Model independent analysis of top FB asymmetry
at the Tevatron
Pyungwon Ko
Korea Institute for Advanced Study (KIAS)
in collaboration with
Dr. J.-S. Lee, Dr. D.W. Jung (and Dr. S.H. Nam)
based on arXiv:0912.1105, PLB 2010.06.040 and
arXiv:1011.5976 and work in preparation
< Seminar at NTCS, NTHU, Dec. 07 (2010) >
Pyungwon Ko (KIAS)
AFB of top quark production
1 / 38
Outline
1
Introduction
2
Effective Lagrangian Approach
Forward-Backward Asymmetry
Helicity Amplitude
Spin-Spin Correlation
3
Models including new resonances explicitly
Spin-1 Resonances
Spin-0 Resonances
Wilson Coefficients from Resonances
Examples of Resonances
4
Longitudinal Pol of (anti)top quark
P violation and Longitudinal Pol’s
5
Summary
Pyungwon Ko (KIAS)
AFB of top quark production
2 / 38
Introduction
Top pair production via strong interaction
Tevatron:
LHC:
∼ 90%
Pyungwon Ko (KIAS)
AFB of top quark production
∼ 10%
3 / 38
Introduction
Motivation
Top physics has began to enter a new era after its first discovery,
due to the high luminosity achieved at the Tevatron, and precision
study will be possible at the LHC in the coming years.
Forward-backward asymmetry AFB in t t̄ production has been off
the SM prediction (∼ 0.078(9)) by 2σ in the t t̄ rest frame (CDF2008):
AtFB ≡
Nt (cos θ ≥ 0) − Nt̄ (cos θ ≥ 0)
= 0.24 ± 0.13 ± 0.04
Nt (cos θ ≥ 0) + Nt̄ (cos θ ≥ 0)
This ∼ 2σ deviation stimulated some speculations on new physics
scenarios
We adopt a model independent approach using effective
Lagrangian in order to accommodate the current measurement of
AtFB , since there is no clear evidence for any new particles
coupling to top at the Tevatron
Pyungwon Ko (KIAS)
AFB of top quark production
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Introduction
New CDF data with 5.6 fb−1 presented this summer
0.158 ± 0.072 ± 0.017
Less deviation than before
→ Any new physics scale is probably too high to be explored
directly at the Tevatron
Still interesting to speculate what type of new physics can modify
top physics at what level
In fact, our approach based on the effective lagrangian could be
more useful in this case, than other approaches
Also could be used to set substructure scale of top quark, as in
the light quark system
Pyungwon Ko (KIAS)
AFB of top quark production
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Introduction
SM contribution to AFB
Series of papers by Kühn and Rodrigo
LO: top quark production angle is symmetric with respect to beam
direction.
NLO: asymmetry due to interference effects.
Pyungwon Ko (KIAS)
Born
Box
ISR
FSR
AFB of top quark production
6 / 38
Introduction
Related works
SM predictions: Kühn and Rodrigo
I
I
I
Interference between tree (one gluon exchange) and one-loop (two
gluon exchange)
(anti)quark-gluon scattering into t t̄g
initial (final) gluon emission q q̄ → t t̄g
Axigluon: Godbole et al.; Rodrigo et al.; Frampton, Shu, Wang;
Chivukular, Simmons, CP Yuan
0
Extra Z : Jung, Murayama, Pierce, Wells
0
Extra W : Cheung, Keung, TC Yuan
RS KK gluon: Djouadi et al.
Color sextet or antitriplet: Tait et al.; CH Chen et al.; Berger et al.;
RPV and LR model: Cao, Heng, Wu, Yang
Comprehensive study: Cao, McKeen, Rosner, Shaughnessy,
Wagner
Effective Lagrangian Approach : this talk
Apologies to those who are not listed
Pyungwon Ko (KIAS)
AFB of top quark production
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Introduction
Wisdom from EW sector
The first evidence of asymmetry was found in angular√distribution
of muons from e+ e− collisions at PETRA in the 80’s ( s ∼ 30
GeV , well below the Z 0 pole)
Source of AFB is a term linear in cos θ from interference between γ
or Z vector coupling and the axial vector Z coupling.
