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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

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?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

?gt1.2

0.8lt?lt1.2

0.3lt?lt0.8

?lt0.3

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 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,

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 ? 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

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? 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, 0.52.647-0.15

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

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 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

way

Fitting a Ptphi 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