Sung-Won Lee 1 Study of Jets Production Association with a Z boson in pp Collision at 7 and 8 TeV with the CMS Detector Kittikul Kovitanggoon Ph. D. Thesis Defense March,

2 Outline Motivation Large Hadron Collier (LHC) and Compact Muon Solenoid (CMS) Overview of Standard Model (SM) Measurements of Angular Distributions for Z+jet events at 7 TeV  Theory  Data Samples and Event Reconstructions  Unfolded Results with Uncertainties Differential Cross Section of Jets Associated to Z boson at 8 TeV  Theory  Data Samples and Event Reconstructions  Unfolded Results with Uncertainties Conclusions

3 Motivation For Z boson decays into μ+μ-, the trigger system is very efficient and nearly background free Provide good feedback to the theoretical physics community to improve the precision of perturbative QCD and to event generator experts Measurements of the rapidity distributions and differential cross sections are one of the crucial test of the SM prediction Major background processes for various new physics searches such as Higgs and Supersymmetry (SUSY)

4 Large Hadron Collider (LHC) A 27 km in circumference To collide rotating beams of protons or heavy ions Maximum energy of proton- proton collisions at = 14 TeV and 4 x cm -2 s -1 In 2011, collision at = 14 TeV and 4 x cm -2 s -1 In 2012, collision at = 8 TeV and 7.7 x cm -2 s -1

5 Compact Muon Solenoid CMS

6 Compact Muon Solinoid CMS

7 Standard Model (SM)

8 Z + Jet Angular Distribution

9 Z+jet '' Z+jet'' events are predominantly produced by quark exchange processes (i.e. qq ̄ → Z 0 g and qg → Z 0 q) In the center-of-momentum frame, the differential cross section is The observed cosθ* distribution can be used to improved pQCD or indicated a new particle.

10 What Do We Measure? Rapidity distributions of Z boson: |y z | Rapidity distributions of leading jet: |y jet | Rapidity difference: y diff = 0.5|y z -y jet |  Related to the scattering angle at the center of momentum frame: tanh(y diff ) = β*cosθ* Rapidity average: y sum = 0.5|y z +y jet |  Rapidity boost from the center of momentum frame to the lab frame Rapidity is defined by

11 Analysis Procedure (1) Selects events containing a Z(→μμ) and a jet that satisfy kinematic and ID selections. (2) Derive efficiency from MC and correct it with data-to-MC scale factors via tag and probe method. (3) Unfold the distribution of y jet  Other variable have unfolding correction consistent with one. (4) Evaluate Systematic uncertainties. (5) Compare shapes with MCFM, MADGRAPH, and SHERPA MC simulations. MCFM Matrix element at NLO,without parton showering or hadronization Scale set to the dilepton mass CTEQ 6.1 m (NLO PDFs) MADGRAPH+PYTHIA Matrix element at LO with MLM matching Scale set to the square root sum of dilepton mass and p T (jet) CTEQ 6L1 m (LO PDFs) SHERPA Matrix element at LO with CKKW matching Scale set to the dilepton mass CTEQ 6.6M (NLO PDFs)

12 Dataset and HLT CMS data collected in 2011 for 5.1 ± 0.1 fb -1 Monte Carlo Simulations JSON: Cert_ _7TeV_ReRecoNov08_Collisions11_JSON.txt High Level Trigger

13 Basic Kinematic Selections

14 Basic Kinematic Properties Well agreements for Z kinematics between data and MC Z mass distribution was created before Z mass selections Discrepancy of Z mass < 50 GeV comes from the generator-level mass selection

15 Basic Kinematic Properties The number of jets accompanying a Z drops by ~α S Non-zero jet mass is attributed to the finite angular spread of the jet in calorimeter

16 Basic Kinematic Properties Well agreements for jets kinematics between data and MC

17 Muon ID Scale Factor and Efficiency ID scale factors from Particle Object Group Use Tag & Probe with Data & MC  Select a pair of muons: one passing tight selections (tag) and the other passing or failing loose selections (probe)  The scale is computed from the ratio of tag+passing probe and tag+failing probe Use Muon Particle Object Group recommendations Obtain the data-to-MC ID efficiency scale factors in bins of p T and η Re-weight the MC events that pass ID selections with the scale factors Obtain efficiency as a function of the four rapidity variables The ID efficiency correction is the reciprocal if the ratio of weighted with ID selections and without ID selection

