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

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First Measurement of Helicity Distributions from Proton-Proton Collisions at the CERN Large Hadron Collider using the CMS Detector


Final Examination

April 28, 2014

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



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.




General Motivation



  • 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





  • 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 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
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
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
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
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
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
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
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
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
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.
systematic uncertainties
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
Angular Resolution
  • CMS measures lepton and photon angles with high resolution and efficiency
  • Detailed analysis shows resolution effects to be negligible.
  • 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
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.
  • 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
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
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 resolution1
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
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