Top quark pair production and asymmetry at the Tevatron and LHC in left-right models

Mariana Frank,1,* Alper Hayreter,1,† and Ismail Turan2,‡

1Department of Physics, Concordia University, 7141 Sherbrooke St. West, Montreal, Quebec, Canada, H4B 1R62Ottawa-Carleton Institute of Physics, Carleton University, 1125 Colonel By Drive Ottawa, Ontario, Canada, K1S 5B6

(Received 8 August 2011; published 6 December 2011)

In light of the recent measurements of the top quark forward-backward asymmetry at the Fermilab

Tevatron experiment, which in some regions of the parameter space shows a discrepancy of 3� compared

to the standard model prediction, we analyze top quark pair production and asymmetry in the context of

left-right models both at the Tevatron and Large Hadron Collider (LHC). We use the minimal manifest

left-right model and an asymmetric left-right model where gauge couplings and flavor mixing in the right-

handed sector are allowed to differ from those in the left-handed sector. We explore the consequences of

including effects from WR and ZR gauge bosons, consistent with phenomenological constraints from

meson mixing and new bounds from ATLAS and CMS, for the t�t cross section, invariant mass distribution

and forward-backward asymmetry at the Tevatron, and predict their values at the LHC. We show that,

choosing parameter benchmarks for the model while preserving agreement with collider, electroweak

precision, and flavor-violation data, the generic left-right model cannot account for the large deviations

of the observed asymmetry at the Tevatron and also that it predicts very small charge asymmetries

at the LHC.

DOI: 10.1103/PhysRevD.84.114007 PACS numbers: 14.65.Ha, 11.30.Er, 12.10.Dm

I. INTRODUCTION

Measurements of top production and decays are ofparticular interest for particle theorists as they likely willshed light on the mechanism of electroweak symmetrybreaking. The Tevatron has produced such measurements,and more are expected to come from the LHC. For in-stance, the t�t total cross section, as well as the differentialcross section with respect to the t�t invariant mass, both ofwhich are sensitive to a variety of beyond the standardmodel (BSM) scenarios of particles decaying into t�t pairs,are completely consistent with the standard model (SM)[1–3].

But recently both the CDF and D0 collaborations havemeasured the forward-backward asymmetry of the top quarkpairs,At�t

FB [4–6]. Based on a data sample of 5:3 fb�1 [4], theasymmetries, evolved to the parton level,1 are

At�tðj�yj< 1Þ ¼ 0:026� 0:118

At�tðj�yj � 1Þ ¼ 0:611� 0:256

At�tðMt�t < 450 GeVÞ ¼ �0:116� 0:153

At�tðMt�t � 450 GeVÞ ¼ 0:475� 0:114

(1.1)

in the t�t rest frame (with mt ¼ 175 GeV). In the SM theasymmetry is produced mainly through one-loop QCD

corrections, with a smaller contribution from electroweakt�t production, and is stable with respect to corrections fromQCD threshold resummation [7]. The next-to-leading-order(NLO) SM predictions at parton level are, by comparison[8–10]

At�tSMðj�yj< 1Þ ¼ 0:039� 0:006;

At�tSMðj�yj � 1 ¼ 0:123� 0:008;

At�tSMðMt�t < 450 GeVÞ ¼ 0:040� 0:006;

At�tSMðMt�t � 450 GeVÞ ¼ 0:088� 0:013:

(1.2)

We note that there has been a recent calculation of theasymmetry including electroweak corrections to Oð�2Þterms, as well as interferences with the QCD diagrams[11]. It seems that SM asymmetry receives non-negligiblesame-sign contributions from the electroweak sector sothat, except the region with Mt�t > 450 GeV, the observeddeviation between theory and experiment diminishes.As the deviation from the expected and the measured

asymmetry is large, this has been interpreted as a signal fornew physics (NP), in particular, a signal for a below-TeVscale physics. A large variety of models has been employedto resolve the discrepancy. These models invoke new par-ticles and new interactions to explain the discrepancy. Ingeneral, one can classify these models according to the newmediators of the new physics as (1) t-channel boson medi-ators (scalars or vectors, such as W 0 or Z0) with flavor-violating couplings to right-handed up quarks [12], (2)s-channel mediators, color sextet or color antitriplet scalarparticles coupling with flavor-violating couplings to up andtop quarks, such as [13], or (3) new flavor multipletscoupling to quarks in a flavor-symmetric way [14].

*mfrank@alcor.concordia.ca†alper@physics.concordia.ca‡ituran@physics.carleton.ca1Here and throughout the paper, parton level is used in the

same meaning described in [4]. It refers to deconvolving fromthe data, like detector efficiencies, jet algorithm, selection effi-ciencies, background etc. See [4] for more details.

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Comparative studies of various models also exist, and itwas shown that s-channel particles used to explain theanomaly have maximal axial couplings, while t-channelparticles exhibit maximal flavor-violating couplings [15].As well, a number of analysis have appeared, which studythe implications of models which predict large asymmetryfor LHC phenomenology [16]. These models have beenstudied individually, or in a group, to extract some globalfeatures which would insure generating a large asymmetrywhile contributing a negligible amount to the cross section,and to classify general features. A recent analysis [17]concludes that, among scalar mediated-processes, onlythe t-channel exchange of a QCD-singlet, weak doubletscalar is consistent with flavor and electroweak constraints,and does not conflict with the collider data obtained so far.

Although these models have been shown to produce alarge asymmetry, they all appear designed specifically toresolve this problem, are sometimes insufficiently justified,and thus they seem disconnected from other low-energyphenomenology constraints. In all models, large flavor-violation in the t-u or t-d quark sectors is enhanced, whileflavor changing in the other sectors is suppressed. Thequestion remains of whether such asymmetry can be ob-tained by employing a known and well-studied NP model.In particular, what is the prediction of such a model (al-lowing for maximum flexibility) and how important is forthe prediction of the asymmetry to impose the requirementthat the model satisfies known phenomenological con-straints. We propose to investigate here the effect on theasymmetry and t�t production cross section emerging fromWR and ZR bosons in the left-right symmetric model. Thismodel satisfies some definite conditions:

(i) It is one of the simplest and most natural extensionsof the SM;

(ii) It contains additional particles in both the s- andt-channels which could enhance the forward-backward asymmetry, but also the t�t cross section;

(iii) It has been thoroughly investigated and constrainedthrough many analysis, and, in particular, CDF andD0 have put limits on extra boson masses;

(iv) More information and testing of the model will beprovided soon by LHC (some recent bounds fromcolliders are discussed later).

