T.Dorigo, INFN-Padova 1

Muon Momentum ScaleStatus and plans

M.De Mattia, T.Dorigo, U.Gasparini – PadovaS.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-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 <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 Msignal region, reference mass is mass of resonance; weight is W=+1 If Msidebands, 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

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Status of code and MC Ported original routines in CMSSW Now working with 1_6_0 So far, testing with Zmm 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

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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

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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

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