t tbar charge asymmetry, family and friends
tt ¯ t charge asymmetry, family and friends J A Aguilar-Saavedra, M P´erez-Victoria
Departamento de F´ısica Te´orica y del Cosmos, Universidad de Granada, 18071 GranadaE-mail: [email protected],[email protected]
Abstract.
We present the current status of the Tevatron charge asymmetry and its sisterasymmetry at the LHC. The relation between both is elucidated, using as framework thecollider-independent asymmetries they originate from. Other related observables, such as the t ¯ t differential distribution and top polarisation, are also discussed.
1. Introduction
The measurement of an anomalous forward-backward (FB) asymmetry by the CDF and D0experiments at the Tevatron [1, 2] has fueled a plethora of proposals addressing the apparentdeviation from the predictions of the Standard Model (SM). In most cases, these proposalsinvolve new physics beyond the SM. But the simplest explanations for these departures,including those invoking higher-order SM corrections, also predict an enhancement of the chargeasymmetry at the Large Hadron Collider (LHC). Such an enhancement has not been observed,though it is not excluded either, given the present experimental uncertainties. To make thesituation even more puzzling, new physics models addressing the Tevatron excess often, but notalways, predict related effects in t ¯ t production, such as enhancements in the high t ¯ t invariantmass tail, or a net polarisation of the top (anti)quark. None of these effects have been observed.In the following, we critically review these issues and discuss the intriguing status of the subject.
2. The charge asymmetry at the Tevatron
It is well known that the differential cross section for q ¯ q → t ¯ t , with q = u, d , is not invariantunder the interchange of the t and ¯ t momenta. At the Tevatron, the most commonly usedobservable to measure this difference is the asymmetry A F B = N (∆ y > − N (∆ y < N (∆ y >
0) + N (∆ y < , (1)where ∆ y = y t − y ¯ t is the difference between the rapidities of the top quark and antiquark,taking the z axis in the proton direction. This rapidity difference is invariant under boosts inthe beam direction. The definition above exploits the fact that, to a good extent, in p ¯ p collisionsthe directions of the initial quark and antiquark are known: they are, respectively, the directionsof the proton and the antiproton. This asymmetry is equivalent to an asymmetry in the polarangle θ between the top momentum and the quark direction in the centre of mass (CM) frame, A F B = N (cos θ > − N (cos θ < N (cos θ >
0) + N (cos θ < . (2) Talk given by J.A. Aguilar-Saavedra at Discrete 2012, Lisbon, Portugal, December 3-7 2012 a r X i v : . [ h e p - ph ] F e b A FB (inclusive) CDF dil 5.1 fb -1 D0 l+j -1 naive world avg S M CDF l+j -1 CDF l+j -1 CDF l+j / dil -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 A FB (m tt >
450 GeV) S M CDF l+j -1 CDF l+j -1 Figure 1.
Measurements of A F B at the Tevatron: inclusive (left) and at high m t ¯ t (right).In the SM this asymmetry is small and arises, at the lowest order in perturbation theory, fromthe interference of tree-level and one-loop diagrams for q ¯ q → t ¯ t , plus some contributions fromextra jet radiation. For some time, the two Tevatron experiments have consistently measuredan asymmetry above the SM expectation, in the semileptonic and dilepton t ¯ t decay channel.A summary of the most recent inclusive unfolded measurements is shown in Fig. 1 (left), tobe compared with the SM predictions [3–7], which range from 0.058 to 0.089. The naive worldaverage of the latest measurements in each experiment and t ¯ t decay channel gives an asymmetryof 0 . ± . . σ above the closest of those SM predictions. In contrast with otherrecent anomalies, the trend of the measurements with time and increased luminosity does notapproach the SM prediction but the positive excess persists and it does not look like a statisticalfluctuation. At high t ¯ t invariant mass m t ¯ t ≥
450 GeV (Fig. 1 right) the departure from the SMhas been reduced with respect to the first measurement [8], but the deviation is still significant.These consistent discrepancies have motivated a number of papers proposing new physicsexplanations. As the excess in A F B is of the same size as the one-loop QCD asymmetry, ifthis excess results from new physics it is likely to enter at the tree level in q ¯ q → t ¯ t . The typesof renormalisable new physics that can enter q ¯ q → t ¯ t can be classified by using group theory,requiring that the Lagrangian is invariant under SU(3) C × SU(2) L × U(1) Y . This requirementgives a total of 18 possibilities, 10 for spin-1 vector bosons and 8 for scalars [9]. Among them,the most popular ones are a colour octet G µ (also called “gluon” hereafter) exchanged in the s channel [10], a Z (cid:48) [11], W (cid:48) [12] or scalar doublet φ [13] in the t channel, and a colour sextet Ω or colour triplet scalar ω [14] in the u channel. These “simple” models are phenomenological inthe sense that their goal is to explain the anomaly simply by adding to the SM a new particle. Still, they provide a good basis to test if:(i) A F B can be enhanced without spoiling the good agreement of the total t ¯ t cross section withthe SM prediction.