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Top Quark Physics
Suyong Choi
Korea University
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Top Quark in the Standard Model
Measurement of Production Cross Sections
Properties of the Top Quark
Summary and Outlook
Contents
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TOP QUARK IN THE STANDARD
MODEL
• Discrete quantum numbers
• Spin
• Weak isospin
• Charge
• Mass
• Lifetime or Decay width
• Branching fraction
• Coupling – QCD, EW
Properties of Top Quark
• Top quark carries “color” and interacts with gluons
• Production of top quark pairs is important probe of QCD
interactions
QCD
• Fermion part
𝑢𝑖
𝜈𝑖
𝜓𝑖 = ℓ− 𝑜𝑟 𝑑 ′
𝑖
𝑖
• Interaction with H, W, , Z
Electroweak Lagrangian
• Strong interaction: 𝑔 → 𝑡𝑡
• Coupling to neutral gauge boson: 𝛾/𝑍 → 𝑡𝑡
• Coupling to charged gauge boson: 𝑡 → 𝑊 + 𝑏
• Coupling to Higgs field (boson): 𝐻 → 𝑡𝑡
• Coupling to Higgs field:
𝑔𝑚𝑡
2𝑀𝑊
≈ 0.995
Interactions of Top Quark
in SM
• Decays to physical states
• Top decays almost 100% to W+b
Top Quark Decays
Decays of Top Quark
• 1.3 GeV width for 172 GeV top quark
• 𝜏𝑡𝑜𝑝 = ? s
• Top quarks are produced and decay like free quarks with spin a
t production information intact
• Hadron formation time
1
Λ𝑄𝐶𝐷
≫
1
Γ𝑡
• Hadron formation is governed by light-quark dynamics
• In contrast, B mesons decay isotropically
Top Decay Width
• Top quark polarization is reflected in angular distribution
of decay products
1 𝑑Γi
1 + 𝛼𝑖 cos 𝜃 ∗
=
∗
Γi 𝑑 cos 𝜃
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Particle

Charged lepton
1
Neutrino
-0.31
B quark
-0.41
Polarized Top Quark
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TOP QUARK AND
ELECTROWEAK PRECISION
DATA
• Radiative corrections to W and Z propagator
• Quadratic sensitivity to fermion masses
𝑔2 + 𝑔′2
𝜌=
8𝑀𝑍2
2
𝐺𝐹
𝜌 ≈1+
3𝐺𝐹 𝑚𝑡2
8𝜋 2 2
Top Quark Corrections to
Electroweak Measurements
• W and Z masses
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𝑀𝑊
=
𝜋𝛼
2𝐺𝐹 sin2 𝜃
𝑀𝑍2
=
𝜋𝛼
2𝐺𝐹 𝜌 sin2 𝜃 cos 2 𝜃
• Z mass was measured very precisely at LEP experiments
• 𝑚𝑡 could be inferred with knowledge of 𝑀𝑍 , 𝐺𝐹 , sin2 𝜃
• Test of EW theory
Top Quark and Electroweak
Measurements
• Top quark mass could be
predicted from precision
measurements
170 ± 10+17
−19 𝐺𝑒𝑉
𝑚𝑡 Prediction from LEP
CDF
CDF
DØ
DØ
Top Quark
Runfrom
2 results
Top Mass Distributions
1995 observation paper
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Success of the SM
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• LEP EW precision res
ults from 𝑒 + 𝑒 − → 𝑍 0
Top Quark Mass from
Electroweak Data
• In conjunction with W and Z,
we can gain information on Higgs
mass
Δ𝜌 = −
3
𝑀𝐻
ln
8𝜋 cos 2 𝜃 𝑀𝑊
Connection with Higgs
• Top quark is special
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Most massive
Interaction only within 3rd generation
top-Higgs coupling ~ 1
2
𝑚𝑡 × 𝑚𝑍 ≈ 𝑚𝐻
Boundary between metastability
and stability
The Top Quark
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5 fb-1 @ 7 TeV
20 fb-1 @ 8 TeV
LHC and Experiments
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• Properties
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Mass
Decay width
Spin
Coupling
• Cross section
measurements
• Production and decays
Physics with Top Quarks
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• Higher cross section
and higher luminosity
at LHC
• Top quark factory
• Rare processes with top
quarks
• New physics with top
quarks
• Tevatron and LHC are
complementary
Cross Sections at
Tevatron and LHC
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PRODUCTION
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Pair production
diagams
• Strongly produced
• Contribution of 𝑞𝑞 and
𝑔𝑔 changes as 𝑠
𝑡𝑡 Pair Production
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Dilepton:
ee, e, 
tau+X
Multijet
mu+jets
e+jets
