1. T.Dorigo, INFN-Padova1 Muon Momentum Scale Status and plans M.De Mattia, T.Dorigo, U.Gasparini – Padova S.Bolognesi, C.Mariotti – Torino CMS-Padova – 1 ottobre 2007

2. T.Dorigo, INFN-Padova2 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-  R 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(  ) vs Idea: try to let each muon speak, with a multi-dimensional approach

3. T.Dorigo, INFN-Padova3 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

4. T.Dorigo, INFN-Padova4 Muon Scale Likelihood Use a-priori ansatz of functional dependence of P t 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.

5. T.Dorigo, INFN-Padova5 Likelihood recipe Decide on a-priori bias function, and parameters on which it depends  e.g.: linear in P t - 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 M  signal region, reference mass is mass of resonance; weight is W=+1  If M  sidebands, 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” coefficients Pt’ = Pt * [ A + B * Pt ]  Can then compare mass before/after correction  Also plot average contribution to F in bins of several kinematic variables

6. T.Dorigo, INFN-Padova6 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

7. T.Dorigo, INFN-Padova7 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

8. T.Dorigo, INFN-Padova8 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

9. T.Dorigo, INFN-Padova9 Backup