Top Quark Forward-Backward Asymmetry in the Large Invariant Mass Region

Abstract

The forward-backward asymmetry (FBA) in top-pair production that was observed
in 2008 gets a boost in a recent CDF publication. Not only has the FBA further
been confirmed, but also distributional preferences are shown. Strikingly, the
FBA is the most sizable in the large $M_{t\bar t}$ invariant mass region and in
the large rapidity difference $|\Delta y|$ region. Here we used our previously
proposed $t$-channel exchanged $W'$ boson to explain the new observations. We
show that a new particle exchanged in the $t$-channel generically gives rise to
such observations. Furthermore, we show that the proposed $W'$ can be directly
produced in association with a top quark at the Tevatron and the LHC. We
perform a signal-background analysis and show that such a $W'$ is readily
observed at the Tevatron with a 10 fb$^{-1}$ luminosity and at the LHC-7 with
just a 100 pb$^{-1}$ luminosity.

Full text

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arXiv:1101.1445v2 [hep-ph] 15 Mar 2011
Top Quark Forward-Backward Asymmetry
in the Large Invariant Mass Region
Kingman Cheung1,2,3, and Tzu-Chiang Yuan4
1Division of Quantum Phases & Devices, School of Physics,
Konkuk University, Seoul 143-701, Republic of Korea
2Department of Physics, National Tsing Hua University, Hsinchu 300, Taiwan
3Physics Division, National Center for Theoretical Sciences, Hsinchu 300, Taiwan
4Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
(Dated: March 16, 2011)
Abstract
The forward-backward asymmetry (FBA) in top-pair production that was observed in 2008 gets
a boost in a recent CDF publication. Not only has the FBA further been confirmed, but also
distributional preferences are shown. Strikingly, the FBA is the most sizable in the large Mt¯t
invariant mass region and in the large rapidity difference |∆y| region. Here we used our previously
proposed t-channel exchanged W′boson to explain the new observations. We show that a new
particle exchanged in the t-channel generically gives rise to such observations. Furthermore, we
show that the proposed W′can be directly produced in association with a top quark at the Tevatron
and the LHC. We perform a signal-background analysis and show that such a W′is readily observed
at the Tevatron with a 10 fb−1luminosity and at the LHC-7 with just a 100 pb−1luminosity.
PACS numbers:
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I. INTRODUCTION
The top quark was the last piece of quarks that was discovered more than 15 years ago
[1, 2]. While waiting for the Higgs boson at the LHC, the top quark has been making some
noise about the presence of new physics. The forward-backward asymmetry (FBA) in top-
quark pair production was found in 2008 by CDF [3] and by DØ[4]. While the Standard
Model (SM) only predicts a level as small as a few percent arising from the higher-loop
contributions, the measurement by CDF [3], however, was as large as
At¯t≡Nt(cosθ > 0) − Nt(cosθ < 0)
where θ is the production angle of the top quark t in the t¯t rest frame. The measurement in
Nt(cosθ > 0) + Nt(cosθ < 0)= 0.19 ± 0.065 (stat) ± 0.024 (syst) , (1)
the p¯ p laboratory frame is correspondingly smaller, because of the Lorentz boost (washout)
of the partons along the beam axis.
The anomaly did not die out, but gets a reconfirmation in a recent CDF publication [5].
With a larger data set (5.3 fb−1) the FBA persists at the level of At¯t= 0.158 ± 0.074 [5],
which is a less-than-2σ effect after subtracting the SM contribution of At¯t
SM= 0.058± 0.009
[6, 7]. Though the deviation is slightly smaller, the most striking feature is that the FBA
shows distributional preferences. The FBA is the most obvious in the large Mt¯tinvariant
mass region and in the large rapidity difference |∆y| region. The analysis in the CDF paper
[5] showed that the FBA is consistent with zero for Mt¯t< 450 GeV but a larger-than-3σ
effect in Mt¯t> 450 GeV region. At the same time, the analysis also showed that the FBA is
large in the large rapidity difference ∆y region, which is a 2σ effect. They are summarized in
the third last row in Table I, where we also show in the second last row the SM predictions
from the MCFM [6].
If the FBA is true, it will indicate the presence of new physics, because within the SM
the asymmetry is only up to about 5% [7]. In the past two years, numerous works have
been carried out to explain the anomaly [8–27]. The explanations can be divided into two
categories: (i) a t-channel exchanged particle such as a W′or a Z′with flavor-changing
couplings between the top quark and the d or u quark, and (ii) a heavy s-channel exchanged
particle such as an axial-gluon with specific couplings to the top quark and the light quarks.
In the latter case, the couplings are somewhat contrived in order to achieve a positive FBA.
In a previous work [21], we proposed an extra W′boson that only couples to the d and t
quarks. Thus, the d¯d initial state turns into the t¯t final state via a charged-current exchange
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of the W′boson in the t-channel. We mapped out the suitable parameter space of the W′
mass MW′ and the coupling g′. In this Letter, we show that such a t-channel exchanged
particle can easily accommodate a FBA and also that it naturally gives rise to a large FBA
in the large Mt¯tregion and in the large |∆y| region. We show that for MW′ = 200 − 600
