Measurement of the Top Quark Mass The Low Bias Template Method

using Lepton + jets events

Kevin Black

Meenakshi Narain

Boston University

4 high PT Jets 2 from the b-quarks 2 from hadronically decaying W

1 Isolated high PT lepton Muon or electron Tau not used in this analysis

Neutrino

Backgrounds

W+Jets Real high PT lepton Neutrino Multiple Jets ~12 pb ± 25%

Multijet Events One Jet fakes the signature of

an isolated lepton Mismeasured transverse

momentum

Event Selection

At least 4 jets with

PT > 20 GeV , || <2.5

Isolated Muon or Electron with PT > 20 GeV Muon || <2.0 Electron || <1.1

Missing ET> 20 GeV

+jets

e+jets

From Cross-Section Measurement

Topological Variables

Form log likelihood of signal over background for each variable and combine

Low Bias (“LB”) discriminant is built from four topological variables to give extra discrimination between top and background

ETA ´ 3

2£Smallest eigenvalue of P

KTmin ´(min¢ R i j ) _E

j 2T

E TW

P i j ´Pa pa i pa jPa j~pa j

2

Ltb=P j =4i=4L tbi (f i )

DL B = 11+1:25e¡ L t b

HT 2 ´H T 2H k

Topological Variables

Topological Likelihood

Discriminant

LB disc > 0.4 (optimal cut)● Remove ~50% background● Retain ~ 85% Top

Using each topological variable separately there is some separation between signal and background

however combining them in a likelihood gives optimal separation

Identifying b-quark Jets

Each top event has two b-quarks

travel a few mm and decay

Search for jets which point back to secondary vertex

Largest backgrounds for top do not have heavy flavor

Same event selection, except Jet Pt > 15 GeV Require one or more

tagged jets

Kinematic Fitting

Kinematic Fit: 1 unknown: longitudinal

momentum of the neutrino 3 constraints

Top quark and antiTop quark have the same mass

2 jets have the invariant mass of the W

lepton+neutrino have invariant mass of the W

2C fit for top mass Experimentally see Jets not

partons ! try out every permutation

Kinematic Fitting Complications

g

g

Initial state gluon radiation - extra jet, not from the top-antitop decay

Final stage gluon radiation - extra jet, splits the energy from one parton->2 jets

Neutrino: - 2 possible solutions - different starting points for fit

Performance of the Fit

In parton matched correct solution,RMS ~ 18 GeV,

Lowest 2 all events RMS ~ 30 GeV

In parton matched events,the lowest 2 solution is correct~37% of the time

Effect of b-tagging

Requiring one or more b-tagged jets increases the expected S/B dramatically without tag ~ 1/2.6 with b-tagged ~ 3/1 (also lower jet pT requirement)

Reduction of incorrect permutations: 12: untagged, 6 single tag, 2 double tag

Higher Probability of getting correct solution ! better resolution

Method to measure the top quark mass

Make Templates for signal events 9 different mass points between 150-200 GeV

Background Templates from W+jets MC Use simple Poisson likelihood for the number of signal

and background compared to data constrain the number of background events to the expected.

Signal 175 GeV Background

Multijet Distributions

Event Yield - Topological Analysis

e+jets mu+jets

top 27.5 ± 2.2 20.4 ± 0.9

W+Jets 9.5 ± 2.2 22.0 ± 2.6

Multijet 12.0 ± 0.55 2.6 ± 0.5

e+jets mu+jets

Preselection 87 80

+fit2 <10 78 68

+DLB >0.4 49 45

b

b

p p

E T

jet

jet

jet

Event Yield – b-tagged Analysis

e+jets single tag

e+jets double tag

mu+jets single tag

mu+jets double tag

Preselection 38 9 24 5

Fit Convergence

36 6 22 5

e+jets mu+jets

top 30.5 ± 2.4 22.0 ± 1.75

W+Jets 7.0 ± 0.6 4.3 ± 0.3

Multijet 4.5 ± 0.4 0.7 ± 0.05

Ensemble TestsPull: ~ 1Mean ~0

CalibrationConsistent With Slope 1And 0 offset

Statistical Error (GeV) Statistical Error (GeV)