We first perform an analysis of the t�t pair production andforward-backward asymmetry at the Tevatron, then weexplore the signal at LHC, for both the cross section andpossible asymmetries testable at the LHC. As we wish toallow the model to be as general as possible, we rely on ageneric model, without constraining masses, mixing pa-rameters or gauge couplings, but impose constraints com-ing from low-energy phenomenology, mainly K and Bphysics, but also collider restrictions coming from theTevatron. As the LHC data would be available fast, andthe constraints on particular models are rapidly changing,we are motivated by the fact that the LHC collaborations

are now analyzing unprecedented amounts of top data thatwill clearly rule out models. Thus a clear expectation ofmodel predictions for the LHC is timely.We will work in a parametrization in which the quark

mixing matrices in the left- and right-handed sectors(VL

CKM and VRCKM) are allowed to differ, and so do the

SUð2ÞL;R coupling constants gL and gR. We discuss the

case in which VRCKM ¼ VL

CKM and gR ¼ gL as a particular

case of a larger family of solutions. We are interested in theasymmetries and cross sections which can be obtained inleft-right models which satisfy the low-energy constraints,but also investigate values of the asymmetries in the modelwhen we relax the known constraints. We perform thesame analysis for the LHC, where we investigate the crosssection and LHC asymmetries at both

ffiffiffis

p ¼ 7 TeV andffiffiffis

p ¼ 14 TeV. Prospects for differentiating the left-rightsymmetric model from other BSM scenarios are outlined.Our paper is organized as follows: in Sec. II we describe

briefly our model. We proceed to evaluate the top-pairproduction and forward-backward asymmetry at theTevatron in Sec. III. Section IV we explore the modelpredictions for the LHC. We discuss our findings andconclude in Sec. V.

II. LEFT-RIGHT SYMMETRIC MODELS

We assume a generic left-right (LR) symmetric modelbased on the gauge group SUð3ÞC � SUð2ÞL � SUð2ÞR �Uð1ÞB�L [18]. The matter fields of this model consist ofthree families of quark and lepton fields with the followingtransformations under the gauge group:

QiL ¼ uiL

diL

!� ð3; 2; 1; 1=3Þ;

QiR ¼ uiR

diR

!� ð3; 1; 2; 1=3Þ;

LiL ¼ �i

L

eiL

!� ð1; 2; 1;�1Þ;

LiR ¼ �i

R

eiR

!� ð1; 1; 2;�1Þ;

(2.1)

with the numbers in the brackets representing the quantumnumbers under, respectively SUð3Þc, SUð2ÞL, SUð2ÞR andUð1ÞB�L. The gauge bosons of the left-right model are �,ZL, ZR, in the neutral sector, and W�

L , W�R in the charged

one. The Higgs sector necessary to break the left-rightmodel consists of one bidoublet:

� ¼ �01 �þ

2

��1 �0

2

� �� ð1; 2; 2; 0Þ; (2.2)

with the vacuum expectation values (VEVs)

h�i ¼ k 00 k0

� �: (2.3)

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Additional Higgs multiplets are needed to break the sym-metry to SUð2ÞL �Uð1ÞY and to generate a large massof WR relative to WL. Higgs triplets are a popular choice,as their VEV can also produce a large MWR

mass and

generate a large Majorana neutrino mass through theseesaw mechanism [19]

�L ¼�þ

Lffiffi2

p �þþL

�0L � �þ

Lffiffi2

p

0B@

1CA� ð1; 3; 1; 2Þ;

�R ¼�þ

Rffiffi2

p �þþR

�0R � �þ

Rffiffi2

p

0B@

1CA� ð1; 1; 3; 2Þ;

(2.4)

with VEVs, v�L� vL ¼ 0 and v�R

� vR.

The charged gauge bosonsWL andWR mix to form masseigenstates W1 and W2

WL ¼ W1 cos��W2 sin�;

WR ¼ ei!ðW1 sin�þW2 cos�Þ;(2.5)

with � a mixing angle and ! a CP violating phase. If � issmall, then WL and WR approximately coincide with W1

and W2. The mass matrix for the charged bosons is

M2W

¼1

4

g2Lðjkj2þjk0j2þ2jvLj2Þ �2gLgRk0k?

�2gLgRk0?k g2Rðjkj2þjk0j2þ2jvRj2Þ

!:

(2.6)

For jvRj � ðjkj; jk0jÞ � jvLj the masses become approxi-mately

M21 ’ 1

4g2Lðjkj2 þ jk0j2Þ; M2

2 ’ 12g

2RjvRj2 (2.7)

and the mixing angle is

� ’ � gLgR

2jkk0jjvRj2

: (2.8)

The right-handed bosons contribute to the charged andneutral currents for the quarks, which is

LCC¼ gLffiffiffi2

p �uiL��VLCKMijdjLW

�þL þgRffiffiffi

2p �uiR��V

RCKMijdjRW

�þR ;

(2.9)

LNC ¼ gLcos�W

½ �ui��ðTu3PL � eusin

2�WÞujþ �di��ðTd

3PL � edsin2�WÞdj�Z�

L

þ gR cos�

��ui��

�Tu3PR � 1

6tan2�

�uj

þ �di��

�Td3PR � 1

6tan2�

�dj

�Z�R ; (2.10)

where PL;R ¼ ð1 �5Þ=2 and sin� ¼ gB�Lffiffiffiffiffiffiffiffiffiffiffiffiffiffiffig2B�Lþg2R

p ( sin� ¼tan�W for gR ¼ gL) and similarly for the leptons, which are

allowed tomixwith different Cabibbo-Kobayashi-Maskawa(CKM)-type matrices. We adopt theWolfenstein parametri-zation for the CKM matrix VL

CKM [20]

VLCKM¼

1�2

2 A3ð� i�Þ� 1�2

2 a2

A3ð1�� i�Þ �A2 1

0BBB@

1CCCA: (2.11)

For the right-handed CKMmatrix, there are several left-right scenarios which appear in the literature:(i) In manifest LR symmetric models [21], the CP vio-

lation is generated by complex Yukawa couplings,while the VEVs of the Higgs fields remain real. Thisimplies the same mixing for right and left-handedquarks, VR

CKM ¼ VLCKM, where VL

CKM is the usual

Cabibbo-Kobayashi-Maskawa matrix, and equalgauge couplings for SUð2ÞL and SUð2ÞR, gR ¼ gL.

