Boosting the t tbar charge asymmetry
aa r X i v : . [ h e p - ph ] D ec Boosting the t ¯ t charge asymmetry J. A. Aguilar–Saavedra a , A. Juste b,c , F. Rubbo ca Departamento de F´ısica Te´orica y del Cosmos and CAFPE,Universidad de Granada, E-18071 Granada, Spain b Instituci´o Catalana de Recerca i Estudis Avan¸cats (ICREA), Barcelona, Spain c Institut de F´ısica d’Altes Energies (IFAE), Barcelona, Spain
Abstract
We propose a kinematical enhancement of the t ¯ t charge asymmetry at the LHCby selecting events with the t ¯ t centre of mass frame highly boosted along the beamaxis. This kinematical selection increases the asymmetries and their significance upto a factor of two in a rather model-independent fashion. Hence, it can be a perfectcomplement to enhance model discrimination at the LHC. The observation of an unexpectedly large forward-backward (FB) asymmetry in t ¯ t pro-duction by the Tevatron experiments constitutes one of the most solid hints of new physicsin the top sector. The latest inclusive values reported by the CDF and D0 Collabora-tions [1, 2] are around two standard deviations above the Standard Model (SM) predic-tions [3–7] and even larger departures are found for other related measurements. But theexperimental situation is not yet clear, with the CDF result pointing at a strong mass de-pendence of the asymmetry which is not confirmed by the D0 Collaboration. On the otherside, the CMS [8] and ATLAS [9] Collaborations have measured the charge asymmetry in t ¯ t production at the Large Hadron Collider (LHC), A C = N (∆ > − N (∆ < N (∆ >
0) + N (∆ < , (1)with ∆ = | η t | − | η ¯ t | (CMS) or ∆ = | y t | − | y ¯ t | (ATLAS), being η , y the pseudo-rapidity andrapidity, respectively, of the top (anti)quark and N standing for the number of events.The small, negative asymmetries measured by both experiments are hard to reconcile withpositive deviations at Tevatron [10] but the still large errors in the present measurementsallow for small positive asymmetries, compatible with a Tevatron excess. In this situation,it is of great interest to explore possible ways of enhancing the LHC charge asymmetry,in order to have an independent test of the Tevatron anomalies as sensitive as possible.1he t ¯ t charge and FB asymmetries only arise in the q ¯ q → t ¯ t subprocess, since the gg initial state is symmetric. At the partonic level, the kinematics of q ¯ q → t ¯ t can bedescribed by the partonic centre of mass (CM) energy ˆ s (which equals the t ¯ t invariantmass squared m t ¯ t ) and the CM opening angle θ between the top and the initial quark. Athird relevant quantity, independent of the former two, is the boost of the partonic CMwith respect to the laboratory frame. This boost can conveniently be parameterised bythe velocity of the t ¯ t system along the beam axis in the laboratory frame, β = | p zt + p z ¯ t | E t + E ¯ t (2)being p z , E the momentum along the beam axis and energy, respectively. An asymmetryenhancement can be achieved by a phase space selection involving one or more of thesethree variables m t ¯ t , θ , β , at the expense of reducing the data sample and thus the statistics.In this respect, it is important to stress here that the t ¯ t invariant mass is not a suitableparameter to increase the asymmetry. For some models, like extra Z ′ [11] or W ′ [12]bosons, the asymmetry grows with m t ¯ t while for other models, such as light s -channelcolour octets [13–16] or scalars exchanged in the u channel [17] the m t ¯ t profile of theasymmetry can be completely different and A C may even become negative at high m t ¯ t .Indeed, the asymmetry dependence on the t ¯ t invariant mass is most useful for modeldiscrimination [18].Previous literature already includes proposals on this topic. In the so-called forwardasymmetry [19] A fwd = N ( | y t | > y C ) − N ( | y ¯ t | > y C ) N ( | y t | > y C ) + N ¯ t ( | y ¯ t | > y C ) , (3)with y C some fixed rapidity cut, a selection is effectively placed on the angle θ (alsodepending on β ), to obtain a charge asymmetry larger than the inclusive one. Similarresults are found [20] by requiring the leptonic top quark in the central detector with | η | < . | η | > . | η | < . θ and β . In both proposals, the largestimprovement is found for SM extensions in which the asymmetry is most significant atsmall θ , due to the exchange of a light particle (a Z ′ or W ′ boson) in the t channel. Onthe other hand, for simple new physics models involving new particles in s or u channelsthese kinematical selections do not bring such an improvement [10], and the statisticalsignificance of the asymmetry even decreases with respect to the inclusive measurement.