Muon Momentum Scale Status and plans

1. Muon Momentum ScaleStatus and plans M.De Mattia, T.Dorigo, U.Gasparini – Padova S.Bolognesi, C.Mariotti – Torino CMS-Padova – 1 ottobre 2007 T.Dorigo, INFN-Padova

2. An attempt at a global calibration algorithm • Usually, the dimuon mass of available resonances is studied serially as a function of average quantities from the two muons (average curvature, Phi of the pair, Eta of the pair, opening angle…). However: • correlated biases are hard to deal with • results depend on resonance used and variable studied • Example: • Z has narrow Pt range, back-to-back muons  hard to spot low-Pt effects, unsuitable to track Phi modulations of scale – use for high-Pt • J/Psi has wider Pt range, small-DR muons, asymmetric momenta  better for studies of axial tilts, low-Pt effects – but useless for high-Pt, and beware of non-promptness • Asymmetric decays make a detection of non-linearities harder • A non-linear response in Pt cannot be determined easily by studying M(mm) vs <Pt> • Idea: try to let each muon speak, with a multi-dimensional approach T.Dorigo, INFN-Padova

3. Work Plan • Target two scenarios: (A) “early physics” O(1/pb), (B) O(10/pb) • Reconstruct dimuon resonance datasets inserting artificial pathologies, to model real-life situations we may encounter and learn how to spot and correct them • B field distortions (A, B)  in progress • Global misalignments (A,B)  in progress • Changes in material budget  defer until later • Goal: discover our sensitivity to disuniformities or imprecisions in the physical model, and get ready to intervene with ad-hoc corrections on data already taken • Standard (non-modified) sample will be compared to several modified ones, to mimic the comparison MC/data in different conditions  in progress • Different trigger selections can be studied, possibly to determine whether choice of thresholds are sound  defer until later • Means: an algorithm fitting a set of calibration corrections as a function of sensitive observables • And do it for different quality and characteristics of muon tracks • standalone/global/tracker only  later • low/high Pt, different rapidity ranges  later • Muon quality (ID cuts, isolation…)  later • By-product: check of resolution as a function of their characteristics  starting T.Dorigo, INFN-Padova

4. Muon Scale Likelihood • Use a-priori ansatz of functional dependence of Pt scale on parameters, together with realistic PDF of resonance mass • Compute likelihood of mass measurement, sum over sample and minimize, determining parameters of bias function • Advantages: • can fit multiple parameters at a time • better handling of low statistics • can spot additional dependencies by scanning contribution to Ln(L) of different ranges in several parameters at once (see later) • Sensitive to non-linear behavior – measurement bias of each muon correctly accounted for • Subtleties: • Need meaningful ansatz! • Benefit from better modeling of mass PDF as a function of parameters • May require independent detailed study of resolution • But we are going too far… Let us just have a look at what can be done with simple parametrizations. T.Dorigo, INFN-Padova

5. Likelihood recipe • Decide on a-priori bias function, and parameters on which it depends • e.g.: linear in Pt - 2 parameters (a,b) to minimize; two variables per muon • For each muon pair, compute non-biased mass M and determine if sidebands or signal, and reference mass • If MÎsignal region, reference mass is mass of resonance; weight is W=+1 • If MÎsidebands, reference mass is center of sideband; weight is W=-0.5 • Compute dimuon mass M’(a,b) as a function of parameters, obtain P(M’) from resonance PDF, sum likelihood • Pt(i) = Pt(i) * [ a + b * Pt(i) ] , i = 1, 2  M’ = M’(a,b) • F(a,b) += - 2 * ln ( P[M’(a,b)] ) * W • Iterate on sample, minimize F(a,b), find best estimates A,B of a,b • Once convergence is achieved, apply correction to muon momenta using “best” coefficientsPt’ = Pt * [ A + B * Pt ] • Can then compare mass before/after correction • Also plot average contribution to F in bins of several kinematic variables T.Dorigo, INFN-Padova

6. Status of code and MC • Ported original routines in CMSSW • Now working with 1_6_0 • So far, testing with Zmm Monte Carlo samples • Use those for results to be inserted in note on W,Z cross sections • Now generating misaligned and B-mod samples • Will then obtain accuracy of scale correction function in several scenarios • For now working only with Z – J/psi will come later T.Dorigo, INFN-Padova

7. Playing with the biases • While we learn how to modify the geometry and B field in a meaningful way, we tested the algorithm by inserting biases “by hand”. • Try simple parametrizations of Pt scale bias: • Linear in muon Pt • Sinusoidal in muon Phi • Linear in Pt and |eta| • Linear in Pt and sinusoidal in phi • Linear in Pt and |eta| and sinusoidal in phi • Linear in Pt and quadratic in |eta| • … • Forcefully bias muon momenta using bias functions and ad-hoc parameters • Determine if likelihood can correct the bias • Algorithm working very well even with small datasets T.Dorigo, INFN-Padova

8. Conclusions • Resonance studies started with • Global fitting approach (targeting both early data and 2008 statistics) • Studies Z samples with various biases • Likelihood method stands on its feet • Version working in CMSSW_1_6_0 • Proven to provide better results than simpler means • Technology for biased samples has been obtained • B field modifications (tracker only so far) • Misalignments • Working toward contributing to EWK note on W,Z cross sections • Systematics on acceptance from muon scale • muon resolutions • Several subtleties will be addressed later • Study standalone-global pairs for added stats in “early physics” scenario • More scenarios (B field outside tracker etc.) • GOALS: • Come armed as data flows in • Show we are able to spot defects and correct them on data already taken or suggest very quickly what to fiddle with T.Dorigo, INFN-Padova

9. Backup T.Dorigo, INFN-Padova