Pyungwon Ko (KIAS)
AFB of top quark production
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Effective Lagrangian Approach
Dim-6 Contact Interaction
t t̄ production at the Tevatron dominated by q q̄ channel
Enough to consider dimension-6 four-quark operators assuming
new physics scale is high enough:
i
g 2 X h AB
AB
L6 = s2
C1q (q̄A γµ qA )(t̄B γ µ tB ) + C8q
(q̄A T a γµ qA )(t̄B T a γ µ tB )
Λ
A,B
where
T a = λa /2,
{A, B} = {L, R},
L, R ≡ (1 ∓ γ5 )/2 (q = u, d, s, c, b)
Other d=6 operators are all reducible to the above operators after
Fierzing (Hill and Parke 1994)
We ignore flavor changing dim-6 operators such as dR γ µ sR tR γµ tR ,
since those contributions to the t t̄ production cross section will be
of a order 1/Λ4
Pyungwon Ko (KIAS)
AFB of top quark production
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Effective Lagrangian Approach
Digress on Top Substructure
Our appraoch is useful even if the AFB approaches the SM
prediction
This contact term used to explore light quark substructures
Similar analysis has been done for light quark and lepton systems
using q̄q q̄q, q̄q l̄l, and l̄l l̄l, with various Dirac and color structures
One can do exactly the same analysis for top compositeness scale
The scale Λ in our effective lagrangian could be interpreted as
Compositemess scale of a top quark seen by a light quark
Bound on Λ can be derived from Mt t̄ or pTt distributions at the
Tevatron
Pyungwon Ko (KIAS)
AFB of top quark production
10 / 38
Effective Lagrangian Approach
Helicity Amplitude Squared
The squared helicity amplitude is given by
ŝ
4 gs4 2
2
m 2 + 2 (C1 + C2 ) sθ̂2
|M(tL t̄L + tR t̄R )| =
9 ŝ t
Λ
4
2
g
ŝ
s
|MtL t̄R + tR t̄L )|2 =
1 + 2 (C1 + C2 ) (1 + cθ̂2 )
9
2Λ
ŝ
+ β̂t
(C1 − C2 ) cθ̂
2
Λ
where
LL
RR
C1 ≡ C8q
+ C8q
,
β̂t2 = 1 − 4mt2 /ŝ,
LR
RL
C2 ≡ C8q
+ C8q
sθ̂ ≡ sin θ̂,
cθ̂ ≡ cos θ̂
The term linear in cos θ̂ could generate the foreward-backward
asymmetry which is propotional to ∆C ≡ C1 − C2 .
Pyungwon Ko (KIAS)
AFB of top quark production
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Effective Lagrangian Approach
Allowed region in the (C1 , C2 ) plane
"
4
0.
10
6
=
A
FB
98
7.
"
pb
=
02
7.
II
pb
0
0.
38
I
=
-2
A
FB
C2 (1 TeV/!)2
=
2
IV
-4
III
-6
Pyungwon Ko (KIAS)
-6
-4
-2
0
2
C1 (1 TeV/!)2
AFB of top quark production
4
6
12 / 38
Effective Lagrangian Approach
Validity of our approach
Our Validity Criteria:
I
I
I
σint < r σSM (straight line)
σNP < r σint (ellipses passing through the origin)
σNP < r 2 σSM (ellipses centered at the origin)
Take r = 0.3, r = 0.5, and r = 1.0
Our predictions pass these validity criteria even for r = 0.3, and
could be considered reliable
Another Issue: Violation of Unitarity by dim-6 op’s Any
nonrenormalizable interactions violate √
“unitarity” , which is very
subtle issue at hadron colliders, since ŝ is not fixed
Our criteria is hopefully stronger than unitarity constraint
Pyungwon Ko (KIAS)
AFB of top quark production
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Effective Lagrangian Approach
Validity of our approach
σNP is obtained using
|MNP |2
=
×
4gs4 ŝ2
9ŝ2 4Λ4
n
2
LL 2
RR 2
LL 2
RR 2
9 (C1q
) + (C1q
) + 2 (C8q
) + (C8q
)
û − mt2
2
RL 2
LR 2
RL 2
LR 2
+ 9 (C1q
) + (C1q
) + 2 (C8q
) + (C8q
)
t̂ − mt2
LL LR
RR RL
LL LR
RR RL
+ 9 C1q
C1q + C1q
C1q + 2 C8q
C8q + C8q
C8q
2ŝmt2 ,
where
û − mt2 = −ŝ (1 + β̂t cθ̂ )/2,
Pyungwon Ko (KIAS)
t̂ − mt2 = −ŝ (1 − β̂t cθ̂ )/2
AFB of top quark production
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Effective Lagrangian Approach
Validity region
0.