(ii) In pseudomanifest LR symmetry, both CP and Psymmetries are spontaneously broken [22], suchthat the Yukawa couplings are real. In this case theleft and right-handed quark mixings are relatedthrough VR

CKM ¼ VL?CKMK, with K a diagonal phase

matrix. Here as well, gR ¼ gL.(iii) In asymmetric LR symmetry, left-right symmetry is

assumed to be fundamental, superseding the Higgs,Yukawa, or fermion structure [23]. Here arbitrarymixing between the second and third generations,or between the first and third generations are al-lowed (within unitarity constraints). To simplifythe notation, we drop the CKM subscript and,following [23], denote the parametrizations as ðAÞand ðBÞ, where

VRðAÞ ¼

1 0 00 cos� � sin�0 sin� cos�

0@

1A;

VRðBÞ ¼

0 1 0cos� 0 � sin�sin� 0 cos�

0@

1A;

(2.12)

with � an arbitrary angle (� �=2 � �=2). Inparametrization ðAÞ, depending on the values of �,the dominant coupling could be VR

ts while in ðBÞ,the dominant coupling could be VR

td. The ðAÞ andðBÞ parametrizations are chosen to allow relaxingthe mass limit onWR while obeying the restrictionson �mK without fine-tuning.

The form of the CKM matrix in the right-handed quarksector affects low-energy phenomenology, in particular,processes with flavor violation, and thus restricts themass MWR

and the mixing angle �. These have been

analyzed recently in [24,25]. (For an alternative analysis,concentrating on the CP violation properties of the model,see also [26]).The constraints on the parameter space of the left-right

model, mostly from flavor-violating processes, which are

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relevant to the study of WR phenomenology, come fromK0 � �K0 mixing, B0

d � �B0d and B0

s � �B0s mixing, and

b ! s�. These constraints depend on several parametersand are difficult to summarize analytically; however, theyare included in the evaluation of the t�t cross section andforward-backward asymmetry, analyzed in the nextsection.

We also include restrictions imposed by the availabledata from ATLAS which seems to rule out a Z0 resonancewith MZ0 < 950 GeV, with the exact limit depending onspecific models and specific assumptions [27]. A recent talkat the European Physics Society meeting [28] reports newbounds on Z0 mass, with 50 times more data (�2fb�1) andwith new bounds varying from 1.5 TeV to 1.8 TeV depend-ing on the models. Similarly there are new bounds from theCMS and D0 collaborations [29,30] with total integratedluminosity 1:1 fb�1 and 5:4 fb�1, respectively. While thebounds from CMS are very similar to the ones fromATLAS, D0 bounds are somewhat weaker. A relevant studyby Nemevsek et al. [31] on the bound onWR mass using the33 pb�1 LHC data at 7 TeV reportsMWR

> 1:4 TeV, but is

also spectrum specific and depends on whether the right-handed neutrino is Majorana or Dirac and whether it islighter or heavier than MWR

. We assume the right-handed

neutrino heavier than MWRso that the above bound is

evaded.For the evaluation of the cross section and the asymme-

try, we have chosen two benchmark parameter sets for eachof model A, model B and manifest left-right symmetricmodels, defined as previously. To select particular bench-mark points, we used the results of our previous parameterscans overMWR

, sin�,MH� and gR=gL in [24,25] where we

have presented restrictions over the parameter space ob-tained by imposing low-energy constraints from mesonmixings and b ! s� branching ratio, as well as colliderconstraints on production of extra gauge bosons. The pa-rameter scan leaves very small allowed regions where theWR is light, and/or the flavor violation from the right-handed sector is significant. These points were explicitlychosen from all the allowed parameter space to maximizeflavor violation in the right-handed quark sector, for bothlight and heavy MWR

scenarios. While we work with these

choices, we shall comment on the effect of varying thechosen sets in the parameter space. The parameter sets for

each model, namely, set I and set II, that are used in ourcalculations in accordance with those constraints are givenin Table I. We include, in addition to the set I and set II, aleft-right scenario for each of the three models which is notsubjected to experimental constraints as in [24,25], whichwe call the unconstrained LR set. We require that thismodel is roughly consistent with collider limits on the t�tcross section. Our aim is to show the effects of experimen-tal restrictions on the parameter space and highlight that‘‘relaxing’’ them can produce large asymmetries.

III. t �t CROSS SECTION ANDFORWARD-BACKWARD ASYMMETRY

AT THE TEVATRON

The top quark pair production in p �p collisions is mostlyaccomplished through s-channel quark-antiquark annihila-tion (about 90%) and much less so through gg and qgprocesses. The latest CDF and D0 measurements of thecross section [2] agree with the SM at the next-to-next-to-leading order (NNLO) prediction [32],

�CDFIIðp �p!t�tÞ ¼ 7:50� 0:48 pb; (3.1)

�NNLOðp �p!t�tÞ ¼ 7:39� 0:55 pb: (3.2)

We proceed to analyze the top-pair cross sections in theleft-right models. For consistency, we evaluate here thecross section in the SM, as well as in the LR models underscrutiny: the manifest model, model A and model B, for theset I and set II for each model and, by comparison, for theunconstrained set. Any new model must predict a crosssection which agrees with the experimental data, as thecross section is particularly sensitive to s-channel exoticresonances, thus restricting the mass of the ZR boson in LRmodels.In the calculation of t�t production cross sections we

proceed as follows. We first calculate the LO cross sectionsat

ffiffiffis

p ¼ 1:96 TeV with mt ¼ 172:5 GeV, using CTEQ6M

parton distribution function (PDF) set to go from parton top �p cross sections. We then calculate the NNLO crosssection by multiplying the LO result with the K factor(K ¼ 1:3 for Tevatron [32]) as in the SM. We assume forsimplicity that the K factors are universal, so that the NP/SM ratios at LO and NNLO are the same, minimizing the

TABLE I. Benchmark points set I, set II and unconstrained for left-right symmetric models: Manifest, model A, and model B, usedthroughout the analysis. Note that MZR

is fixed when a value for MWRis chosen but MZR

values are included for reference.