(ii) The inclusive and high-mass measurements of A F B can be reproduced.(iii) The explanation of the Tevatron anomalies is compatible with other data, in particularfrom the LHC.Once we have a model that fulfills these conditions, one can go further and build a more complete In addition to these simple models, proposals have been made with new physics entering at one loop level [15]that give similar predictions. ew physics model that explains the Tevatron measurements of the asymmetry and other relatedones. We now concentrate on the first two tests, which involve Tevatron collider.The first test that these models have to pass concerns their ability to correctly fit the observedtotal cross section and asymmetry. This is nontrivial since the SM prediction of the cross section, σ SM = 7 . ± . σ exp = 7 . ± . σ = σ SM + δσ int + δσ quad , this implies that theinterference between SM and new physics, δσ int , and the new physics quadratic term, δσ quad ,have to fulfill δσ int + δσ quad (cid:39)
0. There are two possibilities for this:(i) The quadratic term is large, which implies that the interference is also large and both termsnearly cancel each other. For this to happen, a fine-tuning of the new physics couplingis needed, since the interference and quadratic terms depend linearly and quadratically,respectively, on this coupling. This is the case, for example, of t -channel models ( Z (cid:48) , W (cid:48) , φ ). If this cancellation is arranged to happen at the Tevatron energy, then it is not expectedto take place anymore at the LHC.(ii) The quadratic term is small. The total interference δσ int must also be small but withsizeable contributions in the forward and backward hemispheres, δσ F int (cid:39) − δσ B int . This isthe case, for example, of an s -channel heavy gluon with axial coupling to either light quarksor to the top quark, in which case the interference identically vanishes. If one drops thecondition δσ F int + δσ B int (cid:39)
0, as for example in u -channel colour sextet models, the generatedasymmetries have to be smaller due to the total cross section constraint.In both cases, it is evident that one needs that the interference with the SM is non-zero [18]which, in principle, can be achieved with all the types of new particles that can contribute to q ¯ q → t ¯ t [9].A second Tevatron test for the new physics proposals concerns whether they can accommodatethe inclusive and high-mass measurements. This is accomplished for most models, as it is shownin Fig. 2. The coloured regions show the model predictions obtained by a parameter spacescan, subject to some loose constraints from the total t ¯ t cross section at the Tevatron and thehigh-mass tail at the LHC [19]. We only consider positive contributions to the asymmetry,which are summed to the SM one [7] in all cases. For the colour octet we consider a veryheavy axigluon represented by four-fermion operators [9, 20–22]. Most of these simple modelscan reproduce very well the inclusive and high-mass asymmetries, except a new Z (cid:48) whichoverpredicts the asymmetry, especially at high t ¯ t invariant mass mass. (For this and otherreasons —see section 5— this model will not be considered further here as a viable candidate.)But a more revealing outcome of this comparison is the observation that the inclusive and high-mass measurements of the asymmetry are “naturally consistent” or, in other words, it does nottake a contrived model to reproduce both. A recent analysis of the polar angle dependence ofthe cross section [24] also supports the internal consistence of the deviation. The differentialcross section can be expanded in terms of Legendre polynomials, dσd cos θ = (cid:88) l a l P l (cos θ ) . (3)The CDF Collaboration finds good agreement of all a l with the SM prediction, except for theterm with l = 1 —corresponding to a term linear in cos θ — that deviates more than 2 σ fromthe SM. This pattern can be nicely fitted with an s -channel colour octet, for example, whichenhances a while keeping higher l coefficients small. More complicated models, for example with a number of s -channel coloured resonances, can reproducecomplicated profiles of A FB versus m t ¯ t [23]. A FB ( m tt >