10
10
=
5
FB
A
=
0.
38
98
7.
=
pb
0
7.
II
2
=
C2 (1 TeV/!)2
"
"
0
A
FB
pb
I
IV
-5
-10
-10
Pyungwon Ko (KIAS)
III
-5
0
C1 (1 TeV/!)2
AFB of top quark production
5
10
15 / 38
Effective Lagrangian Approach
Validity region with the updated data
σ
=
=
A
0.
pb
FB
02
7.
=
=
A
II
pb
C2 (1 TeV/Λ)2
98
FB
7.
σ
2
21
4
0.
09
6
0
I
IV
-2
III
-4
-6
-6
Pyungwon Ko (KIAS)
-4
-2
0
2
C1 (1 TeV/Λ)2
AFB of top quark production
4
6
16 / 38
Effective Lagrangian Approach
Mt t̄ distribution
d! / dMtt [pb " GeV-1]
10-1
10-2
10-3
SM
10-4
Pt.I
Pt.II
Pt.III
Pt.IV
10-5
10-6
CDF II Data, # L $ 2.7 fb-1
0
Pyungwon Ko (KIAS)
200
400
600
Mtt [GeV]
AFB of top quark production
800
1000
1200
17 / 38
Effective Lagrangian Approach
Spin-Spin Correlation
chiral structure of new physics affecting q q̄ → t t̄ is also sensitive
to the top quark spin-spin correlation (in the helicity basis):
−K = C =
σ(tL t̄L + tR t̄R ) − σ(tL t̄R + tR t̄L )
σ(tL t̄L + tR t̄R ) + σ(tL t̄R + tR t̄L )
SM prediction for helicity basis: K = 0.47 (LO) and 0.352 (NLO)
[Bernreuther et al., NPB (2004)]
New CDF data:
K = 0.48 ± 0.48 ± 0.22
New physics should have chiral couplings both to light quarks and
top quark −→ P must be broken
Any new observable ?
Longitudinal top quark polarization
Pyungwon Ko (KIAS)
AFB of top quark production
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Effective Lagrangian Approach
New Spin-Spin Correlation CFB
6
=
FB
FB
SM
II
-0
.3
0
0
=
C
C
=
I
FB
-2
C
C2 (1 TeV/!)2
C=
27
.5 0
-0 .47
30
-0
.4
-0
C=
2
0.
00
-0
.0
2
C=
4
IV
-4
III
-6
Pyungwon Ko (KIAS)
-6
-4
-2
0
2
C1 (1 TeV/!)2
AFB of top quark production
4
6
19 / 38
Effective Lagrangian Approach
Proposing a “NEW” Spin-Spin Correlation
The usual C is correlated with σt t̄ , and not to AFB
We propose a new spin-spin correlation CFB : Separate the events
in forward and backward directions, and form CFB
CFB ≡ C(cos θ ≥ 0) − C(cos θ ≤ 0)
C(cos θ ≥ 0(≤ 0)) implies the cross sections in the numerator of
C are obtained for the forward (backward) region: cos θ ≥ 0(≤ 0)
Advantages of the new CFB :
I
I
Larger spin-spin correlation
Stronger correlation with AFB
This new CFB could be also useful for testing the QCD in the top
sector
Pyungwon Ko (KIAS)
AFB of top quark production
20 / 38
Effective Lagrangian Approach
Spin-Spin Correlation
6
=
FB
FB
SM
II
-0
.3
0
0
=
C
C
=
I
FB
-2
C
C2 (1 TeV/!)2
C=
27
.5 0
-0 .47
30
-0
.4
-0
C=
2
0.
