Measurement of sin 2 w via the likelihood method in z
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Measurement of sin 2  W via the likelihood method in Zµ + µ -. EWK dilepton meeting, 03.02.2011 Alessio Bonato, Andrei Gritsan, Zijin Guo, Nhan Tran Johns Hopkins University Efe Yazgan Texas Tech University. Motivation. Measure spin and couplings of a new resonance

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Measurement of sin2Wvia the likelihood method in Zµ+µ-

EWK dilepton meeting, 03.02.2011

Alessio Bonato, Andrei Gritsan, Zijin Guo, Nhan Tran

Johns Hopkins University

Efe Yazgan

Texas Tech University


  • Measure spin and couplings of a new resonance

  • In dilepton channel, consider amplitude of some generic particle X with spin J decaying to two fermions

Terms suppressed by chirality

More details, see arXiv:1001.3396

By studying the angular distributions, we can measure the spin and couplings of particle X


  • By including dilepton mass-dependence, we can improve sensitivity to non-narrow resonances and interference with SM processes: d/(dm*dcos)

  • The SM already provides testing ground: pp*/Zl+l-

  • Recall, for the SM Z (J=1): 1 = cV(W) and 2 = cA(W)

  • In developing the formalism for generic dilepton resonances, we provide a measurement of the SM couplings and the Weinberg angle, sin2W.

Analysis Outline

  • Use analytic per event likelihood formalism to extract maximal information

    • Requires probability distribution function, P, of signal and background

    • RooFit implementation outlined in CMS-AN-2010-351

  • Building the likelihood function

    • DY mass-angle distribution: P (m,cos)

    • Include partonic luminosities and dilution: P (m,cos,Y)

    • Include acceptance: P (m,cos,Y)xGacc(m,cos,Y)

    • Include resolution+FSR: [P (m,cos,Y)  R (m)] x Gacc(m,cos,Y)

  • Model built at LO, consider (N)NLO MC (data) as correction to measurement

More details:

DY process and PDF factorization

Desribe the DY process:P (m,cos)

Reduces to usual ~ A(1+cos2) + Bcos


Differential cross-section depends on PDFs (fa (m,Y)/ fb(m,Y)):

Probability Distribution Function for DY process: P (m,cos,Y)

*Requires analytical parameterization of PDFs (see backup for more details), using CTEQ6.6




*black points: LO Pythia, blue line: probability distribution function


  • Quark direction is ambiguous in pp collisions.

  • Use Z boost direction, Y, to determine angle, cos.

  • Dilution term determined analytically from PDFs.

Probability Distribution Function including dilution: P (m,cos,Y)

Undiluted case

Diluted case



*black points: LO Pythia, blue line: probability distribution function

Trigger and Acceptance

Acceptance sculpts further the Y and cosdistributions

Probability Density Function ~P (m,cos,Y)xGacc(m,cos,Y)

Lepton cuts ( < Ymax;pT > pTmin) yield conditions:

cos < tanh(Ymax - Y); cos < [1-(2pTmin/m)2]1/2


Before acceptance/after acceptance

Choose pTmin< 25 GeV in the CS frame - covers standard cuts and triggers: pTmin,1 > 20 GeV and pTmin,2 > 7 GeV in the lab frame

Resolution + FSR

Account for resolution+FSR via convolution

Probability Density Function ~[P (m,cos,Y)  R (m)] x Gacc(m,cos,Y)

Assume resolution function,R (m), unknown. Approximated by quadruple Gaussian,R4g(m), for analytical convolution. Parameters obtained from fit of data.

Test formalism: take LO Pythia + FSR and do “fast smear” of track parameters. Fit full probability distribution function to the data and obtain R4g(m) parameters from the fit

Gen level

FSR + smear

Convolution of resolution function


Results at LO

Putting it all together…

Probability Density Function ~[P (m,cos,Y)  R4g(m)] x Gacc(m,cos,Y)

Generate 3M events of DY LO Pythia and fit for sin2W




Fit result: sin2W = 0.2315  0.0011

Compare with generated value: sin2W = 0.2312

Formalism holds together at LO with negligible biases.

Systematics from NLO

*Further discussion later


Rest of slides dedicated to “new-ish” results and would be slightly altered for pre-approval talks.

