Massive color-octet bosons and the charge asymmetries of top quarks at hadron colliders
IIFIC/08-49arXiv:0809.3354 [hep-ph]
Massive color-octet bosons and the charge asymmetries of topquarks at hadron colliders
Paola Ferrario ∗ and Germ´an Rodrigo † Instituto de F´ısica Corpuscular, CSIC-Universitat de Val`encia,Apartado de Correos 22085, E-46071 Valencia, Spain.
Abstract
Several models predict the existence of heavy colored resonances decaying to top quarksin the TeV energy range that might be discovered at the LHC. In some of those models,moreover, a sizable charge asymmetry of top versus antitop quarks might be generated. Thedetection of these exotic resonances, however, requires selecting data samples where the topand the antitop quarks are highly boosted, which is experimentally very challenging. Weasses that the measurement of the top quark charge asymmetry at the LHC is very sensitiveto the existence of excited states of the gluon with axial-vector couplings to quarks. Weuse a toy model with general flavour independent couplings, and show that a signal can bedetected with relatively not too energetic top and antitop quarks. We also compare the resultswith the asymmetry predicted by QCD, and show that its highest statistical significance isachieved with data samples of top-antitop quark pairs of low invariant masses.IFIC/08-49September 19, 2008 ∗ E-mail: paola.ferrario@ific.uv.es † E-mail: german.rodrigo@ific.uv.es a r X i v : . [ h e p - ph ] S e p Introduction
The Large Hadron Collider (LHC) will start-up very soon colliding protons to protons. In a first run, at acenter of mass energy of √ s = 10 TeV, about pb − of data are expected to be collected. The 2009 runwill operate at the full √ s = 14 TeV design energy with an initial low luminosity of L = 10 cm − s − (equivalent to fb − /year integrated luminosity). The production cross section of top-antitop quarkpairs at LHC is about pb at TeV, and pb at 14 TeV [1]. The LHC will produce in the firstphase of operation a sample of t ¯ t -pairs equivalent to the sample already collected at Tevatron during itswhole life, and millions of top-antitop quark pairs in the next run at TeV. This will allow not onlyto measure better some of the properties of the top quark, such as mass and cross section, but also toexplore with unprecedented huge statistics the existence of new physics at the TeV energy scale in thetop quark sector.At leading order in the strong coupling α s the differential distributions of top and antitop quarks areidentical. This feature changes, however, due to higher order corrections [2], which predict at O ( α s ) acharge asymmetry of top versus antitop quarks. A similar effect leads also to a strange-antistrange quarkasymmetry, s ( x ) (cid:54) = ¯ s ( x ) , through next-to-next-to-leading (NNLO) evolution of parton densities [3]. AtTevatron, the charge asymmetry is equivalent to a forward–backward asymmetry because the top and theantitop single inclusive distributions are related by N ¯ t (cos θ ) = N t ( − cos θ ) through CP invariance ofQCD. The inclusive charge asymmetry receives contributions from two reactions: radiative correctionsto quark-antiquark annihilation (Fig. 1) and interference between different amplitudes contributing togluon-quark scattering gq → t ¯ tq and g ¯ q → t ¯ t ¯ q . The latter contribution is, in general, much smallerthan the former. Gluon-gluon fusion, which represents only of all the events at Tevatron, remainscharge symmetric. QCD predicts that the size of the inclusive charge asymmetry is 5 to 8% [2, 4, 5],with top quarks (antitop quarks) more abundant in the direction of the incoming proton (antiproton). Theprediction for the charge asymmetry is, furthermore, robust with respect to the higher-order perturbativecorrections generated by threshold resummation [6]. The forward–backward asymmetry of the exclusiveprocess p ¯ p → t ¯ t + jet receives, however, large higher order corrections [7].At LHC, the total forward–backward asymmetry vanishes trivially because the proton-proton initialstate is symmetric. Nevertheless, a charge asymmetry is still visible in suitably defined distributions [2].In contrast with Tevatron, top quark production at LHC is dominated by gluon-gluon fusion (
84 % at TeV, and