Manifest Model A Model B

Set I Set II Uncons. Set I Set II Uncons. Set I Set II Uncons.

MWR(GeV) 700 1500 500 700 1000 500 1100 1300 500

MZR(GeV) 1172 2511 837 2189 1674 734 3441 2176 734

gR=gL 1 1 1 0.6 1 2 0.6 1 2

sin� - - - 0.5 0.25 0.7 �0:2 �0:1 0.7

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impact of the NNLO corrections to the LR model contri-butions (See our comments in the next paragraph). We listthe cross sections obtained in Table II.

The CDF and D0 results impose that in addition to thetotal production cross section of t�t, the differential crosssection with respect to the invariant mass of t�t should alsoagree with the SM prediction. Thus, in Fig. 1 we graph thedifferential cross sections in LR models with respect to thet�t invariant mass distributions and compare our calculationwith the CDF II measurement. In the three panels of Fig. 1we show in sequence the differential cross sections for themanifest, model A and model B for the two parameter sets,set I (red), set II (green), as well as the unconstrainedset (blue). We include in the figure the uncertainties inour calculations, as given by the numerical routine. TheCDF data is given as black lines, and includes uncertaintiesin each bin. Note that care must be taken when comparingthe new physics cross sections against the SM cross sec-tion, as the selection efficiencies for NP models can belower. The predicted NNLO SM cross section requires aSMK factor of 1.3, while the NNLO corrections to the newphysics have not been calculated, so any comparison be-tween the observed cross section and the t�t productioncross section is subject to some uncertainty [33].Comparing our results to the central value of the combinedCDF t�t production cross section to the cross section of SMplus new physics for all three parameters sets show fairlygood agreement with the Mt�t distribution measured byCDF II, and given our comments above, it probably mayyield even better agreement. Thus we insured that, for theparameters chosen, both the total and the differential crosssections are consistent with the data. Note however theslight enhancement of the differential cross section in theunconstrained set for Mt�t > 500 GeV, due to low MZR

¼734 GeV for models A and B. The raise is shifted and (notseen due to an uneven bin choice) for the unconstrained setof the manifest model, where MZR

¼ 837 GeV.

We proceed next by examining the asymmetry in theproduction and decays of the t�t system. The forward-backward asymmetry of top quark pairs (At�t

FB) in p �pcollisions is seen as a precision test of the SM. The t�tpair production in SM at the lowest order is symmetric

under charge conjugation. At NLO, the interference ofQCD processes involving initial and final state gluon emis-sion q �q ! t�tg and qg ! t�tq will exhibit a small forward-backward asymmetry. The NLO calculations in the SMyield an asymmetry due to virtual corrections arising frominterference effects, which are opposite in sign and largerthan the real emission component.The forward-backward asymmetry is defined in terms of

top quark rapidities as

A FB ¼ Nð�y > 0Þ � Nð�y < 0ÞNð�y > 0Þ þ Nð�y < 0Þ ; (3.3)

where �y ¼ yt � y�t is the difference of top and antitop

rapidities and N is the number of events in the forward(�y > 0) and backward (�y < 0) regions. While the cross

sections measured by CDF and D0 agree with the SMexpectations, the measured asymmetries deviate from theNLO SM calculation, by as much as 50% in the large Mt�t

invariant mass bin. It is the challenge of any new BSM togenerate the asymmetry without disturbing the cross sec-tion; it is our intention to verify if this is possible for arealistic left-right model.We proceed as follows. Since the kinematical cuts in

Tevatron analysis are very restrictive, we generate 5� 106

signal events in order to minimize the statistical errors. Wegenerate events with CALCHEP 3.1 [34] using CTEQ6M PDFs.The factorization and renormalization scales �F ¼ �R ¼mt are used, and we take the top quark mass mt ¼172:5 GeV. We use PYTHIA 6.4.18 [35] for showering andPGS 4 [36] for jet reconstruction, b-tagging and a rough

detector simulation.We start the analysis by producing the t�t pair, then

decaying top quarks semileptonically and hadronically.We concentrate our analysis on the leptonþ jets topology,where one top quark decays semileptonically (t ! bl�)and the other hadronically (t ! bq �q0), as in Fig. 2. Weselect events with one single lepton (electron or muon) plusmissing energy to account for the associated neutrino and aminimum of 4 jets with one jet b-tagged and with thefollowing kinematical cuts,

j�lj< 1; j�jj< 2; plT > 20 GeV;

pjT > 20 GeV; 6ET � 20 GeV; j�bj< 1;

(3.4)

where l, j, b denote lepton (e, �), jet (u, d, c, s) andb-quark parameters, respectively. The jets are recon-

structed using a cone algorithm with �R ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi��2 þ ��2

p< 0:4. Here b-jets, tagged with the loose

SECVTX algorithm, are restricted to j�bj< 1. We used

the default b-tagging efficiency and functions forTevatron given in PGS 4. The efficiency of the signal topass through the cuts (after showering, clustering anddetector simulations) allows only 2% signal events tosurvive the kinematical cuts to yield the forward-backwardasymmetries.

TABLE II. The NNLO t�t production cross sections at Tevatron(ffiffiffis

p ¼ 1:96 TeV) for the SM, and Left-Right models: Manifest,model A and model B, for the benchmark points chosen.

SM

�NNLO (pb) 7:36� 0:007Manifest Set I Set II Uncons.

�NNLO (pb) 7:37� 0:007 7:37� 0:007 7:43� 0:008Model A Set I Set II Uncons.

�NNLO (pb) 7:36� 0:007 7:37� 0:007 8:35� 0:008Model B Set I Set II Uncons.