450 GeV) A F B : : : Z ′ A FB ( m tt >
450 GeV) A F B : : : W ′ A FB ( m tt >
450 GeV) A F B G µ A FB ( m tt >
450 GeV) A F B : : : φ A FB ( m tt >
450 GeV) A F B : : : Ω A FB ( m tt >
450 GeV) A F B : : : ω Figure 2.
Inclusive versus high-mass asymmetries at the Tevatron, for several new physicsmodels. The numbers in the legends indicate the mass range for the new particle, in GeV.The crosses correspond to the experimental measurements in Fig. 1, with the shaded boxescorresponding to the 1 σ uncertainty.Finally, at the Tevatron there are additional constraints from the cross section at the high- m t ¯ t tail, but the measurements in that region are not very precise and the new physics contributionsmay have a much lower detection efficiency than SM top pair production, due to the limiteddetector acceptance [25]. This is the case, for example, of light t -channel mediators. For thisreason we do not use the measurements in that region as a further constraint.
3. The younger sister: the LHC charge asymmetry
At a pp collider as the LHC, the symmetry of the initial state implies that, for a fixed choice of z axis to measure rapidities, the FB asymmetry in Eq. (1) vanishes. Then, one has to considerdifferent observables to test an asymmetry in q ¯ q → t ¯ t . This can be done, for example, byexploiting the fact that valence quarks have larger average momentum fraction than antiquarks,leading to a non-vanishing asymmetry [26] A F B = N (∆ | y | > − N (∆ | y | < N (∆ | y | >
0) + N (∆ | y | < , (4)with ∆ | y | = | y t | − | y ¯ t | . This asymmetry has been measured by the ATLAS and CMSCollaborations, with the results shown in Fig. 3. The naive average of the latest measurementsis A C = 0 . ± . A F B and the LHC A C are not the same observable. Therefore, a measurement of A C consistent with the SM isnot in conflict with a Tevatron excess [28]. On the other hand, comparing predictions for A F B A C (inclusive) ATLAS l+j -1 ATLAS l+j / dil naive world avg S M CMS l+j -1 CMS l+j -1 ATLAS dil 4.7 fb -1 CMS dil 5.0 fb -1 Figure 3.
Measurements of A C (inclusive)at the LHC. A FB -0.0200.020.040.060.080.10 A C ATLAS + CMS CD F + D SM φ W ′ ω Ω G µ Figure 4.
Comparison of predictions forthe inclusive asymmetries A F B and A C forseveral simple models.and A C within a given model brings important consequences for the model [29], as it is clearlydepicted in Fig. 4. In particular, the W (cid:48) models are clearly disfavoured, as they predict valuesof A C more than 3 σ above present data when accommodating the Tevatron asymmetry. Forthe rest of simple models the fate is uncertain as they are consistent with data at the 2 σ level.The difficulty to simultaneously reproduce the central values of A F B and A C has motivated theappearance of several less simple models [30, 31] that can accommodate the central values of theTevatron and LHC asymmetries, by introducing some type of cancellation among contributions.(See also Refs. [32, 33].)
4. The parents: the collider-independent asymmetries.
The Tevatron asymmetry A F B and the LHC asymmetry A C originate from the “intrinsic”partonic asymmetries in u ¯ u → t ¯ t , d ¯ d → t ¯ t , which will be denoted hereafter as A u , A d ,respectively [28]. At leading order (LO), these asymmetries only depend on the partonic CMenergy ˆ s . As a consequence of this, for a suitably narrow interval of m t ¯ t the asymmetries A u , A d are nearly the same at the Tevatron and the LHC. The “daughter” asymmetries A F B , A C can be regarded as different combinations of A u and A d , the differences arising because • at these two colliders the importance of u ¯ u → t ¯ t and d ¯ d → t ¯ t , relative to the total t ¯ t production rate, changes due to parton density functions (PDFs); • at the LHC the asymmetry A C suffers from a “dilution” because not always the initialvalence quark has larger momentum fraction than the sea antiquark. In case that theantiquark has larger momentum fraction, a “forward” event, that is, with the top quark inthe direction of the incoming quark (cos θ > | y | < A C .Then, a possible experimental test of the consistency of A F B (higher than the SM prediction)with A C (consistent with the SM) would be to measure the “collider-independent” asymmetries A u and A d . In experiments, the intrinsic asymmetries A u , A d can be extracted