00
-0
.0
2
C=
4
IV
-4
III
-6
Pyungwon Ko (KIAS)
-6
-4
-2
0
2
C1 (1 TeV/!)2
AFB of top quark production
4
6
21 / 38
Spin-1 Resonances
One can consider the following interactions of quarks with spin-1
flavor-conserving (changing) color-singlet V1 (Ṽ1 ) and color-octet
V8a (Ṽ8a ) vectors (A = L, R) relevant to AtFB :
i
Xh
A
A
LV = gs V1µ
g1q
(q̄A γµ qA ) + g1t
(t̄A γµ tA )
i
X hA
aµ
A
A
+gs V8
g8q
(q̄A γµ T a qA ) + g8t
(t̄A γµ T a tA )
+gs Ṽ1µ
A
X
A
g̃1q
(t̄A γµ qA ) + Ṽ8aµ
X
A
Pyungwon Ko (KIAS)
A
g̃8q
(t̄A γµ T a qA ) + h.c.
A
AFB of top quark production
22 / 38
Spin-0 Resonances
Following interactions of quarks with spin-0 flavor-changing
color-singlet S˜1 and color-octet S̃8a scalars could also contribute to
AtFB :
X
X A
A
LS̃ = gs S̃1
η̃1q (t̄Aq) + S̃8a
η̃8q
(t̄AT a q) + h.c.
A
A
One can also consider color-triplet Skγ and color-sextet scalars
Sijαβ with minimal flavor violating interactions with the SM quarks
(Arnold, Pospelov, Trott, Wise):
hη
i
3
α β γ
α β αβ
LS = gs
αβγ ijk uiR
ujR Sk + η6 uiR
ujR Sij + h.c.
2
Pyungwon Ko (KIAS)
AFB of top quark production
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Wilson Coefficients from Resonances
After integrating out the heavy vectors and scalars, we obtain the
Wilson coefficients as follows:
LL
C8q
1 L L
1 L 2
1
L 2
= − 2 g8q g8t − 2 2|g̃1q | −
|g̃ |
Nc 8q
Λ2
mV
m
Ṽ
RR
C8q
1 R R
1 R 2
1
|η3 |2 2|η6 |2
R 2
=
−
2|
g̃
+
g
|
−
|
g̃
g
|
−
−
1q
Nc 8q
Λ2
mV2 8q 8t m2
mS2 3
mS2 6
Ṽ
LR
C8q
1 L R
1
1
L 2
L 2
|η̃ |
= − 2 g8q g8t − 2 |η̃1q | −
2Nc 8q
Λ2
mV
m
S̃
RL
C8q
1 R L
1
1
R 2
R 2
= − 2 g8q g8t − 2 |η̃1q | −
|η̃ |
2Nc 8q
Λ2
mV
m
S̃
Pyungwon Ko (KIAS)
AFB of top quark production
24 / 38
Examples of Resonances
Axigluon model corresponding to flavor universal chiral couplings
L = g L = −g R = −g R = 1
(Pati and Salam 1975): g8q
8t
8q
8t
0
New gauge boson Z with dominant coupling to u − t (Jung,
Murayama, Pierce, and Wells 2009):
0
R =g ,
R =g V1 = Ṽ1 = Z , gs g̃1q
gs g1q
(|U | . 1)
X
X U
0
New charged gauge boson W ± contributions (Cheung, Keung, and
0
A = g0 g
Yuan 2009): Ṽ = W , gs g̃1q
A
Some RS scenarios with large flavor mixing in the right-handed
quark sector (Aquino et al 2007; Agashe et al 2008):
L = g R = g R ' −0.2,
L = g L ' (1 ∼ 2.8)
g8q
g8t
8q
8b
8b
R ' (1.5 ∼ 5),
L 'V ,
R '1
g8t
g̃8q
g̃8q
tq
Pyungwon Ko (KIAS)
AFB of top quark production
25 / 38
Scores for each model
New particle
couplings
C1
C2
g L,R
8q,8t
indefinite
indefinite
Ṽ1 (spin-1 FV singlet)
L,R
g̃1q
−
0
Ṽ8 (spin-1 FV octet)
L,R
g̃8q
+
0
S̃1 (spin-0 FV singlet)
L,R
η̃1q
0
−
S̃8 (spin-0 FV octet)
L,R
η̃8q
0
+
×
S3α (spin-0 FV triplet)
η3
−
0
S6αβ (spin-0 FV sextet)
η6
+
0
×
√
