Table Of ContentOne-side Forward-backward Asymmetry in Top Quark Pair Production at
CERN Large Hadron Collider
You-kai Wang1∗, Bo Xiao1†, and Shou-hua Zhu1,2‡
1 Institute of Theoretical Physics & State Key Laboratory of Nuclear
Physics and Technology, Peking University, Beijing 100871, China
2 Center for High Energy Physics, Peking University, Beijing 100871, China
(Dated: February 1, 2011)
1
1 Both D0 and CDF at Tevatron reported the measurements of forward-backward asymmetry in
0 toppairproduction,whichshowed possibledeviationfrom thestandardmodelQCDprediction. In
2 this paper, we explore how to examine the same higher-order QCD effects at the more powerful
n Large Hadron Collider.
a
J PACSnumbers: 14.65.Ha,12.38.Bx
9
2
The top quark is the heaviest ever known of A in the MCFM is the cross section at the
FB
] fermion and is thought to be related to the next leading order QCD, while the leading order
h
p mechanismofelectroweaksymmetry breakingand cross section in Ref. [6–8]. Therefore they differ
- physics beyond the standardmodel (SM). Since it by a factor of k 1.3.
p ∼
was discovered more than one decade ago, mea- Such FB asymmetry is equivalent to the charge
e
h suring its properties is one of the most active asymmetry provided that CP is conserved. It
[
fields. Most of the measured properties such as is strange at first glance that vector like theory
3 mass,width, productionrateandsoonareconsis- QCD can induce FB asymmetry. The fact is that
v tent with SM predictions, however the CDF and such asymmetry arising from higher-order effects,
5
D0 Collaborationshave observeda possible devia- namely,theinterferencebetweentree-levelandvir-
8
tion on forward-backward(FB) asymmetry. At tt¯ tual box diagrams of tt¯ production, as well as
6
2 frame A is defined as among diagrams of real processes of qq¯ tt¯g (cf.
FB
→
8. Figs.1-3). SimilarasymmetryofQEDwasnoticed
0 AFB = σσ((∆∆YY>>00))−+σσ((∆∆YY<<00)), (1) even 37 years ago [9].
0 Obviouslyonly less than 3σ deviationis notthe
1
: where∆Y ≡Yt−Yt¯isthedifferencebetweenrapid- evidence that the SM is failed. Though the pur-
v ityofthetopandantitopquark,whichisinvariant suitofpossiblenewphysicsbeyondtheSM(BSM)
Xi under tt¯or pp¯rest frame. implied by the deviation is exciting, the investiga-
r The measurements of CDF and D0 are [1, 2], tion of the same inference effect at more power-
a
ful Large Hadron Collider (LHC) is more neces-
ACDF =0.158 0.072 0.017, with 5.3fb−1; sary. Once the deviationis confirmedatthe LHC,
FB ± ±
AD0 =0.08 0.04 0.01, with 4.3fb−1. themeasurementsmaybethefirstBSMsignature.
