Helicity of the W in Single-lepton ttbar Events

1
Helicity of the W in Single-lepton ttbar Events

• Florencia Canelli
• University of Rochester D?
• APS Meeting April 20, 2002

2
Introduction
-

• In the Standard Model
• 1. If mb0, only W0 and W- helicities
• 2. W0 fraction 0.703 with mt 175GeV
• and mW80.4GeV
• 3. W fraction 0.04, larger W fraction will
• indicate VA coupling at the tbW vertex

b
-
q
p
-
l
W-
-
q
W
p
n
W
b
b
ttbar Single-lepton jets
Top rest frame

• Kinematics of ttbar Single-lepton jets
• (e jets and ?jets)
• Branching ratio of about 30
• 24 permutations among jets

t
t
Momentum direction
W
b
Spin direction
W0
W-
3
Matrix Element
no ttbar spin correlation included
sqt sine of angle between q and t in the qq CM
b top quark's velocity in the qq CM
gs strong coupling constant
Leptonic decay
Hadronic decay
Mt, MW pole top and W mass mt top mass in any
event men ,mdu invariant mass of the en and du
(or cs) system Gt, GW top and W width gW weak
coupling constant w(cos jeb,db) angular
distribution of the W decay
4
Angular dependence of the Matrix Element
n
b
t
W
In SM (with mb 0),
j
e
where a MW2/Mt2
W rest frame
w-(cosj) 3/8(1-cosj)2 w0(cosj)
3/4(1-cosj2) w(cosj) 3/8(1cosj)2
Left handed
Longitudinal
Left-handed
Longitudinal
Right-handed
Right handed
5
ttbar Probability
Sum over 12 combinations of jets and neutrino
solutions ?1 momentum of one of the
jets m1,m2 top mass M1,M2 W
mass f(q1),f(q2) parton distribution function
(CTEQ4) q1,q2 parton momentum ?6
phase space W(x,y) probability of
measuring x when y was produced We chose these
variables of integration since the M2 is almost
negligible except near the four peaks of the
Breit-Wigners within M2.
6
Acceptance Corrections
Likelihood
Detector Acceptance
Measured probability
Detector Acceptance
Produced probability
where
and Ngen is the number of generated events
7
Transfer functions W(x,y)
W(x,y) probability of measuring x when y was
produced x jet variables, y parton
variables
where Ey energy of the
produced quarks Ex measured
and corrected jet energy pye
produced electron momenta pxe
measured electron momenta ?y j
?xj produced and measured jet angles
Energy of electrons is considered well measured.
And due to the excellent granularity of the D?
calorimeter angles are also considered as well
measured
8
Transfer functions Wjet(x,y)
Model the smearing in jet energies from effects
of radiation, hadronization, measurement
resolution and jet reconstruction algorithm
These effects produce asymmetry
Correcting on average, and considering these
distributions to be Gaussian, can underestimate
the jet energy
Use 2 Gaussians, one to account for the peak and
the other to fit the asymmetric tails,
9
Test of the Transfer Function to tt events
Angular decay of the W
Top Mass
Histogram Herwig D0 Run I simulation and
reconstruction and standard criteria Solid Line
Exact calculation using transfer function
In red Pythia events after applying transfer
function and standard criteria In black Herwig
D0 Run I simulation and reconstruction and
standard criteria
10
Test of the Transfer Function for Wjets
Angular decay of the W
3 jets invariant mass
3 jets invariant mass using Wjets events from
VecbosIsajet with 4 jets without requiring
matching to initial partons.
In red VecbosIsajet Wjets events In black
Herwig ttbar events
11
Event Sample
Events 80,000 ttbar ejets PYTHIA with mt
175 GeV, mW 80.4 GeV at

a 0.211 and F0 0.703
Jet Resolutions Wjet(x,y)
Selection Criteria jets
4 jets, ETjgt15 GeV and ?lt2
electron ETgt20 GeV, ?e lt2
missing ET gt20 GeV

• Run I statistics
• Signal
• 29 ttbar-gtleptonjets
• Background
• Wjets 30
• QCD 10

--- before cuts --- after cuts
--- before cuts --- after cuts
12
MC Results
30 experiments of 30 events
Pull

• Using only the angular part of
• the M.E.
• P(a) (1cosj)2 a (1-cosj2)
• Right assignment of jets
• Correct neutrino momentum
• Extract F00.67?0.15

Leptonic decay
Hadronic decay
LepHad decays
Using 100 events
13
MC Results

• Using the full probability calculation
• Sum over all the combination of jets
• Sum over the neutrino solutions
• W(x,y)
• Obtain F00.64?0.16

Using 30 events
14
Conclusions

• We use developed a method based on the full
  probability calculation to measure the
  longitudinal W helicity fraction in Monte Carlo
  events
• Events were smeared using a realistic transfer
  function
• Not knowing the neutrino momenta or the right
  combination does not increase the error in the
  measurement substantially
• We can recover the W helicity fraction after
  apply acceptance corrections
• With a MC sample comparable in statistics to the
  Run I dataset we obtain a value for the
  longitudinal fraction F0 of 0.64?0.16

15
Linearity with 30 events