�NNLO (pb) 7:36� 0:007 7:36� 0:007 8:17� 0:008

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The number of events are scaled to the NNLO crosssections using the standard K factor for the Tevatron. Wehave calculated the left-right contribution at the LO (in-cluding the LO SM, LR and the interference between thetwo) to the asymmetries. We listed asymmetries obtainedfor the four different regions, for all models studied, inTable III. The first two rows are parton-level asymmetries,the first row obtained by unfolding the CDF data and thesecond for the Monte Carlo for FeMtobarn processes

(MCFM). The remaining rows compare the CDF signaldata to our various models2 As it is seen from theTable III, the LO left-right contributions to the asymmetriesare relatively small. The results might have been enhancedif the left-right contributions were calculated at the NLO

FIG. 1 (color online). t�t invariant mass distribution of differential cross section in manifest LR model (upper panel), model A (lowerleft panel) and model B (lower right panel) in comparison with CDF II 5:3 fb�1 data. Parameter sets (set I, set II and unconstrained set)for each model are given in the Table I. We include as well the uncertainties in our numerical evaluation.

2In fact, the signal-level data for the regions j�yj � 1 orj�yj 1 are not presented in [4]. So, we have used the data-level values including the background.

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which is beyond the scope of this work. We have chosen tocompare our results, simulated to the final states, with theCDF signal. The reason is that the errors in the signal resultsare much smaller than the ones evolved to parton level, andthus this comparison gives a better measure of the deviationof our results from the data. We include a reduced 2

analysis as a measure of how well the models perform.As expected all the scenarios other than unconstrained LRmodel A and model B give asymmetries more than 4 sigmaaway from the observed ones. The situation for the model Aand B of the unconstrained LR is close to 1 sigma.

It is apparent from Table III that, while the models yielda slightly enhanced or slightly suppressed forward-backward asymmetry with respect to the SM in one regionor another, none of the phenomenologically viable LRmodels can reproduce large enough anomaly seen at theTevatron. The results for the benchmark points chosenfor manifest, model A and model B are however fairly

consistent in the both sign and size of the anomaly.Moreover the asymmetry seems to depend sensitively onMWR

and on the ratio gR=gL, but to a lesser extent on sin�,

the measure of flavor violation in the right-quark sector.From our previous investigations of the parameter spacewe know that MWR

and gR=gL are closely correlated, as a

decrease or increase in one forces a decrease or increase inthe other to satisfy low-energy constraints. We are thusconfident that results for the sets chosen are a true indica-tion of LR model predictions. As sets I and II representvery different regions of the parameter space, and differentvariants of the model, this is further confirmation that ourresults are robust and do not depend on the specific pointschosen in the parameter space of the LR model. One canobtain higher asymmetries (consistent with the data) in aLR model not subjected to experimental constraints (lasttwo rows in Table III), as indeed is the case for modelsconstructed specifically to explain the asymmetry.We proceed to investigate the features of the signal in LR

models. In Fig. 3 we show the distributions of rapiditydifferences �y in the upper row, and top quark rapidity ytin lower row, for three different LR models. In order togenerate a large asymmetry in the high invariant mass bin,the rapiditymust be increased and skewed significantly withrespect to the SM distribution. Additional high mass gaugebosons could sometimes produce this effect. We show themanifest model (left panel), model A (middle panel) andmodel B (right panel) with set I (blue) set II (green) theunconstrained (red) and the SM (black) in each panel. Wedid not perform a global fit to the data, as our results do notagree with the CDF measurements. The results are howeverconsistent among the different models obeying low-energyconstraints, and parameters sets chosen, at least making theleft-right model very predictable.In Fig. 4 we give invariant mass distributions in PYTHIA

of LR models at Tevatron, for the manifest LR model

FIG. 2. t�t production and decay topology in hadronic andsemileptonic events. V0

� represents neutral gauge bosons �, g,

Z, ZR and V�� the charged ones, W�

L , W�R . The diagram with the

top quark decaying hadronically is shown but both possibilitiesare included.

TABLE III. The forward-backward asymmetry at the Tevatron in the LR models: Manifest, model A and model B, compared withthe CDF data. We include, in the first two rows, the unfolded CDF results and the MCFM calculation. Parameter sets (set I, set II andunconstrained) for each model are given in the Table I.

At�tFB At�t

FB At�tFB At�t

FB 2red

j�yj< 1 j�yj � 1 Mt�t < 450 GeV Mt�t � 450 GeV (4 d.o.f.)

CDF (parton level) 0:026� 0:118 0:611� 0:256 �0:116� 0:153 0:475� 0:114MCFM (parton level) 0:039� 0:006 0:123� 0:008 0:040� 0:006 0:088� 0:013CDF (signal level) 0:021� 0:031 0:208� 0:062 �0:022� 0:043 0:266� 0:062LR Manifest-I 0.0025 0.0174 0.0030 0.0086 6.8

Manifest-II 0.0098 0.0162 0.0091 0.0137 6.7

Model A-I 0.0063 0.0143 0.0065 0.0096 6.9

Model A-II 0.0043 0.0131 0.0051 0.0072 7.0

Model B-I 0.0077 0.0121 0.0062 0.0118 6.9

Model B-II 0.0035 0.0038 0.0029 0.0044 7.3

Uncons. LR Manifest 0.0065 0.0280 0.0024 0.0222 6.1

Model A 0.0532 0.2400 0.0078 0.1832 0.9

Model B 0.0444 0.2189 �0:0084 0.1751 0.7

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FIG. 3 (color online). �y (upper row) and yt (lower row) distributions in manifest LR model (left panel), model A (middle panel) andmodel B (right panel) at the Tevatron. Parameter sets (set I, set II and unconstrained) for each model are given in the Table I.

FIG. 4 (color online). t�t invariant mass distributions at the Tevatron in manifest LR model (left panel), model A (middle panel) andmodel B (right panel) in comparison with the SM. Parameter sets (set I, set II and unconstrained) of each model are given in the Table I.

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(left panel), model A (middle panel) and model B (rightpanel). The number of events are scaled to NNLO crosssections with standard K factor. Comparison with the SMexpectations again shows consistency.

Both this figure and the previous one show that realisticLR models, which obey low-energy constraints, cannotyield the measured CDF asymmetry. The unconstrainedmodel shows an increase in the differential cross section,corresponding to a ZR peak around 734 GeV in models Aand B, and a less pronounced one at 837 GeV in themanifest left-right case. These are close to the experimen-tal limit at the Tevatron, and the first two are likely alreadyruled out. Changing the ratio gR=gL and lowering the WR

mass may be able to achieve consistency of left-rightmodels with the asymmetry data, but these models do notsatisfy other phenomenological constraints and are thusunrealistic.

