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Irakli Chakaberia Final Examination April 28, 2014

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Our Picture of Particle Physics: A Quantum Field Theory of Quarks and Leptons Interacting via Gauge Bosons 2

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Helicity Helicity: the projection of spin onto the direction of motion of the particle The helicity operator is rotationally invariant thus very convenient for the calculations of angular distributions Angular distributions allow for a more complete description of scattering processes 3

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4 Large Hadron Collider

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General Motivation Feasibility Particular Interest My Analysis Zγ production is sensitive to new physical interactions forbidden in the standard model. A helicity analysis provides sensitivity to interference terms between different helicity states and the sign of the individual helicity amplitudes. Thus enhances the sensitivity to new physics. This analysis has not been performed at a hadron collider 6

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Data Theory Method Result Helicity formalism is used to calculate the angular distribution function for Zγ production. Helicity amplitudes become the free parameters to be measured, the result. Presence of new physics may affect the angular distribution relative to expectations from the standard model. 5 fb -1 of integrated luminosity from the LHC 2011 Run A and Run B is used for the analysis Data selection is optimized for the Zγ analysis The process under study is q + q - →Zγ→ℓℓ - γ where leptons are electrons or muons Develop parameterization of the angular distribution function in terms of helicity parameters, given certain assumptions to be listed later. Estimate helicity parameters in the data using an event-by-event maximum likelihood technique. Compare helicity parameters from data to standard model expectations Estimate statistical and systematic uncertainties. 7

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8 Process under study here Not considered (a correction To a well known process)

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Data Selection 9 CMS Preliminary

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Monte Carlo vs. Data 10 Electron Channel Muon Channel

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Description of the Four Helicity Angles 11

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Distribution Function, I 12

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Distribution Function, II 13 Same helicity is suppressed due to the negligent lepton masses compared to the Z mass

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Effective Parity Conservation This analysis deals with two parity violating processes (production and decay) However, the symmetry of the proton-proton collisions provide the effective parity conservation for the production process (integrated over the entire production range). This effective parity conservation is used to further reduce the number of independent parameters: 14

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t-channel Correction 15

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Maximum Likelihood Method 16

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Likelihood Function 17

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Fit Results – Electron Channel Projections over angles 18 Data = points; Fit = histogram

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Fit Results – Muon Channel Projections over angles 19 Data = points; Fit = histogram

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Final Measurement Results 20 SM Data 0.00.10.41.32.01.13.40.0 SM Data 0.0 0.20.1 1.0

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Final Measurement Results 21 SM Data 0.0 4.90.0 0.80.20.91.4 SM Data 0.0 0.80.50.60.50.30.10.0

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Systematic Uncertainties Event-by-event likelihood function is used – relying on a high resolution. Background is not considered in the likelihood function – relying on a low background. Standard model prediction is based on the LO monte carlo. Distribution function is calculated for the LO production process. All the above are the sources of the systematic errors. 22

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Angular Resolution CMS measures lepton and photon angles with high resolution and efficiency Detailed analysis shows resolution effects to be negligible. 23

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Background 24

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NLO Effects 25

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Summary 26

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Backup Slides 27

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Monte Carlo vs. Data 28

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Monte Carlo vs. Data 29

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Anomalous Trilinear Gauge Couplings ATGC are usually studied by looked at the transverse energy (E T γ ) of the photon. Presence of ATGC will show up in high energy tail of E T γ ; In particular, the production and decay angles (helicity angles) of particles (gauge bosons and final state leptons). 30 However, there is more kinematics information that can be used; MC Simulation

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Acceptance / Efficiency Due to the form of the likelihood function detector acceptance and efficiency of the selection criteria can be wrapped into the discrete parameters These parameters are estimated using monte carlo simulation Where N MC G and N MC R are number of generated events and number of reconstructed evens, accordingly. and W p are the event weights ε n depends on the detector and selection cuts and is independent of data sample 31

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Angular Resolution First fit is performed on the fully reconstructed events dataset Second fit is performed on the generated events that are matched to the selected reconstructed event candidates In order to minimize the effects from the parameter correlation every parameter is minimized individually 32 RES 0.10.0 0.10.0 0.10.0 0.1 RES 0.0 0.1

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Template Method This method uses the electromagnetic shower shape variable σ ηη as the discriminator between data and background; Final fit is performed on the data in the p T bins, separately for the endcap and barrel regions of the electromagnetic calorimeter 33 Background Yield 30-3532.450.7 35-4038.637.7 40-6036.364 60-9017.325.1 90-120013.7 120-1505.27.5

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Uncertainties due to the background 34 BKGD 1.81.00.17.24.61.10.71.20.8 0.0 0.20.0 0.10.0 BKGD 0.00.30.70.40.01.60.51.0 0.0 0.10.60.10.0 0.1

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Uncertainties from the NLO effects 35 LO vs. NLO 1.00.00.20.90.60.10.01.60.8 0.20.00.80.00.20.60.30.11.5 LO vs. NLO 0.06.70.70.42.31.43.79.1 0.11.00.20.11.03.62.20.3

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