18 Muon ID Efficiency

19 Unfolding Unfolding methods 1. Bayesianwith 3 iterations 2. Bin-by-Bin 3. Singular Value Decomposition with kreg=10 Criteria: if unfolding correction is consistent with zero within MC statistical uncertainty, do not unfold In order to compare experimental result with theoretical prediction, the experimental need to be corrected due to the detector effects. ==> The method is called unfolding. Response matrices of rapidity: the comparison shows mostly diagonal elements Using RooUnfold package MADGRAPH+Pythia as source of response matrices

20 Unfolding Correction on Data Unfolding is consistent at one for all but y jet distribution. Thus, we will unfold y jet.

21 Systematic Uncertainties Jet Energy Scale (JES) Uncertainties Jet Energy Resolution (JER)  Jets are corrected due to the non-uniform and non-linear response of calorimeters  Can cause the bin migration i.e. Z+0jet can fake as Z+1jet etc.  Shifted jet corrections up and down by 1σ  σ is provided by JetMET POG  Re-performing measurements after shifting jet  Finite jet energy resolution can be the threshold effects  Modified the reconstructed jet pT with the pT difference between matched reconstruction-level jets and generator-level jets  c is a factor provided by JetMET POG

22 JES Uncertainties Uncertainty is < 1% for all distributions

23 JER Uncertainties Uncertainty is < 2% for all distributions

24 Comparison to Theories Shape comparisons of CMS data, MADGRAPH, and SHERPA to MCFM are shown.

25 Comparison to Theories

26 Combined Results

27 Combined Results

28 Summary CMS detector was used to measure the angular distributions of the products from Z+1jet events Madgraph+Pythia, Sherpa, and MCFM have similar agreement with data for y z and y jet. For Z + 1jet, Sherpa agrees better with data for y diff and y sum.  Parton showering and matching scheme give the difference. Provide feedback to theory community for improving theoretical predictions.

29 Z + Jets Differential Cross Sections

30 Z+jets

31 What Do We Measure? In this analysis, we measured the Z+jets differential cross sections of up to two jets associated with Z → μ + μ -. The Z+jets production cross section as a function of the jet multiplicity : dσ/ dN J The Z+jets cross section as a function of the jet pT : dσ/ dp T The Z+jets cross section as a function of the jet η : dσ/ dη

32 Dataset CMS data collected in 2012 for 19.8 ± 0.1 fb -1 Monte Carlo Simulations JSON: Cert_ _8TeV_22Jan2013ReReco_Collisions12_JSON.txt High Level Trigger → HLT_Mu17_Mu8_v* with L1_DoubleMu3p5 seed

33 PU Re-Weighting MC productions use an approximate number of pileup interactions Pileup interactions in MC are re-weighted by the data pileup distribution using the entire data-taking period

34 Basic Muon Selections Using PF muon collection matched the trigger objects

35 The First Muon Candidate First muon candidate kinematics are agreed between data and MC

36 The Second Muon Candidate Second muon candidate kinematics are agreed between data and MC The p T plots show good agreement at the kinematic region up to 60 GeV where we expect to find most muons coming from Z decays

37 Efficiency Scale Factor Scale factors of HLT, ID, and isolation from Tag and Probe Provided by Muon POG Obtain the data-to-MC scale factors in bins of p T and η

38 Z Reconstruction Z bosons are reconstructed from opposite charged muons Z mass window of 71 < MZ < 111 are used and agreed with MC

39 Z Reconstruction

40 Basic Jet Selections Jets are AK5 PF after Charged Hadron subtraction Data are using L1FastJet + L2Relative + L3Absolute + L2L3Residual MC are using L1FastJet + L2Relative + L3Absolute Leptons are vetoed from the jet collection by a simple ∆ R cut of 0.5