FB ± ±
(2) Unfortunately, the FB asymmetry defined at the
The measurements are consistent with previous proton-antiproton collider Tevatron is not appli-
ones[3–5]. ThecorrespondingSMpredictionsfrom cable at the proton-proton collider LHC, as LHC
Monte Carlo(MC) simulations are 5.8 0.9% [1] doesnothavethepreferreddirectioninthelabora-
±
by MCFM and 1+2% [2] by MC@NLO. Here D0’s toryframe. Inordertosolvethisissue,the central
−1
measurement and the corresponding MC@NLO charge asymmetry has been proposed [6–8, 10–12]
prediction can not be compared directly with SM
ones because they are not normalized by selecting A = σt(|Y|≤YC)−σt¯(|Y|≤YC). (3)
C
efficiency. The AFB in the SM is calculated to be σt(|Y|≤YC)+σt¯(|Y|≤YC)
7.8%in Ref. [6–8], which is largerthan5.8 0.9% Here A is defined as the ratiobetween the differ-
± C
[1]byMCFM.The reasonis thatthe denominator ence and the sum of the events of the top and the
antitop quark in a central region Y < Y in the
C
| |
laboratory frame. The disadvantage of this defini-
tion is that at the LHC, such asymmetry is quite
∗E-mail:[email protected]
†E-mail:[email protected] small. The reason is that the central region cut
‡E-mail:[email protected] Y < YC can not remove the symmetric tt¯events
| |
2
viaggfusionefficiently. Inthispaper,weproposea with
new definition of FB asymmetry, namely the one-
F = (σ(∆Y >0) σ(∆Y <0))
side FB asymmetry AOFB, to conquer this diffi- ± ± |Ptzt¯>Pczut,Mtt¯>Mcut
culty. A canbelargeandarisesfromthe same (6)
OFB
O(α3)contributionswhichinducetheobservedFB
s B = (σ(∆Y <0) σ(∆Y >0))
asymmetry at Tevatron. This quantity can be ex- ± ± |Ptzt¯<−Pczut,Mtt¯>Mcut
(7)
amined at the LHC and cross-checked to the cor-
The asymmetry defined in Eq.(5) is the same
responding measurements at the Tevatron.
as that in Eq.(4) except the statistics are dou-
At the LHC, up to next-to-leadingorder (NLO)
bled. We will adopt the asymmetry definition in
QCD,toppaireventscanbegeneratedthroughthe
Eq.(5) in the following evaluation. The goal to
achnadngngels qtq¯t¯→atttt¯h,eqpq¯a→rtotnt¯igc,lqegve→l. Btt¯eqinograq¯gpr→ototnt¯q¯- asypmplmyectornicstgragint otnt¯Pevtzt¯enatnsd. MIntt¯Eiqs.(t5o),extchleudaesytmhe-
→
proton collider, LHC does not have the preferred →
metric cross section in the numerator arises from
directions in the laboratory rest frame. However O(α3) in QCD, and the denominator is the to-
s
except the symmetric gluons, the incoming par-
tal cross section. Although some high order ef-
tons do have preferred direction. Usually the va- fects in tt¯production have been considered, such
lence quark momentum is larger than that of the
as soft gluon resummation [14, 15] and the ex-
sea quark. For example, for the process uu¯ tt¯ clusive next-to-leading order cross section of tt¯+
→
(taking the momentum ofthe u quark as the posi-
jet production[16–18], the exactinclusive next-to-
tivez direction),momentumofuismostprobably
leading order asymmetric cross section which in-
larger than that of u¯. On average,this will induce
volvesthe two-loopcontributionsis still unknown.
the z direction tt¯ total momentum in lab frame
For consistency, we choose the lowest order result
Ptzt¯> 0. So even for the pp collider, uu¯ → tt¯can of total cross section at O(α2s) as a rough estima-
contribute an asymmetric tt¯ distribution. How-
tion.
ever, this asymmetry is completely canceled with The typicalFeynman diagrams of O(α2) for the
s
the opposite direction u¯u tt¯events. If we ob-
denominator in Eq. 4 are drawn in Fig. 1.
→
serve only one-side tt¯events, i.e. Pz > 0, such
tt¯
asymmetrywill be kept. Tomaintainthe partonic
t
asymmetryandsuppressthesymmetricevents,we
t t
g
require a cut Pz > Pz on the z direction top u g
pair momentum| tot¯|f the cfiuntal tt¯pair in the pp rest g t g t t t
u g
frame. One may argue that determination of the g
momentuminbeamlinedirectionmaybeproblem-
atic, especially when one neutrino is missing when
FIG.1: TypicalFeynmandiagramsfortt¯pairproduc-
using the associated charged lepton to trigger the
top/antitop event. This issue can be solved by re- tion at LHC at O(α2s).
