T.Dorigo, INFN-Padova1 Studies of the Muon Momentum Scale M.De Mattia, T.Dorigo, U.Gasparini – Padova S.Bolognesi, M.A.Borgia, C.Mariotti, S.Maselli – Torino Apri 23, 2007

T.Dorigo, INFN-Padova2 Introduction A calibration of the momentum scale of muon tracks is crucial to achieve several goals:  Monitoring of tracker and muon chambers and their B field as a function of time, luminosity, run ….  Identification and correction of local effects in the detector  A precise W mass measurement  Reconstruction of decay signals at high invariant mass  Top mass measurements, B physics searches and measurements… The study of low-mass resonance (J/Psi, Y) and Z boson decays to dimuon pairs offers a chance of improving the tracking algorithms (by spotting problems), the simulation (tuning scale and resolution modeling) and understand the data and the physical detector better (material budget, alignments, B field)

T.Dorigo, INFN-Padova3 A first look at Z   Z bosons are special in several ways. When a sizable amount of Z   decays becomes available, it provides the opportunity to study high-Pt tracks and understand, besides effects of B field, alignment, and reconstruction algorithms, biases coming from  Energy loss  QED effects in MC  High-Pt specific biases With studies aimed at a statistics of O(100/pb) and above we have begun to map the kinematical regions to which Z are sensitive  > <  < <  <0.8  <0.3  mass pT(  )>3  (  )<2.5

T.Dorigo, INFN-Padova4 An attempt at a global calibration algorithm Usually, the dimuon mass of available resonances is studied 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 harder 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 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

T.Dorigo, INFN-Padova5 Work Plan Target two scenarios: (A) “early physics” – O(1/pb) (B) Higher statistics – some 100/pb Reconstruct dimuon resonance datasets with different pathologies, to model real- life situations we may encounter and learn how to spot and correct them  B field distortions (A, B)  Global misalignments - axial tilts of subdetectors (A,B), more subtle distortions (B)  Changes in material budget ? (B) Goal: discover how sensitive we are with resonance data to disuniformities or imprecisions in the physical model, and improve our chance of future intervention 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  Different trigger selections can be studied, possibly to determine whether choice of thresholds are sound Means: development of an algorithm fitting a set of calibration corrections as a function of sensitive observables for different quality and characteristics of muon tracks (e.g. standalone/global, low/high Pt, rapidity range, quality…)  By-product: check of muon resolution as a function of their characteristics.

T.Dorigo, INFN-Padova6 MC datasets Generate different samples of resonance decays and backgrounds targeting two scenarios: (A) “early physics” (a few 1/pb) and (B) a higher statistics (a few 100/pb)  J/Psi   (A), (B)  Psi(2s)   (B only)  Y   (B only)  Z   (B only)  pp   X (A), (B) - with different thresholds  pp   X (A), (B) – as above Create a suitable mixture of signal and background to model conditions as realistic as possible  Remove resonances from background samples using MC truth  Remove events with two true “prompt” muons from pp   X sample  Luminosity weighting  Split in two parts of equal statistics Apply distortions to geometric model or B field, re-reconstruct second sample

T.Dorigo, INFN-Padova7 Muon Scale Likelihood Use a-priori ansatz on functional dependence of Pt scale on parameters, together with realistic PDF of resonance mass  Compute likelihood of individual muon measurements and minimize, determining parameters of bias ansatz  Advantages:  can fit multiple parameters at a time  can better spot additional dependencies by scans of contribution to Ln(L) of different ranges in several parameters at once  Sensitive to non-linear behavior  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-Padova8 Nuts and bolts Played with about 65, events so far  W   (1000/nb)  Z   (2500/nb)  J/Psi   (500/nb)  pp   X (2/nb)  pp   X (50/nb) pp   X sample used for realistic test so far, all samples together for algorithm checks Studied global muons, NO quality cuts! Used ANY pair of opposite-signed muons NO matching of generator level muons (mimic real life) Define signal and sidebands region  So far only J/Psi and Z regions  GeV is J/Psi signal, 0.5*[ GeV GeV] sidebands to J/Psi  GeV is Z signal, 0.5*[ GeV GeV] is sidebands to Z Define resonance PDF  So far used gaussian PDFs for both J/Psi and Z – 0.05 GeV and 3 GeV, respectively  Needs tuning

