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Studies of the Muon Momentum Scale


A calibration of the momentum scale of muon tracks is crucial to ... Forcefully bias muon momenta using functions. Determine if likelihood can correct the bias ... – PowerPoint PPT presentation

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Title: Studies of the Muon Momentum Scale

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
  • 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
  • Top mass measurements, B physics searches and
  • 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?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(?)gt3 ?(?)lt2.5
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
  • 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 ltPtgt
  • Idea try to let each muon speak, with a
    multi-dimensional approach

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,
  • 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 ? 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
  • 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

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
  • 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? 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
  • Define signal and sidebands region
  • So far only J/Psi and Z regions
  • 3.097-0.15 GeV is J/Psi signal, 0.52.647-0.15
    GeV 3.547-0.15 GeV sidebands to J/Psi
  • 90.67-8 GeV is Z signal, 0.566.67-8 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 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
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 W1
  • 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 -2ln(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 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)
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.
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 ltPtgt
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.
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

Fitting a Ptphi bias
Small statistics case
  • Resonance studies of low-Pt and high-Pt started
  • Global fitting approach (targeting both early
    data and 2008 statistics)
  • Studies of high-Pt with Z (targeting 2008
  • Likelihood method stands on its feet
  • Many details to improve/tune/correct
  • Several ingredients needed
  • Realistic trigger simulation, luminosity
  • 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
  • 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