IV. CROSS SECTION FOR t �t PAIR PRODUCTIONAND ASYMMETRIES AT THE LHC

As the Tevatron results show interesting discrepancieswith the SM expectation, it is important to evaluate theasymmetries and cross sections for t�t production at theLHC. Naturally one might ask if such a pursuit is worth-while, as we have shown in the previous section that themodel cannot explain the Tevatron asymmetries. The largeforward-backward asymmetry at the Tevatron, although anexciting signal for new physics, may not arise from newinteractions or new particles. It could arise from a kine-matical enhancement of the t�t pair, or from a hidden sector.Even the experimental situation at the Tevatron is not yetclear, as the errors on the measurements are significant;also the CDF results show a strong mass dependence of theasymmetry not confirmed by the D0 measurements. AtLHC different production mechanisms dominate and otherasymmetries are at play. Measurements of the chargeasymmetry at CMS and ATLAS at the LHC (which appearto be small and negative, though the uncertainties are toolarge to make a firm statement) are hard to reconcile withthe Tevatron results. Predictions for both colliders areimportant to understand the dynamics of different gaugesymmetries and their effect on different asymmetries. Thisis particularly interesting for our model, which can repro-duce the Tevatron cross section but not the asymmetry. Thenatural question is: what is the prediction for the LHC?While the Tevatron has collected about a thousand tops, theLHC, even with L ¼ 1 fb�1 has amassed almost an orderof magnitude more, making the errors in the productioncross section at

ffiffiffis

p ¼ 7 TeV already competitive withthose at the Tevatron with L ¼ 5:3 pb� 1, while theinvariant mass Mt�t investigated extends to 2.5 TeV (with200 pb�1), versus 1.8 TeV for the Tevatron. LHC willprovide measurements of top quark properties, sheddinglight on models on NP and electroweak symmetry break-ing. Agreement or disagreement with this data would open

(or perhaps narrow) questions to do with the validity orrestrictions of the model. For example, the CMSCollaboration has recently presented the first measurementof charge asymmetry in t�t production [37]

A�C ¼ �0:016� 0:030ðstatÞþ0:010

�0:019ðsystÞ;AyC ¼ �0:013� 0:026ðstatÞþ0:026

�0:021ðsystÞ:(4.1)

The first one based on pseudorapidities (�), the second onthe rapidity (y) of the two top quarks, while the combined(eþ jets and �þ jets channels) ATLAS [38] result is

AC ¼ �0:024� 0:016ðstatÞ � 0:023ðsystÞ: (4.2)

As seen, these results have so far large statistical uncer-tainties, but this uncertainty is expected to decrease withmore data, while the systematic one will improve withimproved detector simulation.The Tevatron however is a better machine for measuring

the forward-backward asymmetry. At the Tevatron, theforward-backward asymmetry measures the tendency ofthe top quark (in the t�t pair) to move along the direction ofthe incoming quark rather than along the direction of theincoming antiquark. At LHC, the measurement of anyasymmetry is very subtile. Its charge-symmetric initialstate (pp, or the dominant gg, qq partonic level channels)does not provide a framework to differentiate betweeninitial partons in the t�t production. To define an asymmetryone must rely on subleading contributions to the t�t pro-duction cross section from q �q and qg, with different par-tons in the initial state. In this case, the forward-backwardasymmetry represents a charge asymmetry in the decay q �q,qg ! t�tþ X [16], though several other types of asymme-tries have been defined [39] and used to discriminatebetween BSM models.We proceed to analyze the properties of the left-right

model in top-pair production and decays. We evaluate the t�tproduction at the LHC following the same procedure usedin the previous section to analyze the signal at the Tevatron.First, we estimate the total and differential cross section fort�t production for the models under investigation, then weproceed to define and analyze the charge asymmetry.At the LHC, the t�t production is dominated by gluon

fusion in pp collisions. In our calculation we implementthe models in CALCHEP 3.1 for the evaluation of productioncross sections at LO level. We normalize the cross sectionsto NNLO using the NNLOK factor (K ¼ 1:6 for LHC) andwe present them in Table IV for both

ffiffiffis

p ¼ 7 TeV andffiffiffis

p ¼ 14 TeV, for the same parameter sets and models asdiscussed in the previous section and given explicitly inTable I. While the SM and manifest LR model are com-pletely consistent for both set I and set II parameters,models A and B predict a slightly smaller (about 8%)production cross section (but consistent for both set I andII), all of which agree with the measured value (includingerrors) at ATLAS at

ffiffiffis

p ¼ 7 TeV [40] and with the SMpredictions at NNLO [32],

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�ATLASt�t ¼145�31þ42

�27 pb; �NNLOt�t ¼150 pb; (4.3)

while the prediction for the cross section in the SM atNNLO at

ffiffiffis

p ¼ 14 TeV is �NNLOt�t ¼ 919� 4 pb [32]. A

complete analysis of the production cross section shouldinclude subsequent decays of the top quark, as only adetailed analysis would be able to conclude if one candistinguish various scenarios. We present below some de-tails of our analysis.We show in Fig. 5 the number of events in the invariant

mass distributions for t�t obtained after imposing detectorcuts and passing through the detector simulation, in themanifest LR model (left panel), model A (middle panel)and model B (right panel) at the LHC with

ffiffiffis

p ¼ 7 TeV(upper row) and

ffiffiffis

p ¼ 14 TeV (lower row), where wedistinguish between sets I, II, unconstrained and the SMas before. These events are then used to evaluate the charge

TABLE IV. t�t production cross sections at LHC, for bothffiffiffis

p ¼7 TeV and

ffiffiffis

p ¼ 14 TeV.

SM

�7 TeV (pb) 167� 0:17�14 TeV (pb) 921� 1:20Manifest Set I Set II Uncons.

�7 TeV (pb) 168� 0:23 168� 0:20 169� 0:19�14 TeV (pb) 924� 1:99 923� 2:30 926� 1:41Model A Set I Set II Uncons.

�7 TeV (pb) 168� 0:12 168� 0:14 179� 0:11�14 TeV (pb) 922� 1:33 921� 1:46 967� 1:82Model B Set I Set II Uncons.