(A larger asymmetry may still be an advantage if the measurement is dominated bysystematic uncertainties.) In this Letter we explore an alternative way of increasing the Note that the velocity is related to the partonic momentum fractions x , as β = | x − x | / ( x + x ). t ¯ t velocity β but without any restriction on θ or m t ¯ t . As it is well known, one of the reasons for the smallness of the charge asymmetry atthe LHC, compared to the Tevatron, is the smaller fraction of ‘asymmetric’ q ¯ q → t ¯ t eventsin the total t ¯ t sample, dominated by gg fusion at LHC energies. For t ¯ t events originatingfrom q ¯ q annihilation, the partonic CM frame tends to be more boosted along the beamaxis, due to the much higher average momentum fractions for quarks than for antiquarksin pp collisions. Therefore, the requirement of a minimum t ¯ t velocity β min increases the q ¯ q fraction in the sample, as it can be seen in Fig. 1, calculated at the tree-level usingCTEQ6L1 [21] parton density functions (PDFs) for a CM energy of 7 TeV. The choice of β min σ qq / σ Figure 1: Relative fraction of q ¯ q → t ¯ t events as a function of the minimum t ¯ t velocity. β instead of the momentum | p zt + p z ¯ t | to increase the asymmetry [22] is motivated by itssmall correlation with other energy variables such as m t ¯ t , as well as by the fact that it isexperimentally a more robust observable, less affected by uncertainties on the jet energyscale and resolution. Also, this simple cut on β is an alternative to more sophisticatedanalyses [23] to enhance the q ¯ q fraction by using a likelihood function built of severalkinematical variables of the t ¯ t pair and its decay products, whose practical applicationmay suffer from important systematic uncertainties. After these introductory considerations, we proceed to investigate how the asymmetryis increased in SM extensions accommodating the Tevatron measurements, and to whichextent this increase is model-independent. For this, we select three simple benchmarkmodels: (i) an axigluon G µ [24]; (ii) a Z ′ boson; (iii) a colour-triplet scalar ω , whichcorrespond to the exchange of new particles in the s , t , u channels in q ¯ q → t ¯ t , respectively.3heir quantum numbers and interactions are summarised in Table 1. More specifically,our benchmark models are:Label Spin Rep. Interaction Lagrangian G µ , − (cid:0) g qij ¯ q Li γ µ λ a q Lj + g uij ¯ u Ri γ µ λ a u Rj + g dij ¯ d Ri γ µ λ a d Rj (cid:1) G aµ B µ , − (cid:0) g qij ¯ q Li γ µ q Lj + g uij ¯ u Ri γ µ u Rj + g dij ¯ d Ri γ µ d Rj (cid:1) B µ ω , − − g ij ε abc ¯ u Rib u cRjc ω a † + h.c.Table 1: Quantum numbers and relevant interactions for the new particles considered inour benchmark models. • Axigluon: A neutral colour-octet vector G µ with axial couplings g qii = − g uii = − g dii ,exchanged in the s channel in q ¯ q → t ¯ t . There are different proposals [13–16] of lightcolour octets consistent with the t ¯ t invariant mass measurements at Tevatron andLHC; here for simplicity we consider this new particle to be heavy enough not tobe produced on shell, and replace its propagator by a four-fermion interaction [25]. • Z ′ boson: A neutral (colour- and isospin-singlet) vector boson B µ with flavour-violating couplings, exchanged in the t channel in u ¯ u → t ¯ t . We consider only g u non-zero (right-handed couplings) as preferred by B physics constraints. • Colour-triplet scalar: A charge 4/3 colour-triplet ω with a flavour-violating coupling g , exchanged in the u channel in u ¯ u → t ¯ t .The parameters for these three models are chosen so as to have new physics contributions to the inclusive charge asymmetry A newC ≃ . For the heavy axigluon we select C/ Λ =1 .
86 TeV − . For the Z ′ boson we choose a “light” mass M = 150 GeV with a coupling g u = 0 .
55, for which the forward enhancement of the asymmetry at θ ∼ s - and u -channel exchange larger. For the scalarwe use an intermediate mass M = 700 GeV and a coupling g = 2 .