by exploiting Although we use the name “collider-independent” for A u and A d , to be precise it must be noted that at next-to-leading order (NLO) some differences are introduced, of little relevance from a practical point of view. Theseare mainly originated from the need to replace a fixed partonic CM energy ˆ s by a narrow m t ¯ t interval, whichintroduces some deviations due to a residual dependence on PDFs. Besides, the asymmetries in gq → t ¯ tj are he dependence of A F B and A C on the velocity of the t ¯ t pair [35] β = | p zt + p z ¯ t | E t + E ¯ t , (5)because A u and A d are independent of this variable. Thus, A u and A d can be extracted froma fit to A F B ( β ) = A u F u ( β ) + A d F d ( β ) ,A C ( β ) = A u F u ( β ) D u ( β ) + A d F d ( β ) D d ( β ) , (6)where F u,d are the fractions of u ¯ u and d ¯ d events, respectively, and D u,d are factors to reflect thedilution of the asymmetries in pp collisions we have mentioned above. Both F u,d and D u,d canbe computed with a Monte Carlo within the SM and used as input to extract A u and A d fromdata. The SM predictions for these asymmetries are given in Fig. 5. The left panel shows theasymmetries in 50 GeV bins, without any restriction on the transverse momentum of the t ¯ t pair p t ¯ tT . It is important to remark here that, compared with their expected experimental uncertainty,the differences between the Tevatron and LHC asymmetries A u , A d are irrelevent and justifiylabelling these asymmetries as “collider-independent”. The right panel shows the asymmetrieswith a cut p t ¯ tT <
30 GeV that practically eliminates the deviations between the Tevatron andLHC asymmetries.
350 400 450 500 550 600 650 700 750 800 m tt (GeV) A u , d ▲ ▲ ▲ A u ▼ ▼ ▼ A d Tevatron LHC7 LHC8 350 400 450 500 550 600 650 700 750 800 m tt (GeV) A u , d ▲ ▲ ▲ A u ▼ ▼ ▼ A d Tevatron LHC7 LHC8
Figure 5.
Asymmetries A u , A d in the SM, for the Tevatron and the LHC. Left: without a cuton p t ¯ tT . Right: for p t ¯ tT <
30 GeV.The experimental measurement of A u and A d is very challenging, as it may require a three-dimensional data unfolding in β , m t ¯ t and ∆ y (∆ | y | ). But the interest of this measurementmay well be worth the effort. In the first place, if these asymmetries are measured, it can betested whether the Tevatron and LHC results are consistent. We present in Fig. 6 a potentialresult in the bin m t ¯ t ≤
400 GeV, with the crosses representing the NLO SM result and theellipses corresponding to the 1 σ statistical uncertainty. In this example the ellipses intersect byconstruction, since the SM NLO values of A F B and A C have been used as input. But, if thereis an unknown systematic effect in either collider, this may not be the case. If, on the otherhand, the Tevatron and LHC determinations of the asymmetries are consistent, one can combine irrelevant. For an extended discussion see Ref. [34]. Strictly speaking, they are independent at LO and with fixed ˆ s . At NLO, or in finite m t ¯ t bins, one can see thatthe dependence is rather mild [34]. A u -1.5-1-0.500.511.5 A d Tevatron LHC7LHC8 t − Figure 6.
Example of a potential outcomeof the measurement of A u and A d at theTevatron and the LHC. -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 ∆ A u -0.4-0.200.20.40.60.811.2 ∆ A d < Figure 7.
Example of a potential combina-tion of the measurements of A u and A d at theTevatron and the LHC.both and test whether the combined measurement is compatible with the SM prediction. Weshow in Fig. 7 a potential result of a Tevatron-LHC combination, taking a heavy axigluon asa new physics benchmark. The ellipses correspond to the 1 σ combined limits with the SMasymmetries subtracted, so that the SM point in this plot corresponds to zero. It is apparentthat the combination of Tevatron and LHC results on A u , A d has a much higher significancethan the individual measurements.
5. An old friend: the high-mass tail at the LHC
One of the first and most universal predictions for models explaining the Tevatron excess isan enhancement of the t ¯ t differential distribution at high m t ¯ t [9, 36]. The LHC experimentshave not found any sign of tail enhancement [37, 38]. The most stringent limits resultfrom the ATLAS analysis, which measures a cross section slightly below the SM prediction, d log σ/dm t ¯ t (cid:39) ± − for m t ¯ t ≥
