Transcript Measurement of the W Boson Mass

A proposal for the W boson mass
measurement at CDF
Yu Zeng
Duke University
Outline
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The Standard Model
Motivation of W mass measurement
Historical W mass measurements
W mass measurement strategy at CDF
Summary
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Prelim
2
The Standard Model
H?
Z
W
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Prelim
3
The Higgs mechanism for boson masses
• The SM electroweak Lagrangian is given by:
with covariant derivative:
• We can get boson masses via Higgs mechanism
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Prelim
4
The Higgs boson
• In SM, Higgs mechanism gives rise to the Higgs boson.
• Mass of the Higgs is not determined by the theory.
• Direct searches at LEP sets lower bound:
- MH  114.4 GeV 95% CL
• Precision electroweak measurements
sets upper bound:
- MH < 144 GeV 95% CL
• Direct searches are being / will be
carried on at Tevatron and LHC.
CERN website
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Prelim
5
Motivation
• Constrain the mass of undiscovered Higgs.
Measured to 0.002%
Measured to 0.015%
Measured to 0.0009%
r: radiative corrections dominated by tb and Higgs loops
…
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Prelim
6
Theoretical calculation
• Writing out r terms (S. Dawson):
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Prelim
7
Relationship: Mw, Mtop and MH
• Current Mw, Mt relationship
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Prelim
8
Motivation
• If Higgs is found, precise Mw can be used to infer non-SM
particles. SUSY as one example.
…
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Prelim
9
Historical W mass measurements
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Prelim
10
Measurement at CDF (200 pb-1)
• W production and decay via leptons @ Tevatron
- s(p pbargW+X) Br(Wgen) ~ 2.7 nb
- produced ~ 1 in 50106 collisions
• Use data collected from Feb. 2002 – Sept. 2003
- electron channel (L = 218 pb-1)
- muon channel (L = 191 pb-1)
• Event selection leads to clean samples
- mis-identification ~0.05%
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Prelim
11
Transverse mass fitting results (200 pb-1)
T. Aaltonen et al., CDF Collab., hep-ex/0708.3642, submitted for publication in PRD.
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Prelim
12
Implication for the SM
• Including the CDF W mass measurement (200 pb-1):
Left/Right: before/after CDF 200 pb-1 Mw measurement
Implication for Tevatron
• In 2004, the estimated upper
limit for Higgs mass is 250
GeV, however Tevatron only
reach upper limit 170 GeV,
people think Tevatron has no
chance to find Higgs.
Now Tevatron is back into
the competition.
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Prelim
14
Analysis using 2 fb-1 at CDF
• About 10 times more data to analyze
- expect smaller statistical and systematic uncertainties
• Use Wgen and Wgmn channels to measure W mass
- branching ratio ~ 11%
• Use Zgee and Zgmm channels as control sample
- branching ratio each ~ 3.3%
• Use J/,  resonances to calibrate momentum
• Use E/p to calibrate electron energy
• Use information in transverse plane
- information along beam direction incomplete
• Use fast Monte Carlo simulation to extract MW
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Prelim
15
Collider Detector at Fermilab (CDF)
Muon
Detector
Central
Hadronic
Calorimeter
Central
Outer
Tracker
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Prelim
16
The CDF detector
y
x
r

