First Measurement of Helicity Distributions from Proton-Proton

Collisions at the CERN Large Hadron Collider using the CMS Detector

Irakli ChakaberiaFinal 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

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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

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Large Hadron Collider

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Gene

ral

Moti

vatio

n

FeasibilityParticular

InterestMy

Analysis

• 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.

• 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

• The Zγ production 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-1 of luminosity).

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Data

TheoryM

ethod

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.

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Production

• Production of at LHC occurs mainly through quark-antiquark annihilation (t-channel)

Zqq

Process under study hereNot considered (a correctionTo a well known process)

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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

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Monte Carlo vs. Data• Since monte carlo 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?

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Cha

nnel

Muo

n Ch

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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

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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

2

1

2

expcos

cos12

ZZZqq

J

JZ

J

Z id

TdJA

dd

d

Z

Zqq

ZqqZqq

;; qqqqZZ

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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

1,0

1

1,0

1

Z

qq

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:

Zqq Z

JJ

qqZqqZTT ,,,,

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t-channel Correction

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

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d

Z

/1&/1~

ZZ

ZZ

Mssu

Msst

cos

cos2

2

2

22 cos)ˆ(ˆ1

cos)ˆ(ˆ1

4

ˆ)(cos

ZZZZZ MssMss

sT

dd

dOldT

dd

d

ZZ

Z

)(cos

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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{}

,cos,,cos

)()(1

ZZ

N

nnn

par

AW

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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.

dW

dWdP

)()(

)()()(

pD p N

nnn

N

n

N

nnnn dALA ln

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Fit Results – Electron ChannelProjections over angles

Data = points; Fit = histogram

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Fit Results – Muon ChannelProjections over angles

Data = points; Fit = histogram

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Final Measurement Results

SM 1.02 -6.171.8

0.06.3

-0.36.4

0.82.5

0.86.6

2.76.9

2.03.5

Data 1.00.5

-7.84.4

-1.081.7

-2.571.9

3.231.7

-2.00.7

-0.361.3

2.23.1

0.0 0.1 0.4 1.3 2.0 1.1 3.4 0.0

SM 0.95 -11.05 0.36 -0.06 1.82 2.10 4.78 1.831.3

Data 1.06 -11.43 -0.24 -0.64 2.38 2.73 5.42 4.161.9

0.0 0.0 0.2 0.1 0.1 0.1 0.1 1.0

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Final Measurement Results

SM -0.33 -0.17 -0.06 0.09 0.83 -1.02 1.00 0.93 -1.03

Data -0.60 0.231.7

4.061.8

1.91 -0.61 1.36 1.95 -0.66 1.44

0.0 0.0 4.9 0.0 0.0 0.8 0.2 0.9 1.4

SM 0.36 0.11 -0.44 -0.11 1.38 -2.67 2.38 0.81 -3.84

Data 0.42 0.23 0.681.0

-0.87 2.57 -4.84 3.40 0.37 -3.99

0.0 0.0 0.8 0.5 0.6 0.5 0.3 0.1 0.0

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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.

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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.

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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 using the a 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.

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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.

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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, .

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Backup Slides

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Monte Carlo vs. Data

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Monte Carlo vs. Data

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Anomalous Trilinear Gauge Couplings

• ATGC are usually studied by looked at the transverse energy (ET

γ) of the photon. Presence of ATGC will show up in high energy tail of ET

γ;

• In particular, the production and decay angles (helicity angles) of particles (gauge bosons and final state leptons).

• 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 NMCG and NMC

R are number of generated events and number of reconstructed evens, accordingly. and Wp are the event weights

• εn depends on the detector and selection cuts and is independent of data sample

nn d )()(

MCG

MCR

N

n np

N

n npnn

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W

W

)(

1

)(

1)(

16 2

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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

RES

0.1 0.0 0.0 0.0 0.1 0.0 0.0 0.0 0.0

0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1

RES

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1

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Template Method• This method uses the electromagnetic shower shape variable σηη

as 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

[GeV]Background Yield

30-35 32.4 50.735-40 38.6 37.740-60 36.3 6460-90 17.3 25.1

90-120 0 13.7120-150 5.2 7.5

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Uncertainties due to the background

BKGD

1.8 1.0 0.1 7.2 4.6 1.1 0.7 1.2 0.8

0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.1 0.0

BKGD

0.0 0.3 0.7 0.4 0.0 1.6 0.5 1.0

0.0 0.0 0.1 0.6 0.1 0.0 0.0 0.1

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Uncertainties from the NLO effects

LO vs. NLO

1.0 0.0 0.2 0.9 0.6 0.1 0.0 1.6 0.8

0.2 0.0 0.8 0.0 0.2 0.6 0.3 0.1 1.5

LO vs. NLO

0.0 6.7 0.7 0.4 2.3 1.4 3.7 9.1

0.1 1.0 0.2 0.1 1.0 3.6 2.2 0.3