90 % at TeV), which is charge symmetric under higher order corrections. The chargeantisymmetric contributions to top quark production are thus screened at LHC due to the prevalence ofgluon-gluon fusion. This is the main handicap for that measurement. The amount of events initiatedby gluon-gluon collisions can nevertheless be suppressed with respect to the q ¯ q and gq (¯ q ) processes, thesource of the charge asymmetry, by introducing a lower cut on the invariant mass of the top-antitop quarksystem m t ¯ t ; this eliminates the region of lower longitudinal momentum fraction of the colliding partons,where the gluon density is much larger than the quark densities. The charge asymmetry of the selecteddata samples is then enhanced, although at the price of lowering the statistics. This is, in principle, not aproblem at LHC, where the high luminosity will compensate by far this reduction.Several models predict the existence of heavy colored resonances decaying to top quarks that mightbe observed at the LHC [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. Those resonances willappear as a peak in the invariant mass distribution of the top-antitop quark pair located at the mass of thenew resonance. Colored resonances are fairly broad: Γ G /m G = O ( α s ) ∼ . Present lower boundson their mass are about TeV. The latest exclusion limit by CDF [22] at 95% C.L. is
GeV < m G < . TeV for axigluons and flavor-universal colorons (with cot θ = 1 mixing of the two SU (3) ).Some of those exotic gauge bosons, such as the axigluons [8, 9], might generate at tree-level a chargeasymmetry too through the interference with the q ¯ q → t ¯ t SM amplitude [4, 10, 11]. Gluon-gluon fusionto top quarks stays, at first order, unaltered by the presence of new interactions because a pair of gluonsdo not couple to a single extra resonance in this kind of models [9, 14].To discover those resonances, hence, it is necessary to select top-antitop quark pair events with largeinvariant masses; i.e. in the vicinity of the mass of the new resonance. A sizable charge asymmetrycan also be obtained only if gluon-gluon fusion is sufficiently suppressed, i.e. at large values of m t ¯ t .Because the top quarks of those data samples will be produced highly boosted, they will be observedas a single monojet. The standard reconstruction algorithms that are based on the reconstruction of thedecay products, however, loose efficiency very rapidly at high transverse momentum. For p T > GeVnew identification techniques are necessary. This has motivated many recent investigations [23, 24, 25,26] aimed at distinguishing top quark jets from the light quark QCD background by exploiting the jetsubstructure, without identifying the decay products.In this paper we argue that for a measurement of the top quark charge asymmetry at LHC it is notnecessary to select events with very large invariant masses of the top-antitop quark pairs. We showthat the highest statistical significance occurs with moderate selection cuts. Indeed, we find that themeasurement of the charge asymmetry induced by QCD is better suited in the region of low top-antitopquark pair invariant masses. The higher statistics in this region compensates the smallness of the chargeasymmetry. We also investigate the charge asymmetry generated by the exchange of a heavy color-octet resonance. We study the scenario where the massive extra gauge boson have arbitrary flavourindependent vector and axial-vector couplings to quarks. This includes the case of the axigluon that wehave already analyzed in Ref. [4]. We first show the constraints that the recent measurements at Tevatronof the forward–backward or charge asymmetries impose over the parameter space, and then extend2he analysis to LHC. We show that the selections cuts can be tuned such that the maximum statisticalsignificance is obtained with a cut on the invariant mass of the top-antitop quark pair at roughly halfof the mass of the heavy resonance. Due to this fact the measurement of the charge asymmetry haspotentially a better sensitivity to higher masses of the exotic resonances than the direct measurement ofthe dijet distribution.The outline of the paper is as follows. In Section 2 we review the most recent measurements of thetop quark charge asymmetries at Tevatron, and compare the QCD prediction for the asymmetries with thecharge asymmetry generated by the exchange of a color-octet boson with flavour independent vector andaxial-vector couplings to quarks. In Section 3 we evaluate at the LHC the top quark charge asymmetry,as predicted by QCD, in a given finite interval of rapidity, and study its size and statistical significanceas a function of the cut in the invariant mass of the top-antitop quark pair. In Section 4, we extend to theLHC the analysis of the charge asymmetry in the toy model used for Tevatron, and show that a detectionof those resonances is possible with relatively low cuts on the invariant mass of the top-antitop quarkpair; at values much smaller that the resonance mass.