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
z
Prelim
17
The CDF detector (quadrant)
Central Hadronic Calorimeter
Provides precise
measurement of
electron energy
Central E&M Calorimeter
Provides
measurement
of hadronic
recoil objects
Provides precise
measurement of
track momentum
Select W and Z bosons with central (|h| <1) leptons
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Prelim
18
MW
W boson production and decay
• Quark-antiquark annihilation dominates (~80%)
• W transverse motion due to gluon / sea quark
involved production process (~20%)
• W event signature:
- a single, isolated, high pT charged lepton
W   e n e
- a large missing energy due to neutrino
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Prelim
19
MW
Electron identification
High pT electron will
• Leave a track in tracking device
• Deposit a significant amount of
energy in EM calorimeter
Identification can be improved by:
• Matching the energy in calorimeter and
the momentum of the pointing track.
• Cutting on measured energy in areas
surrounding the electron shower.
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Prelim
20
MW
Muon identification
Muon will
• Leave a track in tracking device
• Leave hits in the muon chambers
• Very little energy deposition in
calorimeters
Constraining using beam spot will
• Increase momentum resolution
• Reject cosmic ray events
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Prelim
21
MW
Neutrino inference
Neutrino
• Will not leave direct information
• Can only be inferred in an indirect way
using momentum conservation.
In transverse plane
• Imbalance of the vector sum of lepton
pT and UT
• UT is the transverse momentum carried
by hadronic recoil
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Prelim
22
MW
The hadronic recoil UT
Three contributions to the recoil
• Jet recoiling off the W
• Underlying energy
- multiple interactions
- remnants of the ppbar collisions
• Bremsstrahlung
UT  (ux ,u y )
- photons emitted by lepton which
  E sin  ( cos  ,sin  )
are not in the excluded region
towers
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Prelim
23
MW
Measurement strategy
• Use leptonic decay modes (e, m)
• Use quantities in transverse plane
- n info along beam direction unknown
• Transverse mass:
W   e n e
mT  ( ETl  ETn ) 2  ( pTl  pTn ) 2
 2 pTl  pTn  [1  cos( )]
 2 pTl  | pTl  uT | [1  cos( )]
• Extract MW from transverse mass spectrum mT
- fitting mT (data) with mT (MC)
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Prelim
24
MW
Transverse mass spectrum
(Figure from I. Vollrath PhD thesis)
mT  2 pTl  | pTl  uT | [1  cos( )]
PT(W)=0, perfect
detector resolution
• W mass information
contained in the location
of Jacobian edge
PT(W)=0, finite
detector resolution
PT(W)0, finite
detector resolution
• Relatively insensitive to
PT(W)
 mT / mT ~ ( pTW / MW )2
• Sensitive to detector response to recoil particles.
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Prelim
25
MW
Measurement strategy
• Detector Calibration
Tracker calibration
EM Calorimeter calibration
• Fast Simulation
Data
Binned Likelihood Fit
NLO event generator
Detector response simulation
Hadronic recoil modeling
W boson mass
N
L(m)   pini (m)
i 1
pi(m) is the predicted
probability in bin i, ni is
# of data entries in bin i.
+
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Prelim
W mass templates, bule for 80 GeV, red for 81 GeV
Backgrounds
26
MW
Projected W mass precision
• Statistical uncertainties are expected to decrease as N-1/2
• Systematic uncertainties from measurements that are obtained from
control data samples (expected to decrease as N-1/2)
• Systematic uncertainties from theoretical calculations (unchanged)
• Assuming a constant theoretical uncertainty of 20 MeV (blue line).
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D. Waters, Wmass Workshop 2007
27
Summary
• Precise W mass measurement, in conjunction with the top quark
mass measurement, can constrain the Higgs boson mass.
• Use transverse information of Wgen and Wgmn channels for MW
measurement at CDF.
• MW is extracted by fitting mT(data) vs. mT(MC).
• With 10 times more data, we expect to reach the 25 MeV
uncertainty goal in MW.
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Prelim
