caied by gluons. he intoduction of gluons leads to a moe complex desciption of the potons stuctue: quaks adiate gluons, and gluons poduce q q pais ( sea quaks ) o adiate othe gluons. Figue.4 shows the PDFs of the valence quaks of the poton, the gluon, and the sea quaks. he valence quaks dominate at lage x, wheeas the gluon dominates at low x. he adiation of gluons esults in a violation of the scaling behavio of F and F 2, intoducing a logaithmic dependence on q 2, which is expeimentally obseved (see Figue.6). he functional fom of the PDFs can not be pedicted fom pqcd, but it is possible to pedict thei evolution with q 2. he paton inteactions at fist ode in α s ae gluon adiation (q qg), gluon splitting (g gg) and quak pai poduction (g q q). he pobability that a paton of type p adiates a quak o gluon and becomes a paton of type p, caying faction y = x/z of the momentum of paton p (see Figue.5) is given by the splitting functions: P gg (y) = 6 [ y y + y ] y +y( y) (.0) P gq (y) = 4 +( y) 2 3 y (.) P qg (y) = 2 [y2 +( y) 2 ] (.2) 7

32 Chapte. QCD at Hadon Collides Figue.4: Example of PDFs of the valence quaks of the poton, the gluon, and the sea quaks as a function of x. Figue.5: Diagams at LO of the diffeent paton inteactions. P qq (y) = 4 +y 2 3 y (.3) he evolution of the PDFsas a function of q 2 follow the DGLAP(Dokshitze, Gibov, Lipatov, Altaelli and Paisi) equations [4]: dq i (x,q 2 ) dlog(q 2 ) = α x ( s q i (z,q 2 )P qq ( x 2π z )+g(z,q2 )P qg ( x ) dz z ) z ( x dg(x,q 2 ) dlog(q 2 ) = α s 2π i q i (z,q 2 )P gq ( x z )+g(z,q2 )P gg ( x z ) ) dz z (.4) (.5) he fist equation descibes the evolution of the quak PDF with q 2 due to 8

33 .4. Petubative QCD gluon adiation and quak pai poduction, wheeas the second equation descibes the change of the gluon PDF with q 2 due to gluon adiation and gluon splitting. he equations assume massless patons and theefoe ae only valid fo gluons and the light quaks (u, d and s). F em -log 0 x ZEUS ZEUS 96/97 Fixed aget NLO QCD Fit Q 2 (GeV 2 ) Figue.6: Stuctue function F 2 of the poton as measued by ZEUS, BCDMS, E665 and NMC expeiments..4 Petubative QCD.4. he factoization theoem he QCD factoization theoem is a cucial concept of QCD, that states that coss sections in hadon-hadon inteactions can be sepaated into a a had patonic coss section (shot-distance) component and a long-distance component, 9

34 Chapte. QCD at Hadon Collides descibed by univesal PDFs: σ(p,p2) = i,j dx dx 2 f i (x,µ 2 F)f j (x 2,µ 2 F) σ ij (x,x 2,α s (µ 2 F,µ 2 R),q 2 /µ 2 F) (.6) whee P, P 2 ae the momenta of the inteacting hadons, the sum uns ove all paton types, and σ ij is the patonic coss section of the incoming patons with hadon momenta faction x, x 2. µ R is the scale at which the enomalization is pefomed, and µ F is an abitay paamete that sepaates the had fom the soft component. Both scales ae typically chosen to be of the ode of q 2. Patonic coss sections in leading ode (LO) calculations fo poduction ae O(αs 2 ), since they ae based on 2 2 paton inteactions (gg gg,qg qg,qq qq), as shown in Figue.7. he dominant pocess is the gg scatteing because of the lage colo chage of the gluons. Next-to-leading-ode(NLO) diagams include contibutions fom gluon initialo final-state adiation and loops on the diagams aleady shown. he patonic coss sections at NLO educe the dependence on the nomalization and factoization scales, and ae calculable using pogams such as JERAD [5] and NLOJE++ [6]. Pedictions at highe odes ae not yet available due to the lage numbe of diagams involved. Figue.7: Leading ode diagams fo 2 2 paton inteactions. 0

