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Measurement of sin2W via the likelihood method in
Zµ+µ-
EWK dilepton meeting, 03.02.2011
Alessio Bonato, Andrei Gritsan, Zijin Guo, Nhan Tran
Johns Hopkins UniversityEfe Yazgan
Texas Tech University
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Motivation
• 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
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Terms suppressed by chirality
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By studying the angular distributions, we can measure the spin and couplings of particle X
More details, see arXiv:1001.3396
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Motivation
• 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*/Zl+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, sin2W.
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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) x Gacc(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
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More details: http://indico.cern.ch/getFile.py/access?contribId=0&resId=0&materialId=slides&confId=113453
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DY process and PDF factorization
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Reduces to usual ~ A(1+cos2) + Bcos
*/Z
Desribe the DY process: P (m,cos)
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Differential cross-section depends on PDFs (fa (m,Y)/ fb(m,Y)):
Y mcos
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
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Dilution
Undiluted case Diluted case
coscos
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Probability Distribution Function including dilution: P (m,cos,Y)
• Quark direction is ambiguous in pp collisions.• Use Z boost direction, Y, to determine angle, cos.
• Dilution term determined analytically from PDFs.
*black points: LO Pythia, blue line: probability distribution function
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Trigger and AcceptanceAcceptance sculpts further the Y and cos
distributionsProbability Density Function ~ P (m,cos,Y) x Gacc(m,cos,Y)
Lepton cuts ( < Ymax; pT > pTmin) yield conditions:
cos < tanh(Ymax - Y); cos < [1-(2pTmin/m)2]1/2
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Gacc(m,cos,Y)
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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
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Resolution + FSRAccount 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.
R4g(m)
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
Convolution of resolution functionGen level FSR + smear
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Results at LO
Fit result: sin2W = 0.2315 0.0011Compare with generated value: sin2W =
0.2312
Formalism holds together at LO with negligible biases.
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 sin2W
Y mcos
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Systematics from NLO
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*Further discussion later
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Status
• 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
Rest of slides dedicated to “new-ish” results and would be slightly altered for pre-approval talks.
All results have been integrated into CMS-AN-2011/031
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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 spacehttps://twiki.cern.ch/twiki/bin/viewauth/CMS/ForwardBackwardAsymmetryOfDiLeptonPairs
Cuts Old CutsNew Cuts (tight)
New Cuts (loose)
mll; pT(Z)[66, 116]; < 25
GeV[60, 120]; <25
GeV[60, 120]; < 25
GeV
(CS) < 2.1, 2.1 < 2.1, 2.1 < 2.3, 2.3
(lab) < 2.1, 2.1 < 2.4, 2.1 < 2.4, 2.4
pT (CS) > 25 GeV > 20 GeV > 18 GeV
pT (lab) > 20, 7 GeV > 20, 7 GeV > 18, 7 GeVWe decide to use new loose cuts to provide greatest sensitivity
*Bug found w.r.t. last week in data with new loose cuts
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µ efficiencyWith new loose cuts, make a sanity check of µ
efficiency: Make full set of cuts on both muons (trigger + reco)
and compareEfficiency for < 2.4
Compares favorably with Muon DPG-PH studies:http://indico.cern.ch/getFile.py/access?contribId=2&resId=0&materialId=slides&confId=94653
C. Botta and D. Trocino
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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
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Efficiency of new loose cuts
Efficiency: look at distributions before and after HLT, reconstruction, and lab
vs. CS cuts
Want to see flat efficiency in Y and cos to agree with
our model.
Points: gen. level before any cuts
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Fit results: simulation
Compare with generated value: sin2W = 0.2311Fit result : sin2W = 0.2283 0.0014
Fit for sin2W on CMS NLO MC using new loose cuts
Looser cuts improve error, but hint of bias
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Fit results: data
Fit results : sin2W = ???? 0.0077
mZ = 91.072 0.029
Fit for sin2W on CMS data using new loose cuts
Nominal fit floats momentum scale (Z mass) to reduce systematics, more later.
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Systematic Uncertainties
• 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
List of sources of systematics and treatments
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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
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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
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Outlook
• 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-fitFit result : sin2W = ???? 0.0077 (stat.)
0.0044 (sys.)
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For referenceFor a description of the method and documentation please see:
http://indico.cern.ch/getFile.py/access?contribId=8&resId=0&materialId=slides&confId=124119 (N.T.)http://indico.cern.ch/getFile.py/access?contribId=7&resId=0&materialId=slides&confId=121960 (N.T.)
http://indico.cern.ch/getFile.py/access?contribId=6&resId=0&materialId=slides&confId=114638 (A. Gritsan)http://indico.cern.ch/getFile.py/access?contribId=0&resId=0&materialId=slides&confId=113453 (A. Gritsan)
and
CMS AN-2011/031
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backup
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Parton Distribution Functions
We fit the data (CTEQ6QL) for u,d,c,s,b quarks and gluons with: QuickTime™ and a
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Example: Fit u 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
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Trigger/Selection
• 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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