950 GeV, compared to a SM prediction of 9 PeV − .This leads to an upper limit σ/σ SM ≤ . σ/σ SM ≤ . m t ¯ t ≥ σ/σ SM ≥ .
5, the allowed areas for the Tevatronasymmetries in Fig. 2 shrink to the corresponding ones in Fig. 8. The Z (cid:48) model, already discardedbecause it overpredicts the Tevatron excess, does not give a positive contribution to the Tevetronasymmetry after imposing the LHC tail constraint. The W (cid:48) model, which predicted too largevalues for A C , cannot reproduce the Tevatron asymmetries either. The rest of models are, inprinciple, compatible with t ¯ t cross section measurements at the LHC and the Tevatron. Amongthem, the “least disturbing” one for the differential distribution is an s -channel colour octet,as long as it is heavy (or light) enough. However, if the resonance is at kinematical reach thedifferential cross section enhancement is much larger, and the new particle will appear as a peak(or bump, if it is very wide) in the t ¯ t invariant mass spectrum. Current LHC searches put heavygluon models into trouble as the mass scales probed go higher, because the couplings requiredget too large and nonperturbative. However, these constraints can be avoided by “light” gluonswith a mass of few hundreds of GeV [23, 39–41].
6. A new friend: the top polarisation
Another common signal of new physics contributions to t ¯ t production, which in general maycouple differently to t L and t R , is a change in the polarisation of the produced top (anti)quarks. A FB ( m tt >
450 GeV) A F B Z ′ tail 0.5 − × SM A F B > A F B S M E X C L U D E D A FB ( m tt >
450 GeV) A F B : W ′ tail 0.5 − × SM A FB ( m tt >
450 GeV) A F B G µ tail 0.5 − × SM A FB ( m tt >
450 GeV) A F B : : : φ tail 0.5 − × SM A FB ( m tt >
450 GeV) A F B : : : Ω tail 0.5 − × SM A FB ( m tt >
450 GeV) A F B : ω tail 0.5 − × SM Figure 8.
Inclusive versus high-mass asymmetries at the Tevatron, for several new physicsmodels, imposing a tight constraint on the LHC high-mass tail (see the text).The numbers inthe legends indicate the mass range for the new particle, in GeV. The crosses correspond tothe experimental measurements in in Fig. 1, with the shaded boxes corresponding to the 1 σ uncertainty.The double angular distribution for the production of a t ¯ t pair is1 σ dσd cos θ t d cos θ ¯ t = 14 [1 + B t cos θ t + B ¯ t cos θ ¯ t + C cos θ t cos θ ¯ t ] . (7)with θ t , θ ¯ t the angles between the top (antitop) momenta in the zero momentum frame (ZMF)with respect to some chosen spin axes [42, 43]. The constants B t , B ¯ t correspond to thepolarisation of the top and antitop, respectively. In the SM they vanish at the tree level—that is, top (anti-)quarks are produced unpolarised— due to the vector structure of the QCDcoupling, and they are small at higher orders. The C constant measures the spin correlationbetween the top and antitop, and is nonzero for a suitable choice of spin axes.The spin correlation coefficient C has been measured at the Tevatron, in the “beamline”basis [44–46] (Fig. 9, upper left panel), giving a naive average of C = 0 . ± .
26, in goodagreement with the SM prediction C SM = 0 .
79 [43]. Defining ∆ C = C − C SM , the experimentalmeasurement ∆ C = − . ± .
26 already sets some constraints on the possible contributions to A F B from new physics [47] (Fig. 9, upper right panel).At the LHC, the spin correlation has been determined in the helicity basis [48, 49], with anaverage measurement C = 0 . ± .
06 (Fig. 9, middle left panel). Defining again ∆ C = C − C SM ,with C SM = 0 .
31 [43], this average corresponds to ∆ C = 0 . ± .
06. The measurement of Provided CP is conserved, B ¯ t = − B t if the same axis is chosen to measure the top and antitop spins. Choosingthe helicity basis for each quark, B t = B ¯ t . C S M CDF dil 5.1 fb -1 D0 l+j / dilD0 dil 5.4 fb -1 D0 l+j -1 naive world avg G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:68) A FB (cid:68) D (cid:72) T e v a t r on (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:45) (cid:68) A FB (cid:68) C o ff (cid:72) T e v a t r on (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) (cid:68) A FB (cid:68) C b ea m (cid:72) T e v a t r on (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:68) A FB (cid:68) C h e l (cid:72) T e v a t r on (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:45) (cid:68) A FB B b ea m (cid:72) T e v a t r on (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:68) A FB B h e l (cid:72) T e v a t r on (cid:76) FIG. 7: Correlations between the NP contributions to the inclusive FBA and various spin observables at the Tevatron (see textfor details and definitions). The present experimental results (68% C.L. regions) are shaded in horizontal and vertical bands.The NP model predictions are determined from the global fit as specified in Sec. IV and are bounded by full (axigluon G inthe low ( m G .