The forward–backward asymmetry of top quarks has already been measured at Tevatron [27, 28, 29,30, 31]. The latest CDF analysis [27], based on . fb − integrated luminosity, provides two differentmeasurements in the lepton+jets channel. The first measurement is made in the laboratory frame, andgives A p ¯ p FB = N t (cos θ > − N t (cos θ < N t (cos θ >
0) + N t (cos θ <
0) = 0 . ± .
07 (stat) ± .
04 (sys) , (1)where θ is the angle between the top quark and the proton beam. The second measurement exploits theLorentz invariance of the difference between the t and ¯ t rapidities, ∆ y = y t − y ¯ t , which at LO is relatedto the top quark production angle α in the t ¯ t rest frame by [30]: ∆ y = 2 tanh − ( β cos α ) , (2)where β = (cid:113) − m t / ˆ s is the top quark velocity. The asymmetry in this variable is A t ¯ t FB = N ev . (∆ y > − N ev . (∆ y < N ev . (∆ y >
0) + N ev . (∆ y <
0) = 0 . ± .
13 (stat) ± .
04 (sys) . (3)The measurement at D0 [28] with . fb − integrated luminosity gives for the uncorrected asymmetry A obsFB = 0 . ± .
08 (stat) ± .
01 (sys) . (4)Like CDF, this analysis uses y t − y ¯ t as sensitive variable. In Ref. [28] upper limits on t ¯ t + X productionvia a Z (cid:48) resonance are also provided. Measurements of the exclusive asymmetry of the four- and five-jetsamples are also given by both experiments [27, 28].The corresponding theoretical predictions are [4] A = N t ( y ≥ − N ¯ t ( y ≥ N t ( y ≥
0) + N ¯ t ( y ≥
0) = 0 . , (5)3igure 2: Top quark cross-section at Tevatron in the bidimensional g V - g A plane for different values ofthe resonance mass.Figure 3: Forward-backward asymmetry at Tevatron in the bidimensional g V - g A plane for differentvalues of the resonance mass.for the inclusive charge asymmetry, or forward–backward asymmetry ( A = A p ¯ p FB ), and A Y = (cid:90) dY ( N ev . ( y t > y ¯ t ) − N ev . ( y t < y ¯ t )) (cid:90) dY ( N ev . ( y t > y ¯ t ) + N ev . ( y t < y ¯ t )) = 0 . , (6)for the integrated pair asymmetry, which is defined through the average rapidity Y = ( y t + y ¯ t ) . Thedifferential pair asymmetry is almost flat in the average rapidity, and amounts to about for anyvalue of Y . The corresponding integrated asymmetry is equivalent to the integrated forward–backwardasymmetry in the t ¯ t rest frame: A Y = A t ¯ t FB . The pair asymmetry is larger than the forward–backwardasymmetry A because events where both t and ¯ t are produced with positive and negative rapidities inthe laboratory frame do not contribute to the integrated forward–backward asymmetry, while they docontribute to the pair asymmetry. The experimental measurements of the top quark asymmetry in Eq. (1)and Eq. (3), although compatible with the corresponding theoretical predictions in Eq. (5) and Eq. (6),respectively, are still statistically dominated.We shall consider in the following the production of heavy color-octet boson resonances decayingto top-antitop quark pairs with arbitrary vector and axial-vector couplings to quarks. The correspondingdifferential cross section is given in Eq. (11) of Appendix A. The charge asymmetry is built up fromthe two contributions of the differential partonic cross section that are odd in the polar angle. The firstone arises from the interference with the gluon amplitude, and is proportional to the product of the axial-vector couplings of the light and the top quarks. This contribution, provided that the product of couplings4igure 4: Pair asymmetry at Tevatron in the bidimensional g V - g A plane for different values of the reso-nance mass.is positive, is negative in the forward direction for invariant masses of the top-antitop quark pair belowthe resonance mass, and changes sign above. This leads at Tevatron to a preference for the emission ofthe top quarks in the direction of the incoming light antiquarks (antiprotons) in most of the kinematicphase-space, and then to a negative forward–backward asymmetry. The second contribution, arisingfrom the squared amplitude of the heavy resonance, although always positive for