T.Dorigo, INFN-Padova9 Mass distributions Blue: mass of global muon pairs Red: mass of simulated muon pairs Total sample  Left: low mass Middle: J/Psi Right: Z region pp  mmX sample  Left: low mass Middle: J/Psi Right: Z region

T.Dorigo, INFN-Padova10 Likelihood recipe Decide on a-priori bias function, and parameters on which it depends (e.g.: linear in Pt + quadratic in |eta| - 4 coefficients to minimize; two variables per muon) For each muon pair, determine if sidebands or signal, and reference mass  If signal region, reference mass is mass of resonance; weight is W=+1  If sidebands, reference mass is center of sideband; weight is W=-0.5 Compute dimuon mass M as a function of parameters, obtain P(M) from resonance PDF Add -2*ln(P(M))*W to sum of ln(L) Iterate on sample, minimize L as a function of bias parameters Once convergence is achieved, apply correction to muon momenta using “best” coefficients and plot mass results Also, plot average contribution to ln(L) in bins of several kinematic variables For reference, also try to correct “the old way” – e.g. by fitting mass distributions in bins of the variables (Pt, |eta|) and then fitting dependence of average mass on variables using linear function; plot mass after bias correction, compare to results using more refined method

T.Dorigo, INFN-Padova11 Mass fits – the old way Binning the data as a function of kinematic variables, one can determine how the average Z and J/Psi mass varies, and eventually extract a dependence. Top: Z mass (10 bins in average curvature) Bottom: J/Psi mass (same 10 bins in average curvature, from 0 to 0.5)

T.Dorigo, INFN-Padova12 Mass dependence on kinematics These plots show the fractional difference between reference mass and fitted mass of Z (red) and J/Psi (black) as a function of several kinematic variables. In green the weighted average of the two resonance data. Top row (left to right): average Pt, Average curvature, pair rapidity. Middle row: Pair phi, maximum |eta|,  R between muons. Bottom row: Pair Pt, eta difference, Average momentum.

T.Dorigo, INFN-Padova13 Mass results In red, original mass distributions for J/Psi (left) and Z (right) are shown for the total sample. By assuming only a dependence of the scale on muon Pt, one can fit the DM vs points derived from resonance fits, extracting a scale dependence and correcting momenta. The resulting masses of J/Psi (left) and Z (right) are shown in blue. The likelihood method uses each muon Pt assuming the same linear dependence, with sidebands subtraction. The fitted parameters are used to correct momenta and compute a corrected dimuon mass (in black) for J/Psi and Z.

T.Dorigo, INFN-Padova14 Playing with the biases Try simple parametrizations of Pt scale bias:  Linear in muon Pt  Linear in muon |Eta|  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 functions Determine if likelihood can correct the bias Promising! But we rather need to do it the hard way

T.Dorigo, INFN-Padova15 Fitting a Pt+phi bias

T.Dorigo, INFN-Padova16 Small statistics case

T.Dorigo, INFN-Padova17 Conclusions Resonance studies of low-Pt and high-Pt started with  Global fitting approach (targeting both early data and 2008 statistics)  Studies of high-Pt with Z (targeting 2008 statistics) Likelihood method stands on its feet  Many details to improve/tune/correct Several ingredients needed  Realistic trigger simulation, luminosity weighting  ID cuts on muons Need to obtain meaningful physical models with deformed geometry, odd B field – keep it realistic (use knowledge from CDF experiment) Add subtleties  Resonance PDF  Study standalone-global pairs 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  Optimize trigger cuts ?