1. The new physicscontributions to the Tevatron inclusive asymmetry are A newFB = 0 .
189 ( G µ ), 0.194 ( Z ′ ),0.190 ( ω ). These three benchmark points are in agreement with the constraints on crosssections at Tevatron and LHC used in Refs. [10, 18]. Next-to-leading order (NLO) SM contributions are not included in our analysis; the total asymmetrieswhen these are included as well can be approximately obtained by adding the SM NLO asymmetry tothe new physics contributions presented. Note that for the Z ′ model there is a minimum positive value A newC ≃ .
04 consistent with the total t ¯ t cross section at Tevatron [18]; for a better comparison between s , t and u channels we have also chosen A newC ≃ .
04 for the axigluon and colour-triplet scalar. m t ¯ t and β is presented in Fig. 2 for the threebenchmark models with the parameters above mentioned. In all cases we observe a ne wC A tt m500 1000 1500 β µ G ne wC A µ G ne wC A tt m500 1000 1500 β Z’ ne wC A Z’ ne wC A tt m500 1000 1500 β ω ne wC A ω Figure 2: Charge asymmetry as a function of the t ¯ t invariant mass and velocity in thelaboratory frame, for the three benchmark models.significant asymmetry increase with β , showing the usefulness of requiring a minimum t ¯ t velocity β min to enhance it. In Fig. 3 (left) we plot the actual effect of such a cut at theparton level. (The integrated asymmetries in Fig. 3 are related to the differential ones inFig. 2 by convolution with PDFs and integration over β > β min and all the m t ¯ t range.)We observe that for the three models the integrated asymmetries increase monotonically β min A C G µ ω Z ′ SM
300 400 500 600 700 800 900 1000 m tt (GeV) σ qq ( no r m a li s e d ) β min = 0 β min = 0.6 β min = 0.95 Figure 3: Left: new physics contributions to the charge asymmetry as a function of thelower cut β min , for the three benchmark models (solid lines), and SM contribution (pointswith error bars). Right: normalised m t ¯ t distribution for q ¯ q → t ¯ t in the SM, for severalvalues of β min .up to β min ∼ . q ¯ q fraction in the sample. This feature is quite desirable, since it allows5o use a cut on β to enhance the asymmetry while retaining m t ¯ t as a very useful variablefor model discrimination. The small SM contribution, calculated with MC@NLO [26], is alsodisplayed with error bars corresponding to the Monte Carlo statistical uncertainty. Itexhibits the same relative increase with respect to the inclusive value, as expected. (Thetotal asymmetry is the sum of SM and new physics contributions to a good approximation,so one can safely focus on new physics contributions and add the SM contribution at theend if desired.) For larger β min some differences between the models begin to show up,originated by the different m t ¯ t dependence of the asymmetry in each case (see Fig. 2),and the fact that t ¯ t events with higher longitudinal boost tend to have a smaller invariantmass, due to the strong suppression of the PDFs at high momentum fraction. Thiscorrelation is clearly observed in Fig. 3 (right), where we plot the normalised t ¯ t invariantmass distribution for q ¯ q → t ¯ t in the SM, for β min = 0 , . , .
95. For a moderate value β min ∼ . m t ¯ t distributions are hardly affected by the cut, ensuring thatthe asymmetry enhancement is model-independent. Nevertheless, this is no longer thecase for much larger values such as β min = 0 .
95. This lower average m t ¯ t at high β min isprecisely the origin of the sudden drop of the asymmetries for β min & .
95, despite thelarger q ¯ q fraction, see Fig. 1.Finally, it is worth pointing out that the asymmetry increase with a cut on β iscomplementary to other possible model-dependent enhancements, for example restrictingthe range of variation of θ . To illustrate this, we show in Fig. 4 the charge asymmetryas a function of β min for the same models displayed in Fig. 3 but after the requirement | ∆ y | >
1, a cut which places a selection on the angle θ . There are two remarkable features β min A C n e w ( | ∆ y | > ) G µ ω Z ′ Figure 4: Charge asymmetry at high rapidities | ∆ y | > β min , for the three benchmark models. Since ∆ y is invariant under boosts along the beam axis, | ∆ y | = (cid:12)(cid:12)(cid:12) log β t cos θ − β t cos θ (cid:12)(cid:12)(cid:12) , being β t = p − m t / ˆ s the velocity of the (anti)top quark in the CM frame. | ∆ y | > Z ′ model. As we have mentioned in the introduction, this is expected [10] sincethe forward enhancement is much more pronounced in models with t -channel exchangeof light particles. Second, the asymmetries increase in nearly the same fashion up to β min ∼ .
