Studies of the Muon Momentum Scale

1. 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-Padova

2. 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-Padova

3. A first look at Zmm • Z bosons are special in several ways. When a sizable amount of Zmm 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  mass pT()>3 ()<2.5 >1.2 0.8<<1.2 T.Dorigo, INFN-Padova 0.3<<0.8 <0.3

4. 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-DR 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(mm) vs <Pt> • Idea: try to let each muon speak, with a multi-dimensional approach T.Dorigo, INFN-Padova

5. Work Plan • Target two scenarios: • “early physics” – O(1/pb) • 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-Padova

6. 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  mm (A), (B) • Psi(2s)  mm (B only) • Y  mm (B only) • Z  mm (B only) • pp  mX (A) , (B) - with different thresholds • pp  mmX (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mX 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-Padova

7. 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-Padova

8. Nuts and bolts • Played with about 65,000 1.2.0 events so far • W mn (1000/nb) • Zmm (2500/nb) • J/Psimm (500/nb) • ppmX (2/nb) • ppmmX (50/nb) • ppmmX 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 • 3.097+-0.15 GeV is J/Psi signal, 0.5*[2.647+-0.15 GeV + 3.547+-0.15 GeV] sidebands to J/Psi • 90.67+-8 GeV is Z signal, 0.5*[66.67+-8 GeV + 114.67+-8 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-Padova

9. 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-Padova

10. 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-Padova

11. 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-Padova

12. 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|, DR between muons. Bottom row: Pair Pt, eta difference, Average momentum. T.Dorigo, INFN-Padova

13. 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 <Pt> 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-Padova

14. 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-Padova

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

16. Small statistics case T.Dorigo, INFN-Padova

17. 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 ? T.Dorigo, INFN-Padova