Irakli Chakaberia Final Examination April 28, 2014

1. First Measurement of Helicity Distributions from Proton-Proton Collisions at the CERN Large Hadron Collider using the CMS Detector IrakliChakaberia Final Examination April 28, 2014

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

3. 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

4. Large Hadron Collider

5. Developing new electronics parts for the upgrade Commissioning the pixel detector

6. WebBased Monitoring of the CMS Detector • The analysis described above requires good data; which, on its side, requires good detector and good monitoring/certification. • I had an opportunity to develop such tools. FillReport DataSummary CMS PageZero CMS Page1

7. Zγproduction 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 • The standard model may not be the final theory of the matter and its interactions. • and other di-boson production channels provide a good probe into new physics. Feasibility My Analysis General Motivation Particular Interest • The Zγproduction process has a fairly low background. • CMS measures angles with a very high resolution. • The relatively high cross-section of the process enables this analysis with the available data (5 fb-1of luminosity).

8. 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. • 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-γwhere leptons are electrons or muons Theory Result Data Method • 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.

9. Production • Production of at LHC occurs mainly through quark-antiquark annihilation (t-channel) Not considered (a correction To a well known process) Process under study here

10. Data Selection • Two opposite sign leptons with GeV (lepton = electron or muon). • Photon with GeV. • Angular separation between lepton and a photon . • Leptons and a photon satisfy identification criteria optimized for the analysis (isolation, conversion rejection, etc.). • “Final state radiation” removed by GeV requirement. • 995 events in the muon channel. • 687 events in the electron channel. CMS Preliminary

11. Monte Carlo vs. Data • Since montecarlo simulation is heavily employed in the analysis, it needs to correctly describe the data • Monte carlo has been corrected to account for “pile-up”, differences in simulating the High Level Trigger response, efficiencies for lepton selection, and many other effects • Monte carlo simulations describe production well looking at any single variable. What about correlations? Electron Channel Muon Channel

12. Description of the Four Helicity Angles • – polar and azimuthal angles of boson direction in the center of mass (CM) frame of • – polar and azimuthal angles of positive lepton in the rest frame of the boson

13. Distribution Function, I • Helicity formalism is a very powerful tool to calculate the angular distributions in the relativistic process; • For this analysis it results in the following angular distribution function: • Where is the total angular momentum of the initial quark-antiquark system; s are the helicities of the particles, and are the helicity amplitudes and s are the known Wigner d-functions

14. Distribution Function, II • Helicities of the particles involved in the process are: • Total angular momentum is set to be up to 2 in this model, an assumption Same helicity is suppressed due to the negligent lepton masses compared to the Z mass

15. 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:

16. t-channel Correction • The standard model production process via “t-channel exchange” gives singularities at due to the very high LHC energies:

17. Maximum Likelihood Method • The distribution function can be rewritten as: • Where are algebraic combinations of the unknown helicity amplitudes. • are the known functions. • can be computed for each event in terms of helicity amplitudes. • The maximum likelihood method is used to estimate the helicity amplitudes: Or equivalently {}

18. Likelihood Function • Deriving likelihood from the signal contribution only • Where are the acceptance/efficiency functions related to acceptance of the detector and efficiency of our selection requirements • is the number of selected candidates from data; is the number of parameters in the distribution function; is the integrated luminosity for the data. • Note: acceptance function need not be known point-by-point.

19. Fit Results – Electron ChannelProjections over angles Data = points; Fit = histogram

20. Fit Results – Muon ChannelProjections over angles Data = points; Fit = histogram

21. Final Measurement Results

22. Final Measurement Results

23. 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 montecarlo. • Distribution function is calculated for the LO production process. • All the above are the sources of potential systematic errors.

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

25. Background • production is a fairly clean process, comprised of (standard candle for many studies) and a high energy photon. • The major background for the production comes from events with a real boson, but no real photon. Instead a quack or gluon “jet” mimics a photon. • All other backgrounds, combined, result in just a handful () of events and are completely ignored in the analysis. • Monte Carlo simulation of jets is tricky, thus the estimation of this background is done with control sample in the data using a “template method” • Systematic effects from background are found to be small for muons; but their effects on the electron channel cannot be neglected.

26. NLO Effects • This analysis assumes that standard model production of is dominated by . • Other “higher order” processes can contribute, e.g. • These higher order processes are less important, but they cannot be exactly calculated, only estimated. • No systematic effects are apparent, but better theoretical tools would be useful to further quantify this.

27. Summary • The analysis of the Zγ helicity distributions at the CMS experiment has been presented using an event-by-event likelihood technique. • Measurements do not show significant deviation from the standard model predictions. • It is clear that more data would improve the measurement substantially. • The performed analysis is of general character and could be easily extended. • With more data it is possible to study further kinematic dependences ( mass, rapidity, etc.). • Similar analysis can be performed for the production. • This analysis can be further applied to the or to study the properties of the Higgs boson, .

28. Backup Slides

29. Monte Carlo vs. Data

30. Monte Carlo vs. Data

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

32. 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 montecarlo simulation • Where NMCG and NMCR are number of generated events and number of reconstructed evens, accordingly. and Wpare the event weights • εn depends on the detector and selection cuts and is independent of data sample

33. 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

34. Template Method • This method uses the electromagnetic shower shape variable σηηas the discriminator between data and background; • Final fit is performed on the data in the pT bins, separately for the endcap and barrel regions of the electromagnetic calorimeter

35. Uncertainties due to the background

36. Uncertainties from the NLO effects