35 .4.2 Paton Distibution Functions.4.2 Paton Distibution Functions As aleady explained, petubative QCD(pQCD) can pedict the evolution of the PDFs[7] with espect to q 2 using the DGLAP equations, but not thei functional fom. heefoe, PDFs should be extacted fom expeimental data at a given q 2 = Q 2 0. In paticula, seven functions should be detemined, one fo the gluon and the othes fo each one of the light quaks and anti-quaks. Expeimental data fom a lage vaiety of pocesses is used to constain seveal aspects of the PDFs: measuements of Dell-Yan poduction, inclusive coss sections and W-asymmety in p p collisions, and deep-inelastic e, µ o ν scatteing. ypically, specific functional foms ae postulated fo the PDFs with a set of fee paametes. hese paametes ae obtained optimizing the compaison between expeimental data and pedictions using the PDFs, fo example by minimizing a χ 2. he functional fom assumed fo seveal sets of PDFs is: f i (x,q 2 0) = x α i ( x) β i g i (x) (.7) whee α i and β i ae the fee fit paametes and g i (x) is a function that tends to a constant in the limits x 0 and x. his functional fom is motivated by counting ules [8] and Regge theoy [9], that suggest that f i (x) ( x) β i when x and f i (x) x α i when x 0 espectively. Both limits ae appoximate, and even if these theoies pedict the values of β i and α i, they ae taken as fee fit paametes when computing the PDFs. his appoach is used by thee of the PDFs used in the analyses pesented in this hesis: CEQ [0], MSW [] and HERA [2] PDFs. Fo example in the case of HERAPDFs, g i (x) is: g i (x) = +ǫ i x /2 +D i x+e i x 2 (.8) NNPDFs [3] follow a diffeent appoach, using neual netwoks as a paton paametization. Neual netwoks ae functional foms that can fit a lage vaiety of functions..4.3 Uncetainties hee ae thee main souces of uncetainties in the calculation of pqcd obsevables: he lack of knowledge of highe ode tems neglected in the calculation. It is estimated by vaying the enomalization scale, µ R, usually by a facto

36 Chapte. QCD at Hadon Collides of two with espect to the default choice. he factoization scale, µ F, is independently vaied to evaluate the sensitivity to the choice of scale whee the PDF evolution is sepaated fom the patonic coss section. he envelope of the vaiation that these changes intoduce in the obsevable is taken as a systematic uncetainty. Uncetainties on paametes of the theoy, like the α s and the heavy quak masses, that ae popagated into the obsevable. PDFs have anothe uncetainty coming fom the way the expeimental data is used to detemine the PDFs. his uncetainty is typically estimated using the Hessian method. If a 0 is the vecto of the PDF paametes whee χ 2 (a 0 ) is minimized, all paametes such that χ 2 χ 2 0 < ae consideed acceptable fits, whee is a paamete called toleance. PDF paametes ae expessed in tems of an othogonal basis, and vaiations along the positive and negative diections of each eigenvecto (a + i, a i ) such that χ 2 χ 2 0 = ae pefomed. he uncetainty in the obsevable Γ is: δγ + = max(γ(a + i ) Γ(a 0 ),Γ(a i ) Γ(a 0 ),0) 2 (.9) δγ = i i min(γ(a + i ) Γ(a 0 ),Γ(a i ) Γ(a 0 ),0) 2 (.20) whee Γ(a) is the obsevable computed using the PDFs with the paametes in vecto a. NNPDF use a Monte Calo appoach to evaluate the uncetainties, in which the pobability distibution in paamete space deives fom a sample of MC eplicas of the expeimental data. Figue.8 shows the PDF of the gluon with its uncetainties obtained following diffeent appoaches..5 Monte Calo simulation Complete pqcd calculations ae always pefomed only up to a fixed ode in α s, but the enhanced soft-gluon adiation and collinea configuations at highe odes can not be neglected. hey ae taken into account in the paton showe (PS) appoximation, that sum the leading contibutions of these topologies to all odes. Monte Calo (MC) geneato pogams include the PS appoximation, as 2