6, in agreement with the results shown in Fig. 3.
Having established the enhancement of the asymmetry for t ¯ t events boosted along thebeam axis, it is necessary to investigate further whether this selection may really constitutean advantage in a real experiment or the potential increase is washed out by detector andreconstruction effects. For this purpose, we have performed a fast simulation of threeevent samples for the axigluon model, with C/ Λ = 0 .
93, 1 .
86, 2 .
94 TeV − , resulting in A newC = 0 .
02, 0 .
04, 0 .
06. The selection of these three benchmarks with different values of A newC is intended to explore the sensitivity increase depending on the actual value of theasymmetry. The events are generated with Protos [27] and include the top quark and W boson decay with spin effects. Parton showering and hadronisation is performed by Pythia [28] and the package
AcerDet [29] is used to perform a fast detector simulation andreconstruction of objects such as charged leptons and jets. We focus on the semileptonic t ¯ t decay channel, selecting events which fulfill the following criteria: • exactly one lepton (electron or muon) with transverse momentum p T >
20 GeV andpseudorapidity | η | < . • missing transverse energy E missT >
25 GeV; • at least four jets with p T >
25 GeV and | η | < . b -tagged jet.In particular, extending the jet acceptance to | η | < . b tagging is only availablefor | η | < .
5) is important to maintain a good acceptance for boosted events [20, 30].We assume a per-jet b tagging efficiency of 60% for jets originating from a b quark with | η | < .
5, and a total efficiency for lepton triggering and identification of 70%. This eventselection is similar to those used in the recent measurements by the ATLAS and CMScollaborations [8, 9] and has an efficiency of ∼
25% for semileptonic t ¯ t events. In order tocompute the asymmetry, we perform a simplified t ¯ t event reconstruction by looping overneutrino solutions and jet permutations, and selecting the configuration that minimisesthe function χ = ( m j j − M W ) σ W + ( m j j j − m t ) σ t + ( m ℓνj − m t ) σ t , (4)7here m j j ( m j j j ) is the reconstructed invariant mass of the W boson (top quark)candidate decaying hadronically, m ℓνj is the invariant mass of the top quark decayingleptonically, and we take M W = 80 . m t = 172 . σ W = 10 GeV, and σ t =20 GeV. The chosen values for σ W and σ t are representative of the W boson and topmass reconstruction resolutions provided by the fast simulation. The neutrino transversemomentum is set equal to the vector E missT and the z component of its momentum isobtained by solving the quadratic equation ( p ℓ + p ν ) = M W . In case two real solutionsexist, both of them are considered in the χ minimisation over configurations. If no realsolution exists, the neutrino pseudo-rapidity is set to be equal to the one of the chargedlepton. Only the leading four jets in p T are considered as candidates for the b quarks. Allselected jets are considered as candidates for the hadronic W boson decay, skipping the b -tagged jets whenever there are at least two jets that are not b tagged. The configurationyielding the lowest χ is used to reconstruct the top and anti-top quark four-momenta.The charge asymmetry is computed using ∆ = | y t | − | y ¯ t | . The fraction of events with thesign of ∆ correctly reconstructed is ∼ β min ≃ . | η | < . b tagging.We do not attempt here an unfolding of the simulated measurements to reconstructthe parton-level quantities, as this requires a very delicate analysis. Instead, we presentour results at the reconstruction level and we do not include backgrounds. The lattersimplification is justified by the relatively small background fraction ( ∼ β min , in binsof 0.1 (only statistical uncertainties are shown). The upper right panel corresponds tothe statistical significance of the asymmetries A/σ A , assuming a luminosity of 10 fb − .We can observe that a cut on β already leads to some statistical improvement at the10 −