positive couplings,is suppressed with respect to the contribution of the interference term by two powers of the resonancemass. For large values of the couplings, however, it might compensate the interference contribution, thenleading to a positive forward–backward asymmetry, because it is enhanced by the product of the vectorcouplings. Indeed, for ˆ s = s (cid:48) ≡ m G g qV g tV , (7)the two odd terms cancel to each other, and above that value the contribution to the forward–backwardasymmetry becomes positive.To simplify our analysis we consider that the vector and axial-vector couplings, which are normalizedto the strong coupling α s , are flavour independent: g qV = g tV = g V , and g qA = g tA = g A , where q labelsthe coupling of the excited gluon to light quarks, and t to top quarks. The axigluon of chiral colortheories [8, 9], for example, is given by g V = 0 and g A = 1 . We study how the production cross sectionand the charge asymmetry vary depending on the vector and axial-vector couplings, which we take inthe range [0 , . Within this range the perturbative expansion is still reliable. Moreover, in the flavourindependent scenario the sign of the couplings is not relevant.Results for the difference between the production cross section of the excited gluon and the SM pre-diction in the ( g V , g A ) plane are presented in Fig. 2 for different values of the resonance mass. In all ouranalysis, we use the MRST 2004 parton distribution functions [32], and we set the renormalization andfactorization scales to µ = m t , with m t = 170 . ± . ± . GeV [33]. For comparison, wealso overimpose in Fig. 2 the , and sigma contours obtained from the experimental measurement σ t ¯ t = 7 . ± . (pb) [34], and the SM prediction σ NLO t ¯ t = 6 . ± . (pb) [35]. Similar plots are presentedin Fig. 3 and Fig. 4 for the forward–backward asymmetry and pair asymmetry, respectively. The sigmacontours are calculated from the experimental measurement in Eq. (1) and from the theoretical predictionin Eq. (5) for the forward–backward asymmetry, and from Eq. (3) and Eq. (6) for the pair asymmetry.At C.L. the plots of the production cross section and the asymmetries exclude complementary re-gions of the parameter space. While the production cross section excludes the corner with large vectorcouplings g V and low axial-vector coupling g A , the forward–backward and the pair asymmetry exclude5igure 5: Central charge asymmetry at LHC as predicted by QCD, as a function of the maximum rapidity y C (left plots), and corresponding statistical significance (right plots), for two different cuts on the top-antitop quark pair invariant mass.the corners with higher axial-vector couplings and either low or high vector couplings. This is not sur-prising, because the terms of the differential cross section in Eq. (11) that are even in the polar anglecontribute exclusively to the integrated cross section, while the odd terms contribute to the charge asym-metry only, and they are proportional to different combinations of the vector and axial-vector couplings.The exclusion regions are, as expected, smaller for higher values of the resonance mass. Top quark production at LHC is forward–backward symmetric in the laboratory frame as a consequenceof the symmetric colliding proton-proton initial state. The charge asymmetry can be studied neverthelessby selecting appropriately chosen kinematic regions. The production cross section of top quarks is,however, dominated by gluon-gluon fusion and thus the charge asymmetry generated from the q ¯ q and gq ( g ¯ q ) reactions is small in most of the kinematic phase-space.Nonetheless, QCD predicts at LHC a slight preference for centrally produced antitop quarks, withtop quarks more abundant at very large positive and negative rapidities [2]. The difference between thesingle particle inclusive distributions of t and ¯ t quarks can be understood easily. Production of t ¯ t ( g ) is dominated by initial quarks with large momentum fraction and antiquarks with small momentumfraction, while QCD