GeV with appropriate couplings we can bring the predictions to be within 1 − 1.5σ of the
data. This is our main result.
In addition, since the W′±boson proposed is relatively light, only 200−600 GeV, it can
be directly produced in association with a top quark or antiquark at the Tevatron and the
LHC. The W′−(W′+) produced would then decay right away into¯td (t¯d), giving rise to a
top-quark pair plus one jet in the final state. The irreducible background is QCD production
of t¯t+1j. We show that the increase in t¯t production by direct W′production is within 1σ
error of the measured t¯t cross section. We perform a signal-background analysis based on
parton-level calculations. The cleanest signal of W′production would be the sharp peak of
the invariant mass Mtjdistribution. We require one top quark to decay hadronically while
the other one semi-leptonically. In this case, one has less confusion in jet combinations, and
one can still fully reconstruct the hadronic top and combine with the light jet to form the
peak of W′. We expect the background to give a continuum in the Mtjdistribution. Thus,
we can count the number of events below the peak for the signal and background. At the
end, we can see that the Tevatron can observe such a W′up to 400 GeV while the LHC
operating at 7 TeV can observe such a W′almost immediately. This is an important result
of this work.
Improvements over our previous work are as follows.
1. We use the top-quark mass mt= 172.5 GeV and the most recent published t¯t cross
section, which are the same as in the most recent CDF publications [5, 28].
2. We calculate the FBA as functions of |∆y| and Mt¯t. Through the figures it is clear
that larger FBA in the large |∆y| and large Mt¯tregion is a generic feature of a new
t-channel exchanged particle.
3. With the additional charged W′boson that we proposed, we can bring the overall At¯tto
be around the measured value, the At¯t(|∆y| > 1) within 1σ, and At¯t(Mt¯t> 450 GeV)
within 1.5σ.
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4. We calculate the direct production of the W′associated with a top quark at the
Tevatron and the LHC. We show that in the presence of irreducible background of t¯tj
the W′up to about 400 GeV could be observed at the Tevatron. On the hand, the
W′all the way to 600 GeV could be easily observed at the LHC.
II. THE FORWARD-BACKWARD ASYMMETRY
The production angle θ in the t¯t rest frame is related to the rapidity of the t and¯t in the
p¯ p frame by
∆y ≡ yt− y¯t= 2 arctanh
??
1 −4m2
t
ˆ s
cosθ
?
(2)
where ˆ s is the square of the center-of-mass energy of the t¯t pair. Therefore, the difference
∆y between the rapidities of the t and¯t in the p¯ p frame is a close measure of the production
angle in the t¯t frame. Moreover, the sign of ∆y is the same as cosθ, such that the asymmetry
in Eq. (1) can be given by
At¯t≡Nt(∆y > 0) − Nt(∆y < 0)
Nt(∆y > 0) + Nt(∆y < 0). (3)
Our parton level calculation uses this definition to calculate the FBA.
Suppose the interaction vertex for the W′boson with the down and top quarks is given
by
L = −g′W
′+
µ
¯tγµ(gLPL+ gRPR)d + h.c. ,(4)
where PL,R= (1∓γ5)/2 are the chirality projection operators, gL,Rare the chiral couplings
of the W′boson with fermions, and g′is the coupling constant. In Ref. [21], we demonstrated
that the pure right-handed coupling where gL= 0 and gR= 1 can fit the data in a more
consistent way. Also, the pure right-handed W′is less constrained by the SU(2)Lsymmetry.
We therefore focus on this case of pure right-handed coupling in what follows.
The process d(p1)¯d(p2) → t(k1)¯t(k2) is described by two Feynman diagrams, one s-
channel diagram from the one gluon exchange and one t-channel diagram from the W′
exchange. Ignoring the d quark mass, the spin- and color-summed amplitude squared is
given by
?
|M|2=
9g′4
t2
W′
16g4
ˆ s2
?
s
4?(g4
?u2
L+ g4
R)u2
t+ 2g2
Lg2
Rˆ s(ˆ s − 2m2
?+16g′2g2
t)?+
R)
m4
m4
?
t
W′(g2
L+ g2
R)2(t2
t+ 4m2
W′ˆ s)
?
(5)
+
t+ t2
t+ 2ˆ sm2
t
s
ˆ stW′
(g2
L+ g2
2u2
t+ 2ˆ sm2
t+
m2
m2
t
W′(t2
t+ ˆ sm2
t)
?
,
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where ˆ s = (p1+ p2)2, t = (p1− k1)2, u = (p1− k2)2and
tt= t − m2
t= −1
2ˆ s(1 − β cosθ),ut= u − m2
t= −1
2ˆ s(1 + β cosθ),tW′ = t − m2
W′ , (6)
with β =
?1 − 4m2
t/ˆ s. The initial spin- and color-averaged amplitude squared is given by
?
|M|2=1
4
1
9
?
|M|2. (7)
The differential cross section versus the cosine of the production angle θ is
dˆ σ
dcosθ=
β
32πˆ s
?
|M|2, (8)
where ˆ σ denotes the cross section for the subprocess which is then folded with the par-
ton distribution functions to obtain the measured cross section. The FBA is obtained by
integrating over the positive and negative range of the cosθ variable.
0
0.1
0.2
0.3
0.4
0.5
0.6
400 600 800 1000 1200
Att
Mtt (GeV)
MW’=200 GeV, g’=0.85
MW’=300 GeV, g’=1.2
MW’=400 GeV, g’=1.5
MW’=500 GeV, g’=1.8
MW’=600 GeV, g’=2.1
FIG. 1: The forward-backward asymmetry of top-pair production versus the invariant mass Mt¯t
at the Tevatron for various values of MW′ and g′.
We can also easily calculate the invariant mass Mt¯tdistribution in the forward and back-
ward directions, through which we can calculate the FBA versus the invariant mass. We
show the FBA versus Mt¯tfor various values of MW′ and g′in Fig. 1. The values are chosen
such that it can bring the predictions within 1 − 1.5σ of the data without violating the
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