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Measurement of sin 2 W via the likelihood method in Zµ + µ -

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### Measurement of sin2Wvia the likelihood method in Zµ+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
- 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

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.

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: http://indico.cern.ch/getFile.py/access?contribId=0&resId=0&materialId=slides&confId=113453

DY process and PDF factorization

Desribe the DY process:P (m,cos)

Reduces to usual ~ A(1+cos2) + Bcos

*/Z

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

Y

m

cos

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

Dilution

- 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

cos

cos

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

Trigger and Acceptance

Acceptance sculpts further the Y and cosdistributions

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

Gacc(m,cos,Y)

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

R4g(m)

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 sin2W

Y

m

cos

Fit result: sin2W = 0.2315 0.0011

Compare with generated value: sin2W = 0.2312

Formalism holds together at LO with negligible biases.

Systematics from NLO

*Further discussion later

Status

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

https://twiki.cern.ch/twiki/bin/viewauth/CMS/ForwardBackwardAsymmetryOfDiLeptonPairs

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:

http://indico.cern.ch/getFile.py/access?contribId=2&resId=0&materialId=slides&confId=94653

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 sin2W on CMS NLO MC using new loose cuts

Looser cuts improve error, but hint of bias

Compare with generated value: sin2W = 0.2311

Fit result : sin2W = 0.2283 0.0014

Fit results: data

Fit for sin2W on CMS data using new loose cuts

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

Fit results : sin2W = ???? 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

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-fit

Fit result : sin2W = ???? 0.0077 (stat.) 0.0044 (sys.)

For reference

For 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

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

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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