Lepton+jets
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𝐵𝑟 𝑡 → 𝑏ℓ𝜈 = 10.6% per lepton flavor
Multijet – Highest statistics, but large backgrounds and combinatorics
Lepton+jets – Highest statistics and usually yields best measurement
Dilepton – Smaller statistics but clean, less combinatoric, solving for 2
neutrino momenta not trivial
𝑡𝑡 channels
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• Lepton+Jets
• 1 charged lepton
• 4 hadronic jets (2 are b-quark jets)
• Missing ET
• Problem
• How to correctly assign jets to top or antitop
• How to reconstruct neutrino momentum
Reconstructing tt-bar
Events
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• 1 unknown: neutrino 𝑝𝜈,𝑧
• 𝑝𝜈,𝑥 = 𝑀𝐸𝑇𝑥 , 𝑝𝜈,𝑦 = 𝑀𝐸𝑇𝑦
• 3 constraints:
𝑚 𝑗1𝑗2 = 𝑀𝑊
𝑚 ℓ𝜈 = 𝑀𝑊
𝑚 ℓ𝜈𝑏1 = 𝑚(𝑏2 𝑗1𝑗2)
• Problem of combinatorics
• 2 fold ambiguity – if 2 b-jets tagged
• 6 fold ambiguity – if 1 b-jet tagged
Top Quark Reconstruction
in L+Jets
• Have to consider
• experimental uncertainties on measurements
• finite widths of W and top
• Numerically minimize 𝜒 2 event-by-event
Top Quark Reconstruction
in L+Jets
TOP PRODUCTION CROSS
SECTION
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• Experimental error comparable to theory error
• QCD explains well the inclusive pair production
Pair Production Cross
Section
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s and t channel
• Electroweak production
• Cross section of the same
order as pair production
• Sensitive probe of |𝑉𝑡𝑏 | without
the assumption of 3 generation
of quarks
W associated
Single Top Production
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Single Top Production
t-channel
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Signal Region
𝜎 𝑝𝑝 → 𝑊𝑡 = 23.4+5.5
−5.4 𝑝𝑏
Control Region
6.0𝜎 significance
Observation of Wt Single
Top Production
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• From single top quark production cross section, we can
measure |𝑉𝑡𝑏 | directly without assuming 3 generation of
quarks
• Current best direct measurement:
𝑉𝑡𝑏 = 1.020 ± 0.046(𝑒𝑥𝑝𝑡. ) ± 0.017(𝑡ℎ𝑒𝑜𝑟. )
Measurement of |𝑉𝑡𝑏 |
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PROPERTIES
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• Tevatron: 𝑚𝑡 = 173.20 ± 0.87 GeV – 0.5% accuracy
Mass of Top Quark
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• CPT violated if 𝑚𝑡 ≠ 𝑚𝑡
• 𝑡 and 𝑡 distinguished by electric charged of lepton
Δ𝑚𝑡 = −272 ± 196 𝑠𝑡𝑎𝑡 ± 122(𝑠𝑦𝑠𝑡)
Mass Difference of 𝑡 and 𝑡
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• In SM, top quark width at NLO is
• 1.29 GeV/c2
• Lifetime of 0.5 × 10−24 𝑠
• Decay width reflected
in reconstructed mass distribution
• CDF measures Γ𝑡 = 2.21+1.84
−1.11 GeV
• Γ𝑡 < 6.38 GeV @ 95% CL
Decay Width of Top Quark
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• 𝑄𝑐𝑜𝑚𝑏 = 𝑄ℓ × 𝑄𝑏−𝑗𝑒𝑡
• B-jet charge calculated
from tracks associated
with b-jet
Electric Charge of Top
Quark
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• Use lepton angular
distribution in top rest
frame
• W from top decays
are either left-handed
or longitudinal
W Polarization from Top
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• On average, spin of top and antitop are unpolarized, but event-by-event,
their spins are correlated
• Most prominent in 𝑞𝑞 initial state: aligned top spin
• For gg mostly anti-aligned spins
• Results depend on spin quantization axis chosen
𝑡𝑡 Produced at Rest
Relativistic top
𝑡
𝑞
𝑡
𝑞
𝑡
𝑞
𝑞
𝑡
Spin Correlation in 𝑡𝑡
Production
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• 𝑞𝑞 → 𝑡𝑡 and 𝑔𝑔 → 𝑡𝑡 the spins
of top quarks are correlated
• Due to 𝜏𝑡 ≪ 1/Λ𝑄𝐶𝐷 , spin state
of top at production reflected in
decay products
• Lepton is the most sensitive
probe of top spin polarization
• Tevatron and LHC has different
contributions of 𝑞 𝑞 and 𝑔𝑔
• ATLAS observed spin
correlations at 5.1 s.d.
