Studies of the Muon Momentum Scale

T.Dorigo, INFN-Padova 1

Studies of the Muon Momentum Scale

M.De Mattia, T.Dorigo, U.Gasparini – PadovaS.Bolognesi, M.A.Borgia, C.Mariotti, S.Maselli – Torino

Apri 23, 2007


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)


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

>1.2 0.8<<1.2

0.3<<0.8 <0.3

masspT()>3()<2.5


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 <Pt> Idea: try to let each muon speak, with a multi-dimensional approach


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.


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 ppX sample Luminosity weighting Split in two parts of equal statistics

Apply distortions to geometric model or B field, re-reconstruct second sample


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.


Nuts and bolts Played with about 65,000 1.2.0 events so far

W (1000/nb) Z(2500/nb) J/Psi (500/nb) ppX (2/nb) ppX (50/nb)

ppX 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


Mass distributionsBlue: mass of global muon pairsRed: mass of simulated muon pairs

Total sample

Left: low massMiddle: J/PsiRight: Z region

ppmmX sample

Left: low massMiddle: J/PsiRight: Z region


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


Mass fits – the old way

Binning the data as a functionof kinematic variables, onecan determine how the averageZ and J/Psi mass varies,and eventually extract adependence.

Top: Z mass (10 bins in average curvature)

Bottom: J/Psi mass (same 10 bins in average curvature, from 0 to 0.5)


Mass dependence on kinematics

These plots show the fractionaldifference between reference massand fitted mass of Z (red) and J/Psi(black) as a function of severalkinematic variables. In green theweighted average of the tworesonance 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.


Mass resultsIn red, original mass distributionsfor J/Psi (left) and Z (right) areshown for the total sample.

By assuming only a dependenceof the scale on muon Pt, onecan fit the DM vs <Pt> pointsderived from resonance fits,extracting a scale dependenceand correcting momenta.The resulting masses of J/Psi(left) and Z (right) are shownin blue.

The likelihood method useseach muon Pt assuming thesame linear dependence, withsidebands subtraction. Thefitted parameters are used tocorrect momenta and computea corrected dimuon mass (inblack) for J/Psi and Z.


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


Fitting a Pt+phi bias


Small statistics case


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 ?

Documents

Studies of the Muon Momentum Scale