Mass CalibrationPull

Topological:Expected Error~6.1 GeV

Tagged:Expected Error~4.2 GeV

Topological Analysis Results:

Red: background onlyBlue: background + top

Fit 44.2§ 6.6 ttbar events, expect 47.9 8.8 events

Tagged Analysis Results

Red: background onlyBlue: background + top

Fit 49.2§ 6.3 ttbar events, expect 52.4 4.2 events

Comparison with Expectation

Tagged Selection Topological Selection

Topological Discriminant in Data

Tagged Selection Topological Selection

Systematic Errors: Jet Energy Scale

S =ET

Jet- ET

ET

Photon + Jet Events - electromagnetic scale more precisely known - Compare the transverse energy of the jet and photon and compute S - Do the same with Monte Carlo events and compare the difference between data and MC

Variation of Distributions withthe Jet Energy Scale

Perform Ensemble Tests with +1, -1 compared to nominal

JES up and down for top JES up and down for Wjets

Systematic Errors: Gluon Radiation

g

g

To obtain bounds: - consider the variation seen in events with and without gluon radiation

Conservative approachbut not much is known about gluon radiation intop decays!

Gluon radiation: Kinematics of Jets

MatchedMatched –TaggedGluon JetGluon Jet –Tagged

Systematic Uncertainty

Source Topological (GeV/c2) b-tagged (GeV/c2)

Statistical

Jet Energy Scale

Jet Resolution

Gluon Radiation

Signal Model

Background Model

b-tagging

Calibration (fitting bias)

Trigger

MC Statistics

Total Systematic

Cross-Checks Vary the Discriminant Cut

Drop Constraint

on background

Constrained (Poisson)

Unconstrained

Topological 169.9 ± 5.8 GeV 170.7 ± 6.5 GeV

Tagged 170.6 ± 4.2 GeV 171.8 ± 4.8 GeV

D > 0.25 170.5 ± 5.5 GeV

D > 0.3 170.6 ± 5.5 GeV

D > 0.4 169.9 ± 5.8 GeV

D > 0.45 170.3 ± 6.5 GeV

D > 0.5 169.2 ± 5.6 GeV

D > 0.55 167.0 ± 6.5 GeV

Summary and Outlook

First measurement of the top quark mass at D using b-tagging best for Run II so far

Result Topological analysis

b-tagged analysis

Backup Slides

Event Selection: e+jets

4 jets PT > 20 GeV, || <2.5 1 electron PT > 20 GeV, || <1.1

EM Fraction > 0.9 Isolation < 0.15 Hmatrix < 50 (shower shape) EM Likelihood > 0.85 (multivariate) Track Match

ET > 20 GeV, lepton , ET triangle cuts Second high PT isolated lepton veto Primary Vertex in SMT fiducial range, with at least 3

tracks Primary Vertex within 1 cm of z position of electron track

Muon +Jets

4 jets PT > 20 GeV, || <2.5

1 muon PT > 20 GeV, || <2.0 Isolated from jets

ET > 20 GeV, lepton , ET triangle cuts

Second high PT isolated lepton veto

Primary Vertex in SMT fiducial range, with at least 3 tracks

Primary Vertex within 1 cm in z of muon track

Jet CorrectionsParton Matched Jets from W Parton Matched Jets from Top

Parton Matched Jets Z ! b¹b

Likelihood Function

L(mt, ns, nb) = P(N; N(nb)) P(Nj, Nj(ns, nb))

Nj= nspsj(mt)+ nbpj

b

The product is over the number of binsThe ps and pb are the fraction of events from that template that fall into bin jFor each template the likelihood function finds the signal fraction which minimizes the negative log likelihood and returns the value of the likelihood, and the fit number of top events. Repeated through each top mass template and then a parabola is fit through the resulting likelihoods

Discriminant Cut

Can we combine the two analyses Simplest way – remove the tagged

events from the topological analysis Find 95 events Anti-tag efficiency

Top ~40% W+jets and QCD ~90%

Expect 80% are background after removal of the tagged events.

Redo ensemble tests, expected statistical error ~11.0 GeV

Combined expected error would be ~3.9 (rather then 4.2)

However, systematic dominated so only a few percent overall improvement