28
Backup slides …
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29
MW
Choices of SM parameters
Physical Quantity
No.
Fermion masses (6 quark + 3 lepton) 9
Higgs Boson
1
Quark weak mixing parameter
4
em g gz GF mW mZ sin2 W v Strong CP violation parameter
1
Can be chosen from:
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Strong interaction coupling constant
1
Fundamental EWK parameters
3
Neutrino masses
3
Neutrino mixing parameter
4
Prelim
Total = 26
30
MW
Choices of electroweak parameters
em g gz GF mW mZ sin2 W v
Choice 1.
Follow the pattern that parameters are
masses and coupling constants.
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Choice 2.
Choose parameters measured most precisely.
Prelim
31
MW
Why two coupling constants
e
e
e
g
ne
e
Z0
W
ge  4
gW 
ge
1  ( MW / M Z )
e
2
gZ  ge (M Z / MW )
Thus, only two coupling constants:
1) e2/(4hc)=1/137;
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2) S for strong coupling
Prelim
32
Boosts along beam axis
• Define rapidity:
1 E  pz 1 1  pz / E 1 1  b cos 
y  ln
 ln
 ln
, b  p/E
2 E  pz 2 1  pz / E 2 1  b cos 
• Boosts along the beam axis +z (so cos1) with v=bb will
change y by a constant yb
1  bb
1 1  bb
yb  ln
 ln
 ln[g (1  bb )]
2 1  bb
1  bb
• Boost of velocity bb along +z axis
- pz  g(pz + bb E)
1 E  pz 1 g ( E  b b pz )  g ( pz  b b E )
y  ln
 ln
- E  g(E+ bb pz)
2 E  pz
2 g ( E  b b pz )  g ( pz  b b E )
- Transform rapidity:
1 ( E  pz )(1  bb )
 ln
 y  ln g (1  bb )
2 ( E  pz )(1  bb )
y  y  yb
• Pseudo-rapidity: neglecting mass (b=1)
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33
MW
Particle identification
• Particle detectors measure long-lived particles produced
from high energy collisions: electrons, muons, photons
and “stable” hadrons (protons, kaons, pions)
• Quarks and gluons do not appear as free particles, they
hadronize into a jet.
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34
MW
Some facts about CDF detector
• Central Out Tracker
- Hit position resolution ~140 mm
- Momentum resolution: s(pT)/pT
COT alone: 0.15% pT-1
COT beam constrained: 0.15% pT-1
• Central Calorimeter
- CEM: energy resolution s(E)/E =13.5%/sqrt(E·sin)
- CHA: energy resolution s(E)/E =0.5/sqrt(E)
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MW
Main backgrounds
• For Wgmn:
- largest background comes from Zgmm
- Wgtngmnn events
- cosmic rays
- kaon decays in flight
- events where one jet contains one non-isolated m
• For Wgen:
- Zge+e- Wgtngem
- events where one jet contains one non-isolated e
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MW
Event Selection for W & Z
• Select clean W & Z samples to get maximum ratio of S/N
- trigger info: pt(e, m) >18 GeV
- central lepton selection: |h|<1
- final analysis: pt(e, m) >30 GeV
- W boson further requires:
uT<15 GeV, Et >30GeV
- Z boson: two oppositely charged leptons with opposite
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MW
Helicity and Handedness
• Helicity:
- spin projection (l) of a particle along its direction of motion
- e.g., l1/2 for e; l1/2 for e+
-  = A++ + A
• Handedness:
- a particle state projected out by (1g5)/2
- R= (1g5)/2 ; L= (1g5)/2 
-  = R  L
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38
MW
V-A nature of W boson decay
• The fact that W couples only to left-handed quarks/leptons or
right-handed anti-quarks/anti-leptons are confirmed by
experimentally observed W decay asymmetry.
• cos*= -1 is favored, which means e+ goes predominantly in the
direction opposite to the original proton.
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Prelim
39
Jacobian edge
• First work with ds/dpTe with pT(W)=0 case:
- assume pT(W)=0
ds
ds
2 ds


dpTe M W d sin  M W d sin 
2
2
ds d cos 

M W d cos  d sin 

2
s 0 ( sˆ)(1  cos 2  ) tan 
MW
ds
 s 0 ( sˆ)(1  cos 2  )
d cos 
s 0 (sˆ)  Breit  Wigner
4 pTe
4 pTe 2
1
 s 0 ( sˆ)
(2 
)
2
MW
MW
1  4( pTe / M W ) 2
- Since mT2=4(pTe)2, transfer to ds/dmT
mT
mT 2
ds
1 ds
1
ˆ


s
(
s
)
(1

)
0
dmT 2 dpTe
MW
M W 2 1  (mT / M W ) 2
• Spreading around MW is due to W, pT(W) no equal to zero.
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40
mT/mT
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41
Diagram
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