41 Z+Jets Control Plots

42 Measured Observables Good agreement between data and MC up to 4 jets as expected ExclusiveInclusive

43 Measured Observables p T distributions of the first and second leading jets agree at low pT

44 Measured Observables η distributions of the first and second leading jets also agree in barrel region and show some discrepancy in endcap region as expected from detector performance

45 Unfolding Using MADGRAPH+Pythia as source of response matrices Unfolding methods 1. Bayesian with 3 iterations → used for the final results 2. Bin-by-Bin 3. Singular Value Decomposition with kreg=10 Generator level phase space  Muons are dressed with all the photons that are within the cone of radius 0.1  Stable muons from Z (status =1)  Cuts on muons pt > 20,η < 2.4 after adding photons Background subtraction from data Using MADGRAPH+Pythia as source of response matrices

46 Unfolding Response matrix

47 Unfolding

48 Unfolding

49 Systematic Uncertainties Jet Energy Scale (JES) Uncertainties Jet Energy Resolution (JER)  Jets are corrected due to the non-uniform and non-linear response of calorimeters  Can cause the bin migration i.e. Z+0jet can fake as Z+1jet etc.  Shifted jet corrections up and down by 1σ  σ is provided by JetMET POG  Re-performing measurements after shifting jet  Finite jet energy resolution can be the threshold effects  Modified the reconstructed jet pT with the pT difference between matched reconstruction-level jets and generator-level jets  c is a factor provided by JetMET POG

50 Systematic Uncertainties Smearing jet p T can change Z+0jet to Z+1jet etc Higher the jet mutiplicity, more bin migration JES causes up to 10% uncertainty

51 Systematic Uncertainties JER causes only 2-4% uncertainty

52 Systematic Uncertainties Summary

53 Results

54 Results

55 Z+Jets Summary The differential cross-sections of Z+n jets (n up to 2) are measured as functions of  Jet multiplicity  Jet transverse momentum  Jet rapidity The measurements are done on 8 TeV with integrated luminosity of 19.8 fb −1 Detector effects are corrected by unfolding with Bayes method Results are compared to the following MCFM+Pythia generator prediction

56 Conclusions Jets productions in association with a Z boson in p-p collision provides a good opportunity to test perturbative QCD and important background for new physics Angular distributions for the Z boson and a single jet of 4.7 fb − 1 at 7 TeV have been analyzed  |y z | and |y jet | are found to agree with predictions from SHERPA, MADGRAPH, and MCFM  y sum described by all predictions up to 5% precision for y sum < 1.0  At y sum > 1.0, SHERPA is the best described due to the hybrid calculations that employ NLO PDF  Y diff is best described MCFM

57 Conclusions Differential cross sections for the Z boson and jets of 19.8 fb − 1 at 8 TeV have been calculated The measurements of Z+jets production deferential cross section up to two jets as a function of the  Jet multiplicity: dσ/ dN J  Transverse momentum: dσ/ dp T  Rapidity: dσ/ dη J Results after unfolding and efficiency corrected, compared with different theoretical pQCD predictions in MADGRAPH JES and JER are studied as the main systematic uncertainties Comparisons are agreed with data and MC

58 Back Up

59 Unfolding Correction with SHERPA Use the response matrices of MEDGRAPH to unfold the independent MC prediction of Z+jets, SHERPA

60 PU Systematic Uncertainty for Z + Jet Angular

61 Background Systematic Uncertainty for Z + Jet Angular

62 PU Systematic Uncertainty for Z + Jet Angular

63 Combination of Electron and Muon Best Linear Unbiased Esttimator Andrea Valassi, NIM, A500, 391 Louis Lyons, Duncan Gibaut, and Peter Clifford, NIM, A207, 110 JES and PU uncertainties are 100% correlated between electron and muon channel The covariance matrix has 2N dimension N is the number of bins with non-zero contents For each channel of y jet, the bin-by-bin correlation is obtained from the covariance matrix of RooUnfold after unfolding For every bin of the observable, the uncorrelated uncertainty is at least 3 times of the correlated uncertainty

64 Breakdown Differential Cross Section

65 Breakdown Differential Cross Section