V8 (spin-1 FC octet)
Pyungwon Ko (KIAS)
AFB of top quark production
1 σ favor
√
×
√
√
26 / 38
1-σ favored region for V8
rq= 2
4
rq= 0.5
gR8t / gL8q ( 1 TeV / MV )
rq= -0.5
rq= -1
2
rq= -2
0
-2
-4
-4
-2
0
2
gL8t / gL8q ( 1 TeV / MV )
4
R
L
L
rq = g8q
/g8q
and g8q
=1
Pyungwon Ko (KIAS)
AFB of top quark production
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Constraints on masses and couplings
1-σ favored values of the couplings Updated data:
Ṽ8
S̃1
αβ
S13
1 TeV 2 L 2
1
R 2
|g̃8q | + |g̃8q
:
| ' 0.76(0.64) ,
Nc
mṼ
1 TeV 2 L 2
R 2
|η̃1q | + |η̃1q
| ' 0.62(0.49) ,
:
mS̃
1 TeV 2
|η6 |2 ' 0.76(0.64)
: 2
mS6
These could be discovered and tested at the LHC, by measuring the
mass and the couplings
Pyungwon Ko (KIAS)
AFB of top quark production
28 / 38
AFB implies P violation
LL = C RL , and
If P were conserved in the light quark sector, C8q
8q
LR = C RR
C8q
8q
LL = C LR and C RR = C RL
If P were conserved in the top sector, C8q
8q
8q
8q
In either case, we would have C1 − C2 = 0 , and no effects on AFB
Most important message of nonzero AFB from new physics is
Parity should be vilolated in the quark sector
What would be the observable consequences of this new PV
interaction ?
In the top sector, the top longitudinal polarization can be nonzero
in general, unlike QCD
~t · n̂i =
hS
6 0
If n̂ ∝ ~p, it becomes helicity
Pyungwon Ko (KIAS)
AFB of top quark production
29 / 38
P violation and Longitudinal Pol’s
Keeping only the longitudinal pol’s of (anti)top, we have
(
)
4
g
s
|M|2 = 2 D0 + D1 (PL + P̄L ) + D2 (PL − P̄L ) + D3 PL P̄L .
ŝ
D1 and D2 are P-violating.
D1 term needs strong phase (CP T̃ violating), from the propagator
of the exchanged new particle, which is not seen in our approach
(Future work)
D2 '
i
ŝ h 0
0
2
0
0
2
(C
+
C
)
β̂
(1
+
c
)
+
(C
−
C
)(5
−
3
β̂
)c
t
t
1
2
1
2
θ̂
θ̂
9 Λ2
with
RR
LL
C10 ≡ C8q
− C8q
,
LR
RL
C20 ≡ C8q
− C8q
.
Different informations on the chiral structures of NP from AFB
Pyungwon Ko (KIAS)
AFB of top quark production
30 / 38
When we integrate over the polar angle θ̂, only the first term
involving
RR
LL
LR
RL
(C10 + C20 ) = C8q
− C8q
+ C8q
− C8q
survives.
On the other hand, if we separate the forward and the backward
top samples and take the difference, the orthogonal combination
in the second term survives:
RR
LL
LR
RL
− C8q
− C8q
+ C8q
.
(C10 − C20 ) = C8q
Consider the two new observables:
D ≡
σ(tR t̄L ) − σ(tL t̄R )
,
σ(tR t̄R ) + σ(tL t̄L ) + σ(tL t̄R ) + σ(tR t̄L )
DFB ≡ D(cos θ̂ ≥ 0) − D(cos θ̂ ≤ 0)
which involve the sum and difference of the coefficients C10 and
C20 , respectively.
Pyungwon Ko (KIAS)
AFB of top quark production
31 / 38
-0
FB
=
D
.3
-0
D
3
FB
=
.