predicts that top (antitop) quarks are preferentially emitted into the direction of the6igure 6: Central charge asymmetry and statistical significance at LHC from QCD, as a function of thecut m min .t ¯ t , for TeV energy.incoming quarks (antiquarks) in the partonic rest frame. Due to the boost into the laboratory frame thetop quarks are then produced dominantly in the forward and backward directions, while antiquarks aremore abundant in the central region.We select events in a given range of rapidity and define the integrated charge asymmetry in the centralregion as [4]: A C ( y C ) = N t ( | y | ≤ y C ) − N ¯ t ( | y | ≤ y C ) N t ( | y | ≤ y C ) + N ¯ t ( | y | ≤ y C ) . (8)The central asymmetry A C ( y C ) obviously vanishes if the whole rapidity spectrum is integrated, while anon-vanishing asymmetry can be obtained over a finite interval of rapidity. We also perform a cut on theinvariant mass of the top-antitop quark pair, m t ¯ t > m min t ¯ t , because that region of the phase space is moresensitive to the quark-antiquark induced events rather than the gluon-gluon ones, so that the asymmetryis enhanced. The main virtue of the central asymmetry is that it vanishes exactly for parity-conservingprocesses.In Fig. 5 (left plots) we show the central charge asymmetry at √ s = 10 TeV and TeV as a functionof the maximum rapidity y C for two different values of the cut on the invariant mass of the top-antitopquark pair m t ¯ t > GeV, and TeV, respectively. As expected, the central charge asymmetry isnegative, is larger for larger values of the cut m min t ¯ t , and vanishes for large values of y C . We also show inFig. 5 (right plots) the corresponding statistical significance S of the measurement, defined as S SM = A SM C (cid:113) ( σ t + σ ¯ t ) SM L = N t − N ¯ t √ N t + N ¯ t , (9)7igure 7: Central charge asymmetry and statistical significance at LHC from QCD, as a function of thecut m min .t ¯ t , for TeV energy.where L denotes the total integrated luminosity for which we take L = 20 pb − at √ s = 10 TeV and L = 10 fb − at √ s = 14 TeV. The maximum significance is reached for both running energies at y C = 1 for m t ¯ t > GeV, and y C = 0 . for m t ¯ t > TeV. Surprisingly, although the size of the asymmetry isgreater for the larger value of m min t ¯ t , its statistical significance is higher for the lower cut. This is a veryinteresting feature because softer top and antitop quarks should be identified more easily than the veryhighly boosted ones. The statistical significance for the run at √ s = 10 TeV is, however, rather small.We now fix the value of the maximum rapidity to y C = 0 . and study the size of the asymmetry andits statistical significance as a function of m min t ¯ t . Our results are shown in Fig. 6 for √ s = 10 TeV and L = 20 pb − and in Fig. 7 for √ s = 14 TeV and L = 10 fb − . We also compare the results with andwithout introducing a cut in the transverse momenta of the heavy quarks: p T > GeV. The latter cutproduce a significant effect only at very large values of the invariant mass m min t ¯ t , above TeV, wherethe statistical significance is, however, small. In all cases, the asymmetry increases for larger valuesof m min t ¯ t , while the statistical significance is larger without introducing any selection cut. Note that thesize of the asymmetry decreases again above m min t ¯ t = 2 . TeV because in that region the gq (¯ q ) eventscompensate the asymmetry generated by the q ¯ q events; their contributions are of opposite sign. Thestatistical significance for the initial run at √ s = 10 TeV is again too small. Although we have not takeninto account experimental efficiencies, we can conclude that fb − of data at the design energy of theLHC seems to be enough for a clear measurement of the QCD asymmetry.8igure 8: Central charge asymmetry (left plots) and statistical significance (right plots) at LHC as afunction of the maximum rapidity, for TeV energy and two different cuts on the top–antitop quarkinvariant mass. Two different sets of couplings are shown.