37 .5. Paton Showe Figue.8: PDF of the gluon as a function of x accoding to diffeent PDF goups at q 2 = 2 GeV 2. well as models to epoduce non-petubative effects, such as the hadonization of the patons to cololess hadons and the undelying event (UE)..5. Paton Showe he PS appoximation descibes successive paton emission fom the patons in the had inteaction, as illustated in Figue.9. he evolution of the showeing is govened by DGLAP equations.4 and.5, fom which the Sudakov fom factos [4] ae deived fo the numeical implementation of the paton showe. hese factos epesent the pobability that a paton does not banch between an initial scale (t i ) and a lowe scale (t). Once a banching occus at a scale t a, a bc, subsequent banchings ae deived fom the scales t b and t c. hey can be angle-, Q 2 - o p -odeed. In the fist case subsequent banchings have smalle opening angles than this between b and c, wheeas in the second, paton emissions ae poduced in deceasing ode of intinsic p. Successive banching stops at a cutoff scale, t 0, of the ode of Λ QCD, afte poducing a high-multiplicity patonic state. Since quak and gluons can not exist isolated, MC pogams contain models fo the hadonization of the patons into cololess hadons. 3

38 Chapte. QCD at Hadon Collides Figue.9: Illustation of the paton showe fom the outgoing patons of the had inteaction..5.2 Hadonization he hypothesis of local paton-hadon duality states that the momentum and quantum numbes of the hadons follow those of the patons. his hypothesis is the geneal guide of all hadonization models, but do not give details on the fomation of hadons, that is descibed in models with paametes that ae tuned to expeimental data. hee ae two main models of hadon poduction. he sting model [6] descibes the behavio of q q pais using sting dynamics. he field between each q q pai is epesented by a sting with unifom enegy pe unit length. As the q and the q move apat fom each othe and thus the enegy of the colo field inceases, the sting connecting the two is tightened, until it beaks into a new q q pai. If the invaiant mass of eithe of these sting pieces is lage enough, futhe beaks may occu. In the sting model, the sting beak-up pocess is assumed to poceed until only on-mass-shell hadons emain. In the simplest appoach of bayon poduction, a diquak is teated just like an odinay antiquak. A sting can beak eithe by quak-antiquak o antidiquak-diquak pai poduction, leading to thee-quak states. hee ae moe sophisticated models, but the fomation of bayons is still pooly unde- 4

39 .5.3 Undelying Event stood. he cluste model[7] is based on the confinement popety of petubative QCD, exploited to fom colo-neutal clustes. Afte the petubative paton showeing, all gluons ae split into light quak-antiquak o diquak-antidiquak pais. Colo-singlet clustes ae fomed fom the quaks and anti-quaks. he clustes thus fomed ae fagmented into two hadons. If a cluste is too light to decay into two hadons, it is taken to epesent the lightest single hadon of its flavo. Its mass is shifted to the appopiate value by an exchange of momenta with a neighboing cluste. If the cluste is too heavy, it decays into two clustes, that ae futhe fagmented into hadons..5.3 Undelying Event he UE comes fom the patons that do not paticipate in the had inteaction. hey contibute to the final state via thei colo-connection to the had inteaction, and via exta paton-paton inteactions. Its simulation is based on the eikonal model, that descibes the undelying event activity as additional uncoelated patonic scattes. he numbe of inteactions pe event < n > depends on the impact paamete b. A small b value coesponds to a lage ovelap between the two colliding hadons, and theefoe a highe pobability fo multiple inteactions. Fo a given b, the paton-paton coss section σ had is computed as a function of the tansvese momentum in the cente-of-mass fame of the scatteing pocess ˆp. Since this coss section diveges as ˆp 0 a cut-off paamete ˆp min is intoduced, whee expeimentally ˆp min 2 GeV. < n > is extacted fom the atio between the total hadon coss section σ nd and the paton-paton coss section, < n >= σ had /σ nd, and assumed to be Poisson-distibuted. he UE models ae tuned using expeimental data, such as the shapes descibed in Chaptes 4 and Monte Calo Geneato Pogams PYHIA Monte Calo he PYHIA [8] MC event geneato includes had pocesses at LO, and uses the PS model fo initial- and final-state adiation. he hadonization is pefomed using the sting model. It includes an undelying event model to descibe the inteactions between the poton emnants. 5