=0
1
2
D
.1
FB
0
=-
=0
.
1
(+,–)
D
SM
(+,+)
=0
.3
(–,–)
0
-2
D
3
FB
0.
=-
D
C ′2 (1 TeV/Λ)2
D
.
=0
D
4
.1
6
(–,+)
-4
-6
-6
-4
-2
0
2
C ′1 (1 TeV/Λ)2
4
6
Figure: The P-violating spin correlations D and DFB in the (C10 , C20 ) plane.
The signs of (D , DFB ) are denoted.
Pyungwon Ko (KIAS)
AFB of top quark production
32 / 38
The polarization coefficients could be measured by studying the
angular distributions of the top-quark decay products.
For dilepton decay channels of t t̄ (in the helicity basis), one has
(
4
g
s
∗
∗
|M|2 =
D0 + D1 (cos θ+
+ cos θ−
)
ŝ2
)
∗
∗
∗
∗
+D2 (cos θ+
− cos θ−
) + D3 cos θ+
cos θ−
.
∗ (θ ∗ ) is the angle between the charged lepton l + (l − ) in
where θ+
−
the top (anti-top) rest frame and the direction of the top (anti-top)
in the t t̄ rest frame.
MT 2 could be helpful for this study (Work in progress)
Pyungwon Ko (KIAS)
AFB of top quark production
33 / 38
[t] New particle exchanges and the signs of induced couplings C AB
(A, B = R, L), C1 − C2 , C10 + C20 , and C10 − C20 .
0
0
0
0
Res.
C RR
C LL
C LR
C RL
C1 − C2
C1 + C2
C1 − C2
Ṽ1R
−
0
0
0
−
−
−
Ṽ1L
0
−
0
0
−
+
+
Ṽ8R
+
0
0
0
+
+
+
Ṽ8L
0
+
0
0
+
−
−
S̃1R
0
0
0
−
+
+
−
S̃1L
0
0
−
0
+
−
+
S̃8R
0
0
0
+
−
−
+
S̃8L
0
0
+
0
−
+
−
S2α
αβ
S13
−
0
0
0
−
−
−
+
0
0
0
+
+
+
V8R
±
0
0
0
±
±
±
Pyungwon Ko (KIAS)
AFB of top quark production
√
(
√
34 / 38
0.1
0.075
0.05
~
V8R, V8R, Sαβ
13
~
S
1R
DFB
0.025
0
-0.025
~
S
-0.05
-0.075
1L
~
V8L, V8L
-0.1
-0.1 -0.075-0.05-0.025
0
D
0.025 0.05 0.075 0.1
Figure: The predictions for D and DFB of the models under consideration,
being consistent with the σt t̄ and AFB measurements at the 1-σ level. We
assume only one resonance exists or dominates.
Pyungwon Ko (KIAS)
AFB of top quark production
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Summary
We performed a model independent study of t t̄ productions at the
Tevatron using dimension-6 q q̄t t̄ contact interactions with all the
possible Dirac and color structures.
Our results encode the necessary conditions for the underlying
new physics in a compact and an effective way when those new
particles are too heavy to be produced at the Tevatron.
Proposed a new FB spin-spin correlation CFB ∝ AFB
Suggested to measure PL and PL to probe the chiral structure of
new physics in q q̄ → t t̄
We considered the s−, t− and u−channel exchanges of spin-0
and spin-1 particles whose color quantum number is either
singlet, octet, triplet or sextet.
Pyungwon Ko (KIAS)
AFB of top quark production
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Future Study
AFB vs Mt t̄ or ∆η
Detailed study of resonance productions at the LHC
( Resonances in the t t̄ or t q̄ channel )
Top polarization in general (transverse, longitudinal) at the
Tevatron and at the LHC
In the presence of resonance, there could be nonzero PL + PL →
Need more study the D1 term
Those new particles might leave imprints on the low energy flavor
physics such as K or B physics (mixing and CP violation), if
u(d) − t transitions are employed
Pyungwon Ko (KIAS)
AFB of top quark production
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Thank you very much
Pyungwon Ko (KIAS)
AFB of top quark production
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