quiringinvariantmassoftheneutrinoandcharged
Inthe SM,the leading asymmetriccrosssection
lepton just equal to that of the W boson, which is
arises at O(α3). The related Feynman diagrams
assumedtobethe decayproductofthetopquark. s
Thus Pz is still a measurable quantity [13]. at partonic level can be classified into three cate-
tt¯ gories: (1) the interference among virtual box in
The new one-side forward-backwardasymmetry
Fig. 2 and the leading diagrams for the process
AOFB can be defined in the pp rest frame as qq¯ tt¯in Fig. 1; (2) the interference among ini-
→
tialandfinalgluonradiationdiagramsofqq¯ tt¯g
→
AOFB = σσ((∆∆YY>>00))−+σσ((∆∆YY<<00))|Ptzt¯>Pczut,Mtt¯>Mcut iqngFigt.t¯q3;aannddq¯(g3) ctot¯nq¯trinibuFtiigo.n4s.from diagrams of
→ →
Theasymmetriccrosssectionatthepartonlevel
= σσ((∆∆YY<<00))−+σσ((∆∆YY>>00))|Ptzt¯<−Pczut,Mtt¯>Mcut was given analytically in Ref. [7]. However, we
(4)
carry out independent calculations [19] with the
or
help of FeynCalc [20], FormCalc [21] and QCD-
Loop [22].
F +B σA The asymmetric cross section σA contributed
− −
A = , (5)
OFB F +B ≡ σ from each of the above three categoriesis UV and
+ +
3
collineardivergencesfree. Therealgluonradiation
u u
u u
of category(2) canbe divided into a soft partand u
a hard part by introducing a soft cut δs [23]. Soft g g t u u
t t
d(1iv)eargnedncseosftaprearctantocefloedrmwhaevniratdudailn-sgoftthpeavritr.tuδasl g g t g t t g g t
independence ischeckedbyaddingthe virtual-soft
and hard part [19]. (a)
In our numerical calculations, we choose cteq6l u u
u u
for the leading order calculation and cteq6m for u
higher-orderestimations. The scales are chosenas g t g t u u t
µr =µf =mt and αS(mZ)=0.118. g g t g t t g g t
To check our Fortran code, forward-backward
asymmetry at Tevatron is recalculated indepen-
(b)
dently using our code. A is calculated to be
FB
7.1%, which is in good agreement with the exist- FIG. 4: Typical Feynman diagrams of ug utt¯(a),
ing results [8, 24]. and u¯g u¯tt¯(b). →
→
u g t u g
t %) 10 M>2m
u t u t (OFB 9 Mtt>500tGeV
A 8 tt
u g t u g t 7 Mtt>1000GeV
6
5
4
FIG.2: TypicalNLOvirtualFeynmandiagramswhich
3
contributeto asymmetric cross section.
2
10 200 400 600 800 1000 1200 1400 1600
pz
cut
u g g
u u g tt u u g t t t −1 )sig ( 10 fb 11124680 MMMtttttt>>>251m0000tG0GeVeV
12
10
FIG.3: TypicalrealgluonemissionFeynmandiagrams 8
which contributeto asymmetric cross section. 6
4
2
Figures 5 and 6 show our predictions on A
OFB 00 200 400 600 800 1000 1200 1400 1600
andsignificanceto discoverthe asymmetricevents pz
cut
which is defined as sig = √ σA/√σ ( with =
L L
10fb−1) at LHC with √s = 7 TeV and 14 TeV, FIG.5: AOFB andsignificanceasafunctionofPczut at
respectively. Forno cutsatall(Mtt¯>2mt,Pczut = LHC with √s=7 TeV.
0), the A is not zero but very small, 1.2% and
OFB
0.58% for √s = 7 TeV and 14 TeV, respectively.