40 Chapte. QCD at Hadon Collides he PYHIA tunes DW [9] and Peugia200 [20] use CEQ5L PDFs, and both have been poduced using evaton data. In the fome the PS is Q 2 -odeed, wheeas in the latte it is p -odeed. In autumn 2009, the MRS LO* PDFs [2] wee used in PYHIA fo the fist time in ALAS. his equied to tune the PYHIA model paametes, esulting in the MC09 [22] tune. It was done using evaton data, mainly fom undelying event and minimum bias analyzes. he PS is p -odeed. he PYHIA-AMB [23] tune followed the MC09 one, and also uses MRS LO* PDFs and p -odeed PS. It was deived using ALAS data, in paticula chaged paticle multiplicities in pp inteactions at and 7 ev cente-of-mass enegy. HERWIG HERWIG [24] is a geneal-pupose MC event geneato fo had pocesses in paticle collides. It uses an angula-odeed paton-showe fo initial- and finalstate QCD adiation, and a cluste model to epoduce the hadonization of the patons. he Fotan vesion of HERWIG is intefaced with JIMMY [25] to simulate multiple paton-paton inteactions. HERWIG++ [26] isthe C++vesion ofherwig, that isexpected toeplace the Fotan one at a given point. he undelying event is modeled inside the pogam, that theefoe do not use JIMMY. ME + Paton Showe: Alpgen and Powheg Alpgen [27] is an event geneato of multi-paton had pocesses in hadonic collisions, that pefoms the calculation of the exact LO matix elements fo a lage set of paton-level pocesses. It uses the ALPHA algoithm [28] to compute the matix elements fo lage paton multiplicities in the final state. he advantage of this algoithm is that its complexity inceases slowe than the Feynman diagams appoach when inceasing the paticles in the final state. Powheg [29] is a MC event geneato that includes NLO matix elements. Alpgen and Powheg contain an inteface to both PYHIA and HERWIG fo the paton showeing, the hadonization and the undelying event simulation. 6

41 .6. Jet Algoithms.6 Jet Algoithms Quaks and gluons fom the had scatteing esult on a collimated flow of paticles due to paton showe and hadonization. his collimated flow of paticles is called. hee ae seveal definitions [30] with the main pupose of econstucting s with kinematics that eflect that of the initial paton. hese definitions can be classified in two main types of algoithms: cone algoithms and sequential ecombination algoithms..6. Cone algoithms ypically, conealgoithmsstatbyfomingconesofadiusrinthey φspace aound a list of seeds, that can be all paticles in the final state o those above a given enegy theshold. he cente of the cone is ecomputed fom the paticles inside by following eithe the snowmass o the fou-momentum ecombination. In the fou-momenta ecombination, the momenta is the sum of the momenta of its constituents: (E,p x,p y,p z ) = (E,p x,p y,p z ) i (.2) const. wheeas in the snowmass scheme, the is consideed massless, its tansvese enegy is the sum of the tansvese enegy of its constituents and the (η,φ) aethe aveage of the (η,φ) of the constituents weighted by its tansvese enegy: E = (η,φ) = E const. E i (.22) (η,φ) i E i (.23) const. m = 0 (.24) A cone is fomed fom the new cente and the pocess epeated until the paticles inside the cone ae no longe changed by futhe iteations. Usually the algoithm is allowed to fom ovelapping cones and then decides whethe to mege o split them depending on the faction of enegy they shae. his last step makes the cone algoithms collinea o infaed unsafe, and affects the definition of the paton-level coss section to all odes in pqcd. A algoithm is infaed safe if the addition of an exta paticle with infinitesimal enegy do not change the configuation in the final state. If the eplacement 7

