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### 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

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

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

Developing new electronics parts for the upgrade

Commissioning the pixel detector

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

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).

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.

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

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

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

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

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

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

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:

t-channel Correction

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

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

{}

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.

Fit Results – Electron ChannelProjections over angles

Data = points; Fit = histogram

Fit Results – Muon ChannelProjections over angles

Data = points; Fit = histogram

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.

Angular Resolution

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

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.

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.

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, .

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;

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

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

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

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