Like for Tevatron in Section 2, we study here the charge asymmetry produced at LHC by the decay to topquarks of a color-octet resonance, in the scenario where the vector g q ( t ) V and axial-vector g q ( t ) A couplingsare flavour independent. We evaluate the central asymmetry in Eq. (8), and its statistical significance,defined as S G = A G+SM C − A SM C (cid:113) − ( A SM C ) (cid:113) ( σ t + σ ¯ t ) SM L (cid:39) ( N t − N ¯ t ) G (cid:113) ( N t + N ¯ t ) G+SM , (10)for different values of the couplings and the kinematical cuts.We should mention that in the most popular models of warped extra dimensions the Kaluza-Kleinexcitations of the gluon couple identically to the left-handed and the right-handed light quarks, and thesecouplings are different only for the third generation. A charge asymmetry, or correspondingly a centralasymmetry, can not be generated in this kind of models by the production mechanism. An asymmetrywill arise, however, in the decay products of the top quark. The polarization asymmetry from the angulardistribution of the positron from the top quark decay has been investigated for example in [15]. Theanalysis of the decay products is, however, beyond the scope of this paper. The scenario presented hereincludes, however, the extra dimensional model presented in [20] as a particular subcase.When a heavy color-octet boson resonance is produced considerations similar to those in Section 29igure 9: Central charge asymmetry (left plots) and statistical significance (right plots) at LHC as afunction of the maximum rapidity, for TeV energy and two different cuts on the top-antitop quarkinvariant mass. Two different sets of couplings are shown.lead to predict a positive central asymmetry for values of the cut in the invariant mass of the top-antitopquark pair below the mass of the resonance and a negative asymmetry above. This is true as far as theinterference term has a greater relevance than the squared amplitude of the exotic resonance. If this isthe case, a higher number of antitop quarks will be emitted in the direction of the incoming quarks, andonce the boost into the laboratory frame is performed (cf. discussion in Section 3), a higher number oftop quark will be found in the central region, so that the central asymmetry is positive. Since for highvalues of the cut the sign of the interference term changes, the asymmetry will become negative, andthen it has to vanish at a certain intermediate value of that cut, close and below the resonance mass.Under these conditions, we expect to find two maxima in the statistical significance as a function of m min .t ¯ t /m G . Starting from the threshold, where the asymmetry is small because the gluon-gluon fusionprocess dominates there, the size of the central asymmetry will grow by increasing m min .t ¯ t , as the quark-antiquark annihilation process becomes more and more important. Since the asymmetry induced bythe excited gluon will vanish at a certain critical point, its statistical significance will do as well, andwill reach a maximum at an intermediate value between that critical point and the threshold. Above thecritical point, the asymmetry becomes negative and its statistical significance increases again, until theevent yield becomes too small. A second maximum in the statistical significance will be generated there.For certain values of the vector couplings, however, the critical partonic invariant mass defined inEq. (7) can be located at a rather low scale. In this case, the central asymmetry generated by the exoticresonance will be negative exclusively, and we will find only one maximum in the statistical significance.10n our first analysis we shall determine the value of the maximum rapidity y C that maximizes thestatistical significance. We fix the resonance mass at . TeV, and impose two different cuts on theinvariant mass of the top-antitop quark pair, namely m t ¯ t >
700 GeV and m t ¯ t > . . We choosetwo different combinations of the vector and axial-vector couplings g V and g A . In Figs. 8 and 9, wepresent the results obtained for the central asymmetry and the statistical significance for g V = 0 , g A = 1 and g V = g A = 1 for both values of the centre-of-mass energy, and TeV, respectively. We noticethat for the first choice of the parameters, namely g V = 0 , g A = 1 , the central asymmetry suffers achange of sign by passing from the lower cut to the higher one. This means that it will vanish for a givenvalue of the cut, thus making the statistical significance vanishing also.By looking at the corresponding significance we find that y C = 0 . is a good choice in all cases.Thus, we use this value to find the best cut for the top-antitop quark pair invariant mass. In order to dothat, we choose several values of the parameters and we study the trend of the significance as a functionof m min t ¯ t /m G . The results are shown in Figs. 10 and 11. The optimal cuts depend, of course, on thevalues of the vector and axial-vector couplings, but either m min t ¯ t /m G = 0 . or m min t ¯ t /m G = 0 . provide areasonable statistical