42 Chapte. QCD at Hadon Collides of a paticle by two collinea paticles (which momenta sum is equal to that of the oiginal paticle) do not change the configuation in the final state, the algoithm is collinea safe. In ode to solve this, cone-based algoithms have been fomulated such that they find all stable cones though some exact pocedue, avoiding the use of seeds. hese algoithms ae vey time-consuming fom the computational point of view, which constitutes a disadvantage in high-multiplicity events such as those at the LHC..6.2 Sequential ecombination algoithms Sequential ecombination algoithms cluste paticles accoding to thei elative tansvese momentum, instead of spacial sepaation. his is motivated by the paton showe evolution as descibed in Section.5.. Fo all paticles in the final state, the algoithm computes the following distances: d ij = min(k 2p ti,k 2p tj) R2 ij R 2 (.25) d ib = k 2p ti (.26) whee k ti is the tansvese momentum of paticle i, R ij = y 2 + φ 2 between paticles i and j, R a paamete of the algoithm that appoximately contols the size of the, and p depends on the algoithm: p = fo the k t algoithm, p = 0fotheCambidge/Aachenalgoithm,andp = fothe algoithm. he distance d ib is intoduced in ode to sepaate paticles coming fom the had inteaction than those coming fom the inteaction between emnants. he smallest distance is found, and if it is d ij, paticles i and j ae combined into one single object. If instead it is d ib, paticle i is consideed a an emoved fom the list. he distances ae ecalculated with the emaining objects, and the pocess epeated until no paticle is left in the list. Jets ae defined as those objects with p above a given theshold. hese algoithms ae vey convenient, mainly because they ae infaed and collinea safe and computationally fast. In paticula, the algoithm [3] poduces s with a conical stuctue in (y, φ), as illustated in Figue.0, that facilitates dealing with pile-up. It is the default finding algoithm in the LHC expeiments. 8

43 .6.2 Sequential ecombination algoithms Figue.0: A sample paton-level event clusteed with the algoithm. 9

44 Chapte. QCD at Hadon Collides 20

45 Chapte 2 he ALAS Detecto at the Lage Hadon Collide he analyses descibed in this hesis ae pefomed using poton-poton collision data poduced by the Lage Hadon Collide (LHC) and collected by the ALAS detecto. In this Chapte, the LHC and the ALAS detecto ae descibed, giving moe emphasis to the elements that ae elevant fo the analyses. 2. he Lage Hadon Collide he LHC [32] is a supeconducting acceleato built in a cicula tunnel of 27 km in cicumfeence that is located at CERN. he tunnel is situated between 45 to 70 m undegound, and staddles the Swiss and Fench bodes on the outskits of Geneva. wo counte otating poton beams injected into the LHC fom the SPS acceleato at 450 GeV ae futhe acceleated to 3.5 ev while moving aound the LHC ing guided by magnets inside a continuous vacuum. Duing 200, the instantaneous luminosity was inceased ove time, with a maximum peak at cm 2 s, and the total integated luminosity deliveed by the LHC was of 48 pb fom which ALAS ecoded 45 pb (see Figue 2.). hee ae fou main detectos placed along the acceleato line: ALAS and CMS, that ae geneal-pupose detectos, ALICE, dedicated to heavy-ions physics, and LHCb, dedicated to B-physics. 2

46 ] Chapte 2. he ALAS Detecto at the Lage Hadon Collide s - ] cm Peak Luminosity [ ALAS Online Luminosity LHC Deliveed 32 Peak Lumi: 2. 0 cm -2 s - s = 7 ev 24/03 2/049/05 6/06 4/07 /0808/0906/0 03/ Day in otal Integated Luminosity [pb ALAS Online Luminosity LHC Deliveed ALAS Recoded - otal Deliveed: 48.9 pb - otal Recoded: 45.0 pb s = 7 ev 0 24/03 2/049/05 6/06 4/07 /0808/0906/0 03/ Day in 200 Figue 2.: Maximum instantaneous luminosity (left) and cumulative integated luminosity (ight) vesus day deliveed by the LHC and ecoded by ALAS fo pp collisions at 7 ev cente-of-mass enegy duing stable beams in he ALAS expeiment he ALAS detecto [33] is an assembly of seveal sub-detectos aanged in consecutive layes aound the beam axis, as shown in Figue 2.2. he main subdetectos ae the Inne Detecto, the Caloimetes and the Muon System, that ae descibed in the next Sections. ALAS is 46 m long, 25 m wide and 25 m high, and weights 7000 t. he ALAS coodinate system and its nomenclatue will be used epeatedly thoughout this hesis, and is thus descibed hee. he ALAS efeence system is a Catesian ight-handed coodinate system, with the nominal collision point at the oigin. he anti-clockwise beam diection defines the positive z-axis, while the positive x-axis is defined as pointing fom the collision point to the cente of the LHC ing and the positive y-axis pointing upwads. he azimuthal angle φ is measued aound the beam axis, and the pola angle θ is measued with espect to the z-axis. he pseudoapidity is defined as η = ln(tan(θ/2)). he apidity is defined as y = 0.5 ln[(e+p z )/(E p z )], whee E denotes the enegy and p z is the component of the momentum along the beam diection. he ALAS detecto was designed to optimize the seach fo the Higgs boson and a lage vaiety of physics phenomena at the ev scale poposed by models beyond the Standad Model. he main equiements that follow fom these goals ae: Given the high LHC luminosity, detectos equie fast, adiation-had electonics and senso elements. In addition, high detecto ganulaity is 22