20% level, which is not always achieved for s -channel models with other propos-als [19, 20]. Nevertheless, the real advantage of having larger asymmetries results whensystematic uncertainties are taken into account, which eventually dominate for large datasamples. The lower two plots in Fig. 5 show the significance assuming common systematicuncertainties of 0.01 (left) and 0.02 (right), independent of β min in a first approximation.These assumed values represent reasonable extrapolations of the total systematic uncer-tainty ( ∼ . t ¯ t production. (A careful assessment of system-8 in β ne w C A A=0.02A=0.04A=0.06 min β A σ ne w C A A=0.02A=0.04A=0.06 min β A σ ne w C A = 0.01 syst σ A=0.02A=0.04A=0.06 min β A σ ne w C A = 0.02 syst σ A=0.02A=0.04A=0.06
Figure 5: Top, left: charge asymmetry at the reconstruction level, as a function of β min (only statistical uncertainties, corresponding to a luminosity of 10 fb − , are shown). Top,right: statistical significance of the asymmetry. Bottom: significance assuming systematicuncertainties of 0.01 (left), 0.02 (right).atic uncertainties at higher values of β min , such as e.g. those resulting from increased jetenergy scale uncertainties for forward jets, is detector-dependent and beyond the scopeof this study.) A lower cut on β can increase the significance up to a factor of 1 . − β . Besides, in the benchmarks considered in this9ection the asymmetry also grows with the t ¯ t invariant mass (see the next section forillustration of other possibilities). Then, it is interesting to check that at higher invariantmasses a cut on β still improves the significance in this case. This is shown in Fig. 6,where we see that a cut on β increases the significance of the asymmetry, up to factors of1 . − min β ne w C A > 450 GeV tt m A=0.02A=0.04A=0.06 min β A σ ne w C A > 450 GeV tt m A=0.02A=0.04A=0.06 min β A σ ne w C A = 0.01 syst σ > 450 GeV tt m A=0.02A=0.04A=0.06 min β A σ ne w C A = 0.02 syst σ > 450 GeV tt m A=0.02A=0.04A=0.06 Figure 6: The same as in Fig. 5 but for m t ¯ t >
450 GeV.10
Improving model discrimination
We finally illustrate how our proposal for a kinematical enhancement of the charge asym-metry constitutes a perfect complement to the model discrimination by the analysis ofthe m t ¯ t dependence of the asymmetry [16, 18]. We have selected two difficult scenariosfor the LHC with a small charge asymmetry, consistent with the most recent CMS andATLAS measurements. The first one is the heavy axigluon G µ of the previous sectionwith A newC = 0 .
02. The second one is model P in Ref. [16], a colour octet with a mass M = 870 GeV and a large width Γ = 0 . M , yielding A newC = 0 . ne wC A -0.08-0.06-0.04-0.020.000.020.040.060.080.10 [GeV] tt m500 1000 1500 β P ne wC A -0.08-0.06-0.04-0.020.000.020.040.060.080.10 P Figure 7: Charge asymmetry as a function of the t ¯ t invariant mass and velocity in thelaboratory frame, for model P (see the text).asymmetry as a function of m t ¯ t after simulation and reconstruction, without any cut on β (left) and setting β min = 0 . β min = 0 . t ¯ t velocity β . Of course, the increase of the asymmetries makes model discrimination easieronce systematic uncertainties, not included in these plots, are taken into account. In this Letter we have proposed a kinematical enhancement of the charge asymmetry in t ¯ t production at the LHC, by using the velocity β of the t ¯ t CM in the laboratory frame.Being an adimensional quantity (in natural units), β is expected to be less sensitive to11 [GeV] tt m500 1000 ne w C A -0.2-0.10.00.10.2 , A=0.02 µ G P [GeV] tt m500 1000 ne w C A -0.2-0.10.00.10.2 , A=0.02 µ G P Figure 8: Charge asymmetry at the reconstruction level, without cut (left) and for β min =0 . − , are shown.experimental uncertainties associated to the jet energy scale and resolution. In contrastwith other proposals, which require a different event selection or a different definition ofthe asymmetry, a lower cut β ≥ β min is easy to implement in the current ATLAS andCMS analyses to increase the asymmetry and its significance. This asymmetry increase isindependent, and complementary, to other model-dependent enhancements such as a lowercut on | ∆ y | . For moderate values β min . . m t ¯ t dependence of the asymmetry forthe purpose of model discrimination. Acknowledgements
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