�7 TeV (pb) 168� 0:15 168� 0:12 178� 0:10�14 TeV (pb) 919� 1:31 921� 1:04 962� 1:52

FIG. 5 (color online). Events in the t�t invariant mass distributions at LHC in manifest LR model (left panel), model A (middle panel)and model B (right panel) in comparison with the SM. Top row shows the distribution for

ffiffiffis

p ¼ 7 TeV, the bottom row is forffiffiffis

p ¼14 TeV. Parameter sets (set I, set II and unconstrained) for each model are given in the Table I.

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TABLE V. Forward and central charge asymmetries at LHC at signal level. Parameter sets (set I, set II and unconstrained) for eachmodel are given in the Table I.

At�tC (7 TeV) At�t

F (7 TeV) At�tC (14 TeV) At�t

F (14 TeV)

0< jyj< 1:5 1:5 jyj< 2:5 0< jyj< 1:5 1:5 jyj< 2:5

SM �0:0024 0.0157 0.0011 �0:0028

LR Manifest-I �0:0014 0.0097 �0:0035 0.0050

Manifest-II 0.0013 �0:0091 �0:0031 0.0133

Model A-I �0:0045 0.0236 0.0002 �0:0035

Model A-II �0:0020 0.0127 0.0033 �0:0234

Model B-I 0.0021 �0:0142 �0:0002 0.0003

Model B-II �0:0001 �0:0038 �0:0053 0.0179

Uncons. LR Manifest �0:0013 0.0063 �0:0084 0.0260

Model A �0:0117 0.0650 �0:0063 0.0217

Model B �0:0087 0.0469 �0:0075 0.0158

FIG. 6 (color online). Top (upper row) and antitop (lower row) rapidity distributions in manifest LR model (left panel), model A(middle panel) and model B (right panel) at LHC (

ffiffiffis

p ¼ 7 TeV). Parameter sets (set I, set II and unconstrained) for each model aregiven in the Table I.

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asymmetries at the LHC. The events generated are consis-tent among the models studied, and show a modest bumpfor the unconstrained model corresponding to the ZR reso-nance production. It is evident from the figure that the Mt�t

invariant mass distribution for all models chosen is thesame, and indistinguishable from the one in the SM. Theimportant distinction lies in the possible discovery of aZ0 ¼ ZR boson, which in the manifest LR model set I has amass of 1200 GeV, as well as the ones around 730–830 GeV for the unconstrained sets (depending on themodel considered). These appear as a resonance bump int�t production. For the set I and set II of model A andmodel B, the resonances are heavier and out of the Mt�t

range presented.We proceed to evaluate the asymmetries at the LHC.

As previously mentioned, due to the pp initial state, t�tasymmetries at the LHC can be defined as forward andcentral charge asymmetries. The division of top quark

rapidity yt between forward and central regions of thedetector distinguishes the two asymmetries. The separationparameter y0 defines the forward jytj> y0 and centraljytj< y0 regions of the detector. As an optimum choiceof separation parameter we use y0 ¼ 1:5 [16]. We definethe forward charge asymmetry

A Fðy0Þ¼Ntðy0< jyj<2:5Þ�N�tðy0< jyj<2:5ÞNtðy0< jyj<2:5ÞþN�tðy0< jyj<2:5Þ (4.4)

and the central charge asymmetry

A Cðy0Þ ¼ Ntðjyj< y0Þ � N�tðjyj< y0ÞNtðjyj< y0Þ þ N�tðjyj< y0Þ ; (4.5)

whereNtð�tÞ represent the number of top (antitop) quarkswith

given asymmetry. To calculate the asymmetries, we used thesame procedure as in the case of the Tevatron, employingCALCHEP-PYTHIA-PGS for event generation, parton shower-

FIG. 7 (color online). Top (upper row) and antitop (lower row) rapidity distributions in manifest LR model (left panel), model A(middle panel) and model B (right panel) at LHC (

ffiffiffis

p ¼ 14 TeV). Parameter sets (set I, set II and unconstrained) for each model aregiven in the Table I.

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ing, jet reconstruction and detector simulation. For theanalysis we used the same leptonþ jets topology with onesemileptonic and one hadronic top decays. We proceed byselecting single lepton events with an associated neutrinoand a minimum 2 jets with at least one b-quark tagged. Weimposed the following kinematical cuts for event selection atthe LHC (using the same symbols as before)

j�lj< 2:5; j�jj< 2; plT > 15 GeV;

pjT > 20 GeV; 6ET � 20 GeV; j�bj< 1:

(4.6)

The jets are reconstructed using a cone algorithmwith�R¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi��2þ��2

p<0:5. Here again b-jets, taggedwith the loose

SECVTX algorithm, are restricted to j�bj< 1. Please note

that b-tagging efficiency and functions given in PGS 4 arebased onTevatronparameters. Thuswe follow the proceduregiven in [41] to update the b-tagging functions according tothe Eq. (2) of [41]. In the LHC analysis jet events are muchmore energetic due to the high center of mass energy of thecollision, and thus the jet reconstruction algorithm in PGS 4

consumes huge amount of computing time. Since the kine-matical cuts are fairly relaxed in the LHC case, we havechosen lesser amount of events (2� 105) simulated forevery asymmetry evaluation with reasonable statistical er-rors. After imposing all the detector cuts, asymmetries arecalculated using the 10% signal events surviving. The cal-culation for the LHC asymmetry in the SM as well as LRmodels is based on simulating events normalized to the crosssections at NNLO level by using the standard K factor. Theresults are shown in Table V. The asymmetries are verysmall, and the asymmetries in LRmodels can have differentsigns than in the SM, although unfortunately this seemshighly parameter-dependent. At this point, these asymme-tries appear consistent (of the same size) with the ATLASand CMS measurements and most tend to be small andnegative. To make a more definite statement, one mustwait for more precise experimental data. The LHC resultsare obtained over thewhole rapidity parameter values, whileour results are divided into regions for better understandingof model dynamics. The experimental results have largeuncertainties,making themnot yet very predictable; a higherluminosity might change that. The charge asymmetrychanges sign when measured in the forward region fromthe onemeasured in the central region of the detector in bothSM and LR models.