The reason is simply due to the large denomina- two impacts on A . First, as symmetric events
OFB
tor σ which arises mainly from gg tt¯. To in- gg tt¯lie mainly in the small Pz region, the Pz
→ → tt¯ tt¯
crease AOFB, we apply cuts on Ptzt¯ and Mtt¯. The cut can remove them effectively. Second, as men-
key point is to suppress gg fusion contributions to tioned above, it is most probably that the valence
the denominator while decreasing the numerator quark’s momentum is larger than that of the sea
σA as small as possible. From the figures, we can quark,but itdoes has some smallprobabilitythat
see clearly that Pz cut can increase A greatly thevalencequark’smomentumissmallerthanthat
tt¯ FB
while Mtt¯ cut is not so efficient. The Ptzt¯ cut has of the sea quark. This will cause an opposite con-
4
every events. Second, A is based on a centralre-
C
(%)AOFB 78 MMtttt>>520m0tGeV |gPiotzt¯n| >|Y|P<czutY.CB,ewcahuilseeAoOfFthBeisdidffeefirnenedt minomaernegtuiomn
6 distribution of the quarks and the corresponding
M>1000GeV
5 tt sea quarks in the proton, the top pair events pro-
4 ducedviaqq¯annihilationareverylikelybeboosted
in the z direction. For the centralchargeasymme-
3
try, a small Y cut cannot cover these z direction
2 C
boosted events. However, a large Y cut will in-
1 C
clude nearlyequalnumberoftandt¯events,which
00 500 1000 1500 2000 2500 p30z00 makes AC approach zero [11]. AC vanishes if the
cut
wholerapidityspectrumisintegrated. OptimalY
C
−1 )0 fb 25 Mtt>2mt efovrenAtCs tishaatboreuatc1h.tOoutrhAeOedFgBecoafntchoevedrettehcettoorp, spoaiitr
1 M>500GeV
g ( 20 tt can have more statistics. Third, the denominator
si Mtt>1000GeV σ inbothcasesismainlycomposedofthesymmet-
15 ric gg tt¯events. This makes both asymmetries
→
small, especially for A [11]. A kinematic feature
C
10 ofgg tt¯eventsisthattheyaremostlylocatedin
→
a small Pz region. So by requiring a higher Pz ,
tt¯ cut
5 top pair events via gg fusion can be removed ef-
0 500 1000 1500 2000 2500 3000 ficiently. The central charge asymmetry does not
pz
cut take this advantage so A is smaller than A .
C OFB
FIG.6: AOFB andsignificanceasafunctionofPczut at To summarize, both CDF and D0 at Tevatron
LHC with √s=14 TeV. reported the measurements of forward-backward
asymmetry in top pair production. Theoretically
such asymmetry is due to the higher-order QCD
tributions to the asymmetric cross section in our
processes. The measurements showed a possible
definition of A . The Pz cut can reduce such
OFB tt¯ deviation from the theoretical prediction. In this
kindofpollution. Infigureswealsoshowthesignif-
paper,weexplorehowtoexaminethesamehigher-
icance to discover the asymmetric events from the
orderQCDeffects atthe more powerfulLHC.Un-
background symmetric events. Such measure can
like Tevatron, the proton-proton LHC has no pre-
be utilized to optimize the cut conditions, namely
ferred direction in the laboratory frame. Thus we
Mtt¯> 2mt Pczut ∼ 500 GeV is the optimal one at define a new one-side forward-backward asymme-
√s = 7 TeV and Mtt¯ > 2mt Pczut ∼ 1.2 TeV is try AOFB [cf. Eqs.(4) and (5)] in terms of the top
the optimal one at √s = 14 TeV though A is
OFB pair kinematical information. Our studies show
not the largest here. Note that sig √ , here we
∝ L that the cut on top pair momentum in the z di-
choose = fb−∞. The value of sig varies with
L ∞′ rection can increase asymmetry greatly. Provided
theintegratedluminositybutoptimalcutcriterion
that huge tt¯events will be produced at the LHC,
should be stable.
A can be precisely measured and compared
OFB
It’s interesting to compare A proposed in
OFB withthecorrespondingmeasurementsattheTeva-
this paper with the central charge asymmetry A
C tron.
proposed before [cf. Eq.(3)]. First, A only ac-
C
counts for the single top or antitop in Y < Y Acknowledgements: This workwassupportedin
C
| |
regions, while the new asymmetry A needs to part by the Natural Sciences Foundation of China
OFB
include the top pair kinematical information for (No. 10775001,No. 10635030and No. 11075003).
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