47 2.3. Inne Detecto needed to handle the paticle fluxes and to educe the influence of ovelapping events. Lage acceptance in pseudoapidity with almost full azimuthal angle coveage. Good chaged-paticle momentum esolution and econstuction efficiency in the inne tacke. Vey good electomagnetic caloimety fo electon and photon identification and measuements, complemented by full-coveage hadonic caloimety fo accuate and missing tansvese enegy measuements. Good muon identification and momentum esolution ove a wide ange of momenta and the ability to detemine unambiguously the chage of high p muons. Highly efficient tiggeing on low tansvese-momentum objects with sufficient backgound ejection is a peequisite to achieve an acceptable tigge ate fo most physics pocesses of inteest. 2.3 Inne Detecto he Inne Detecto (ID) was designed in ode to pefom high pecision measuements with fine detecto ganulaity in the vey lage tack density events poduced by the LHC. he ID, that is ±352 m long and 50 mm in adius, is built out of thee components, in inceasing ode of distance with espect to beam axis: the Pixel detecto, the Semiconducto acke (SC) and the ansition Radiation acke (R). he pecision tacking detectos (pixels and SC) cove the egion η < 2.5, and ae segmented in φ and z, wheeas the R cove the egion η < 2 and is only segmented in φ. he ID has aound 87 million eadout channels, 80.4 millions in the pixel detecto, 6.3 millions in the SC and 35 thousand in the R. All thee ae immesed in a 2 magnetic field geneated by the cental solenoid, which extends ove a length of 5.3 m with a diamete of 2.5 m. he ID is used to econstuct tacks and poduction and decay vetices, and povides a position esolution of 0, 7 and 30 µm (Pixel, SC, R) in the 23

48 Chapte 2. he ALAS Detecto at the Lage Hadon Collide Figue 2.2: View of the full ALAS detecto. φ plane as well as 5 and 580 µm (Pixel, SC) in the z plane. he momentum esolution as a function of p of the tack is paametized as: σ p p = P P 2 p (2.) and the values P =.6±0.% and P 2 = (53±2) 0 5 GeV wee detemined using cosmic ays [34]. Extapolation of the fit esult yields to a momentum esolution of about.6% at low momenta and of about 50% at ev. 2.4 Caloimetes he caloimete systems of ALAS, illustated in Figue 2.3 suound the Inne Detecto system and cove the full φ-space and η < 4.9, extending adially 4.25 m. he caloimete systems can be classified in electomagnetic caloime- 24

49 2.4. Liquid Agon Caloimete tes, designed fo pecision measuements of electons and photons, and hadonic caloimetes, that collect the enegy fom hadons. Caloimete cells ae pseudopojective towads the inteaction egion in η. he ganulaity of the electomagnetic caloimete is typically in η φ, wheeas the hadonic caloimetes have ganulaity of in most of the egions. he enegy esponse of the caloimete to single paticles is discussed in the next Chapte. Figue 2.3: View of the caloimete system Liquid Agon Caloimete he electomagnetic caloimete is a lead-la detecto with accodion-shaped kapton electodes and lead absobe plates ove its full coveage. he accodion geomety povides complete φ symmety without azimuthal cacks. he caloimete is divided into a bael pat ( η <.475) and two end-cap components (.375 < η < 3.2), each housed in thei own cyostat. Ove the cental egion ( η < 2.5), the EM caloimete is segmented in thee layes in depth, wheeas in the end-cap it is segmented in two sections in depth. Figue 2.4 shows an sketch of a module of the LA caloimete Hadonic caloimetes he ile Caloimete is placed diectly outside the electomagnetic caloimete envelope. Its bael coves the egion η <.0, and its two extended baels the 25