𝑓 𝑆𝑀 = 1.30 ± 0.14 𝑠𝑡𝑎𝑡
+0.27
−0.22 (𝑠𝑦𝑠𝑡)
Spin Correlation
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Top Coupling with Vector
Bosons with 𝑡𝑡𝑊and 𝑡𝑡𝑍
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• Major background to
𝑡𝑡 + 𝐻(→ 𝑏𝑏)
• Number of b-tagged
jets distribution
𝑡𝑡 + 𝑏𝑏 Production
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SEARCHES WITH TOP QUARKS
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Search for Resonances
Decaying into 𝑡𝑡
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Anomalous Single Top
Search for 𝑡 → 𝑍𝑞
• 𝑔𝑞 → 𝑡
𝐵 𝑡 → 𝑍𝑞 < 0.0021 @ 95% 𝐶𝐿
Search for FCNC
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• Top-Higgs coupling almost 1
• Consistent with backgrounds
• Cross section limits at
Search for 𝑡𝑡 + 𝐻
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• Approaching 20 years of rich physics program at hadron
colliders with top quark events
• Top quark production and properties consistent with SM
• Many measurements systematics limited.
What can you do with millions of top quark events?
Summary and Outlook
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BACKUP
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• When Υ was discovered in 1977, it was considered as a bound
state of 𝑏𝑏 quarks. Hence extra quark was thought to exist.
• It took a long time until top quark was discovered in 1995 by
CDF and D-Zero experiments using Fermilab Tevatron
accelerators
• Being the most massive quark, it may hold the key.
• With the luminosity and energy reach of the LHC at CERN,
top quarks can be studied with unprecedented precision.
• 1.96 TeV → 8 TeV
Introduction
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• 6th quark discovered
• Partner to bottom quark predicted after discovery of Υ
• “gauge anomaly” of SM must be absent
• Electric charge inferred from Υ → 𝑒 + 𝑒 − using quarkonium mo
del
• Weak isospin inferred from forward backward asymmetry
• 1995 by D-Zero and CDF experiments @ Fermilab
The Top Quark
Channel
Luminosity
CDF Lepton+jets
9.4 fb-1
0.094+0.032
−0.029
D0 Lepton+jets
9.7 fb-1
0.047+0.025
−0.027
D0 Dilepton
9.7 fb-1
0.058 ± 0.053
𝐴ℓ
SM prediction @ NLO: 𝐴𝑙 = 0.036 ± 0.002
Lepton AFB in 𝑡𝑡
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• 𝜎𝑡𝑡 is a function of 𝑚𝑡 and 𝛼𝑠 𝑀𝑍
Strong Coupling Constant
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• Dilepton channel – 2 leptons + 2 b-jets + Missing ET
• 𝑀𝐸𝑇 = (𝑝𝜈,𝑥 + 𝑝 𝜈,𝑥 , 𝑝𝜈,𝑦 + 𝑝 𝜈,𝑦 )
• Unknowns
• Neutrino momentum components – 2 x 3 = 6
Top Quark Reconstruction
in Dilepton
• Lepton asymmetry reflects
• Asymmetry in production
• Polarization of 𝑡𝑡: 𝑡𝑅 𝑡𝑅 vs 𝑡𝐿 𝑡𝐿
• SM predicts small asymmetry in production and no
polarization
Lepton ForwardBackward Asymmetry
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𝑚 ℓ1 𝜈1 𝑏1 = 𝑚(ℓ2 𝜈2 𝑏2 )
• Constraints
2-fold ambiguity in
Lepton-jet assignment
𝑚 ℓ1 𝜈1 = 𝑀𝑊
𝑚 ℓ2 𝜈2 = 𝑀𝑊
𝑝𝜈1,𝑥 + 𝑝𝜈2,𝑥 = 𝑀𝐸𝑇𝑥
𝑝𝜈1,𝑦 + 𝑝𝜈2,𝑦 = 𝑀𝐸𝑇𝑦
System is
Underconstrained!
Top Quark Reconstruction
in Dilepton
• If top quark mass is assumed, then the number of constraints =
number of unknowns
• But, still, up to 4 solutions are possible – intersection of 2 ellipses
in 2-D space * 2 fold ambiguity
• Numerically maximize likelihood event-by-event
• Assume momentum and mass spectra of 𝑡𝑡 system
Top Quark Reconstruction
in Dilepton