significance for almost all the combinations of the couplings. This is an importantresult, because it means that a relatively low cut – at about half of the mass of the resonance or evenbelow – is enough to have a good statistical significance, and a clear signal from the measurement of thecharge asymmetry.We now fix m min t ¯ t /m G = 0 . and m min t ¯ t /m G = 0 . , and we study how the central asymmetry andits statistical significance vary as a function of the vector and the axial-vector couplings, for a givenvalue of the resonance mass. These choices, for which we have found the best statistical significances,are of course arbitrary and are not necessarily the best for all the values of the vector and axial-vectorcouplings. For illustrative purposes are, however, good representatives. We have chosen m G = 1 . , and TeV. The results are presented in Figs. 12 and 13 in the ( g V , g A ) plane for √ s = 10 TeV and TeV, respectively. It is possible to see that the pattern of the size of the asymmetry is quite similarindependently of the value of the resonance mass; it depends mostly on the ratio m min t ¯ t /m G . A sizableasymmetry is found whatever the value of the resonance mass is. The statistical significance, as expected,decreases with the increasing of the resonance mass. We have analyzed the charge asymmetry in a top-antitop quark pair production through the exchangeof color-octet heavy boson with flavor independent coupling to quarks. We have considered the exper-imental setups of Tevatron and LHC, studying different observables and we have found that a sizableasymmetry can be found in both.At Tevatron, the forward-backward asymmetry and the pair asymmetry, together with the total crosssection exclude complementary corners of the parameter space. At the LHC, the central charge asymme-try is an observable that is very sensitive to new physics. We have studied the statistical significance ofthe measurement of such an asymmetry, and we have found that it is possible to tune the selection cutsin order to find a sensible significance. The maximum of the statistical significance for the measurementof the asymmetry as predicted by QCD is obtained without introducing any cut in the invariant mass ofthe top-antitop quark pair, even if the asymmetry is smaller in this case.11hen a heavy resonance is considered, one or two maxima in the significance spectrum are found,depending on the size of the couplings. The position of the peaks depends on the ratio m min t ¯ t /m G andnot on the resonance mass. One of the peaks can be located at an energy scale as low as one half of theresonance mass, or even below. Data samples of top and antitop quarks that are not too energetic canthen be used to detect or exclude the existence of this kind of resonances. Acknowledgements
We thank S. Cabrera, C. Carone, J.H. K¨uhn, M. Sehr, and M. Vos for very useful discussions. The workof P.F. is supported by an I3P Fellowship from Consejo Superior de Investigaciones Cient´ıficas (CSIC).Work partially supported by Ministerio de Ciencia e Innovaci´on under Grants No. FPA2004-00996 andCPAN (CSD2007-00042), and European Commission MRTN FLAVIAnet under Contract No. MRTN-CT-2006-035482.
A Born cross-section
The Born cross-section for q ¯ q fusion in the presence of a color-octet vector resonance reads dσ q ¯ q → t ¯ t d cos ˆ θ = α s T F C F N C πβ s (cid:32) c + 4 m + 2ˆ s (ˆ s − m G )(ˆ s − m G ) + m G Γ G (cid:104) g qV g tV (1 + c + 4 m ) + 2 g qA g tA c (cid:105) + ˆ s (ˆ s − m G ) + m G Γ G (cid:20) (cid:16) ( g qV ) + ( g qA ) (cid:17) (cid:18) ( g tV ) (1 + c + 4 m )+ ( g tA ) (1 + c − m ) (cid:19) + 8 g qV g qA g tV g tA c (cid:21)(cid:33) , (11)where ˆ θ is the polar angle of the top quark with respect to the incoming quark in the center of mass restframe, ˆ s is the squared partonic invariant mass, T F = 1 / , N C = 3 and C F = 4 / are the color factors, β = √ − m is the velocity of the top quark, with m = m t / √ ˆ s , and c = β cos ˆ θ . The parameters g qV ( g tV ) , g qA ( g tA ) represent the vector and vector-axial couplings among the excited gluons and the lightquarks (top quarks).There are two terms in Eq. (11) that are odd in the polar angle and therefore there are two con-tributions to the charge asymmetry. The first one arises from the interference of the SM amplitudewith the resonance amplitude, and the second one from the squared resonance amplitude. The formerdepends on the axial-vector couplings only, while the latter is proportional to both the vector and theaxial-vector couplings. For large values of the resonance mass, the second term is suppressed, and thecharge asymmetry will depend mostly on the value of the axial-vector couplings, and residually on thevector couplings. The decay width is given by: Γ G ≡ (cid:88) q Γ( G → qq ) ≈ α s m G T F (cid:34) (cid:88) q (cid:16) ( g qV ) + ( g qA ) (cid:17) + (cid:118)(cid:117)(cid:117)(cid:116) − m t m G (cid:32) ( g tV ) (cid:32) m t m G (cid:33) + ( g tA ) (cid:32) − m t m G (cid:33)(cid:33) (cid:35) . 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