  • So far, analysis steps…

    • Agreement good at LO and with CMS NLO MC

    • Implement a blind analysis fit on first data

  • Next steps

    • 35pb-1 40 pb-1 improve statistics

    • Push to the limits! Improve sensitivity and statistics

      • Loosen phase-space cuts and extend µ acceptance

    • Understand systematic effects, estimate uncertainty

  • Goal: statistical error < 0.01 while keeping systematic errors small

All results have been integrated into CMS-AN-2011/031

CMS MC and Data

  • Samples used:

    • Data: 40 pb-1, Dec22 Re-Reco (processed by Efe)

    • MC:/DYToMuMu_M-20_CT10_TuneZ2_7TeV-powheg-pythia/

  • Standard cuts used in Afb analysis (selections/triggers in backup)

    • Use tracker-only isolation moving to 40 pb-1 (HCAL issues)

    • Relax cuts on pT and  of µ± to expand phase space

We decide to use new loose cuts to provide greatest sensitivity

*Bug found w.r.t. last week in data with new loose cuts

µ efficiency

With new loose cuts, make a sanity check of µ efficiency:

Make full set of cuts on both muons (trigger + reco) and compare

Efficiency for < 2.4

Compares favorably with Muon DPG-PH studies:

C. Botta and D. Trocino

Effect of new loose cuts

  • Start with sample with standard RECO cuts including mass [60,120] and pT(Z) < 25 GeV, except for  and pT

  • Apply cuts subsequently: (CS), (lab), pT(CS), pT(lab), and see how cuts sculpt distributions.

  • Want to lose as few events as possible going from CS cuts to lab cuts

Efficiency of new loose cuts

Efficiency: look at distributions before and afterHLT, reconstruction, and lab vs. CS cuts

Points: gen. level before any cuts

Want to see flat efficiency in Y and cos to agree with our model.

Fit results: simulation

Fit for sin2W on CMS NLO MC using new loose cuts

Looser cuts improve error, but hint of bias

Compare with generated value: sin2W = 0.2311

Fit result : sin2W = 0.2283  0.0014

Fit results: data

Fit for sin2W on CMS data using new loose cuts

Nominal fit floats momentum scale (Z mass) to reduce systematics, more later.

Fit results : sin2W = ????  0.0077

mZ = 91.072  0.029

Systematic Uncertainties

List of sources of systematics and treatments

  • ISR and LO model: contributions from NLO suppressed by cut on pT of Z, linear scaling

    • Variation at level of 0.002, tests statistics-limited, error ~0.001

  • Parton Distribution Function uncertainty

    • First attempt, make same measurement using MSTW2008 PDF set, variation at ~0.001, statistics-limited

    • More sophisticated methods under investigation

Systematic Uncertainties

  • Resolution model and FSR: take resolution+FSR from MC and apply it in data

    • In data, float resolution model parameters in addition - observe difference in central values from nominal fit: 0.0015

  • Momentum scale and mis-alignment/calibration

    • Float Z mass in nominal fit: 91.072 ± 0.029 to reduce sensitivity to momentum scale, in agreement with MuScle corrections

    • Further systematics by comparing central fit values in data with and without MuScle corrections: 0.0016

  • Fit model (efficiency, triggers)

    • MC fit shows hint of bias, conservatively ~0.003

  • Background

    • Statistical considerations estimate ~0.0006, to do more careful treatment fitting background shapes

Systematic Uncertainties

  • Some systematics limited by statistics, conservative estimates made, require larger MC sample (currently ~1fb-1 of statistics)

  • Systematics overlap, correlated, overall estimation of systematic uncertainties convservative

  • In some cases, simplistic estimate, more detailed study underway


  • Push analysis to the limits, use as much phase space (loose cuts) and statistics (40 pb-1) as possible

    • Converged on loosest possible cuts

  • Investigation of systematic uncertainties

    • Consider ISR and LO model, PDF uncertainties, resolution+FSR model, momentum scale, fit model, and background contributions

    • Continue further studies on systematics

  • Finalize statistical tests: toy MC experiments, pulls, and goodness-of-fit

Fit result : sin2W = ????  0.0077 (stat.)  0.0044 (sys.)

For reference

For a description of the method and documentation please see: (N.T.) (N.T.) (A. Gritsan) (A. Gritsan)


CMS AN-2011/031


Parton Distribution Functions

We fit the data (CTEQ6QL) for u,d,c,s,b quarks and gluons with:

Example: Fitu quark parton distribution function, x*fu(x,Q2), for a given value of Q (left); then fit parameters for Q-dependence (right)

Fit performed over relevant x range


  • Triggers (OR of singleMuXX and doubleMu3)

    • Run 136033-147195: singleMu9

    • Run 147196-148107: singleMu11

    • Run 148108-149442: singleMu15

  • Standard AFB selection

    • Oppositely charge global & tracker muon

    • dxy < 0.2 for both muons

    • HLT trigger matching

    • Pixel hits >= 1

    • Tracker hits > 10

    • Normalized 2 < 10

    • Muon hits >= 1

    • N muon stations > 1

    • Isolation: (Tracker+HCAL)/pTµ < 0.15

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