In Figs. 6 and 7 we show the top and antitop rapiditydistributions in LRmodels at the LHC for

ffiffiffis

p ¼ 7 TeV andffiffiffis

p ¼ 14 TeV, in manifest LR model (left panel), model A(middle panel) and model B (right panel). Parameter sets(set I, set II and unconstrained) for each model are distin-guished (by blue, green and red curves). The SM distribu-tions are given by black curves. These figures should becompared to Fig. 3 from the Tevatron section. By compari-son, the LHC asymmetries are even more dominated byevents at, or near zero charge asymmetry for both top andantitop quarks and do not showmeasurable deviations in LR

models. Thus a significant charge asymmetry for top orantitop quarks at the LHC would be indicative of BSMscenarios other than left-right models—so far, this doesnot appear to be the case. It may be difficult to use the chargeasymmetry to distinguish between various models, eventhose which predict large asymmetries at the Tevatron, as acomprehensive analysis of their predictions at the LHCshows that they seem to be small, though some modelsmay differ when evaluated at high invariant masses, whichare especially sensitive to the q �q contribution [42].

V. CONCLUSIONS

The observation of a large forward-backward asymme-try in t�t production at the Tevatron offers tantalizing sig-nals of physics beyond the Standard Model. For largerapidities and large invariant t�t mass distributions, themeasurements deviate by 3� or more from the SM expec-tations. This seems to indicate that the phenomenology ofthe top quark, which has a mass of the order of electroweaksymmetry breaking, may offer a window into new muchanticipated BSM. Several models have been producedspecifically to deal with the measurements. Though in-structive, they seems like a band-aid solution. In addition,recent investigation of whether the increase in the asym-metry at large invariant massMt�t can be accounted for by atree-level scalar exchange indicates that the range of mod-els who remain consistent with other top-related measure-ments, flavor-violation constraints, electroweak precisionmeasurements and collider data, is far more restricted thaninitially thought. There are at present other measurementswhich indicate deviations from the SM, which are notexplained by most of the ad hoc models which provide afix for the forward-backward asymmetry.One can then ask, what about the BSM scenarios favored

on theoretical grounds, and already analyzed and subjectedto relevant phenomenological and experimental tests. Inthis work, we analyze the left-right model, in fact a generalversion of this model, where left and right coupling con-stants are not equal, and the quark mixing matrices in theleft and right sectors are unrelated. The model is subjectedto constraints coming from meson mixing (K0 � �K0, B0

d ��B0d and B0

s � �B0s) and b ! s�. The production of WR has

been previously studied in this model and limits on themasses, coupling constants and right-handed quark mixinghave been included. It is worthwhile to ask whether such amodel can explain the deviation of the predicted asymme-try from the observed one at the Tevatron. The LR modelhas the features desired for a resolution: a WR in thet-channel which can be responsible for the asymmetry,and a heavier ZR in the s-channel, which may affect theobserved cross section.Our analysis shows that, if the cross section agrees with

the SM model one, as confirmed by the CDF data, themodel is not able to generate sufficient asymmetry at theTevatron to explain the observed discrepancy. We should

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add that this result survives variations in coupling con-stants, boson masses and right-handed CKM mass mixingparameters in the allowed parameter space determined bylow-energy data. Relaxing these constraints would defi-nitely yield bigger asymmetries and would provide largeenough asymmetries to agree with the Tevatron data, as theunconstrained version of LR models shows. This model isthus unlike models which explain the asymmetry throughexchange of a light W 0 in the t-channel, coupling with alarge coupling to only the t-d quark sector, and whichrequires additional fermions for anomaly cancellation.

We analyze the t�t cross section and asymmetries at theLHC. The cross section agrees with the one predicted by SMand measured at

ffiffiffis

p ¼ 7 TeV. One would expect to see theZR resonance for increased CM energy: so far, the indica-tions are negative, pushing the Z0 mass into the TeV range(although the precise values depend on the model and pa-rameters chosen). It is also likely that the LHC, looking fortop jet resonances, would either validate or rule out at>3�level any extra Z0 or W 0 models which can reproduce theTevatron asymmetry. The left-right models predict a negli-gible charge asymmetry (the relevant defined parameter atthe LHC), in either forward or central regions, at both

ffiffiffis

p ¼7 and 14 TeV. The predictions for the asymmetry are notalways well-defined in sign, but the LR models are consis-tent with the SM predictions and so far, with the experimen-tal results form ATLAS and CMS. The forward and centralcharge asymmetry have opposite signs. The arbitrariness insign is unfortunate as it was shown that a definite positive(central-value) charge asymmetry at the LHC wouldstrengthen the Tevatron results, while a definite negative(central-value) asymmetry would be unexpected and itsexplanation conflict with models that pass the Tevatronrequirements [42]. One can draw two conclusions. One isthat while the LRmodels predictions for the cross sections attheTevatron andLHC and the asymmetry at LHCagreewiththe experimental data, these models cannot provide an ex-planation for the observed Tevatron forward-backward

asymmetry. We can ascertain this with confidence, as it isvalid for a large region of the parameter space and validindependent of whether we chose manifest, model A ormodel B. The questions still remain: are the Tevatron andLHC results inconsistent with each other (this will becomeclear with more precise LHC data), and what is the origin ofthe large forward-backward asymmetry. The second con-clusion is that, while predictions for charge and forward-backward asymmetries are important in comparing modelsto experimental data, they not good indicators of left-rightmodels because they are very small. A more promisingalternatives would be to search for WR bosons, predictedto be lighter than ZR; measurements of top quark polariza-tion which could indicate right-handed physics; andmeasuring left-right, rather than forward-backward, asym-metries. These tests are beyond the scope of this work andwill be presented elsewhere.There is however another issue that arises. Except

for the ad hoc models (some of which are already ruledout by a more careful analysis), it appears likely that noneof the better-known BSM scenarios can produce largeforward-backward asymmetries. Should negative asymme-tries survive at LHC, consistency with Tevatron measure-ments would be challenging and demonstrate that topquark physics has subtleties not fully yet understood.Should asymmetries at the LHC be found to be small andpositive, the challenge would be in how to understand theirenhancement in p �p but not pp (within normal expectationsof symmetries in pp initial states). But before measure-ments, one must know what results to expect from estab-lished BSM scenarios. As many such scenarios are plaguedby uncertainties due to a large parameter space, a clearresult is important, as it would restrict BSM possibilities.

ACKNOWLEDGMENTS

M.F. and A.H. would like to thank NSERC of Canadafor partial financial support under Grant No. SAP105354.

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