450 GeV in black) and high ( m G &
700 GeV in gray) mass regions), dashed (scalar color triplet ∆), dotted(scalar color sextet Σ) and dot-dashed (neutral component of the scalar isodoublet φ in the low ( m φ . m t in darker shade)and high ( m φ >
200 GeV in lighter shade) mass region) contours.
B. Results
In this section we present predictions for the various top spin observables at the Tevatron as well as the 7 TeV (and8 TeV) LHC within the various NP model parameter regions which are able to address the FBA puzzle, as determinedin Sec. IV. In particular we present correlations between the inclusive and high m t ¯ t FBA values as measured at theTevatron, and the shifts of the various spin observables from their corresponding SM values. We define (see Sec. III)∆ A F B ≡ A F B − A SM F B , ∆ C i ≡ C i − C SM i and ∆ D ≡ D − D SM . On the other hand since QCD produced top quarks arenot polarized, (neglecting tiny electroweak contributions) we assume B SM i ’ B i in presenceof NP directly. The predictions for the relevant spin observables at the Tevatron are shown in Fig. 7. First notethat the results for the SM q ¯ q off-diagonal axis at the Tevatron turn out to be almost identical to the beamline axis(and very similar at the LHC, see Fig. 8). Both bases provide good potential discrimination between color sextet onone hand, and color triplet or isodoublet scalar models on the other hand. The off-diagonal basis exhibits marginallybetter sensitivity only for the axigluon ( G ) model. However, since purely axial couplings of G to quarks do notproduce polarized top quarks, B i vanishes for the axigluon model and consequently we do not plot B off dependenceseparately.We observe that existing spin observable measurements at the Tevatron do not overly constrain selected NP mod- -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 C S M ATLAS dil 2.1 fb -1 CMS dil 5.0 fb -1 naive world avg G' Φ (cid:68)(cid:83) (cid:68) A FB (cid:68) D (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:68) A FB (cid:68) C o ff (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:45) (cid:68) A FB (cid:68) C b ea m (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:68) A FB (cid:68) C h e l (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:68) A FB B b ea m (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:45) (cid:68) A FB B h e l (cid:72) L H C (cid:76) FIG. 8: Correlations between the NP contributions to the inclusive FBA at the Tevatron and various spin observables at the7 TeV LHC (see text for details and definitions). The present experimental results (68% C.L. regions) are shaded in horizontaland vertical bands. For ∆ C hel we also show the 95% C.L. contour in thin dashed line. The NP model predictions are determinedfrom the global fit as specified in Sec. IV and are bounded by full (axigluon G in the low ( m G .
450 GeV in black) and high( m G &
700 GeV in gray) mass regions), dashed (scalar color triplet ∆), dotted (scalar color sextet Σ) and dot-dashed (neutralcomponent of the scalar isodoublet φ in the low ( m φ . m t in darker shade) and high ( m φ >
200 GeV in lighter shade) massregion) contours. els. Some sensitivity to the light scalar isodoublet model is exhibited by the recent beamline axis spin correlationmeasurement by DØ [39] as seen in the center left plot in Fig. 7. On the other hand (anti)top polarization ( B i both in the beamline and in the helicity basis) offers a very powerful probe of scalar t -channel models and a O (20%)precision measurement (in helicity basis) could already test (and discriminate between) the scalar color triplet (∆)and isodoublet ( φ ) model explanations of the FBA. Finally, the axigluon ( G ) models in general give very smallcontributions to the chosen spin observables. For example, at the Tevatron, spin correlation measurements at O (2%)precision would be required to probe such FBA explanations.The results for the relevant spin observables at the 7 TeV LHC are shown in Fig. 8. Among these, presently themost powerful probe of FBA inspired models is the helicity basis spin correlation as measured recently by ATLAS [41].In particular it already represents a non-trivial constraint for the scalar isodoublet and heavy axigluon models. Inthe light scalar isodoublet scenario, the large negative deviation in ∆ C hel can be traced to sizable non-standard The results for ∆ D , ∆ C i and B i at the 7 TeV and 8 TeV LHC are almost identical and we do not show the later separately. -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 B S M CMS dil 5.0 fb -1 ATLAS l+j -1 naive world avg G' Φ (cid:68)(cid:83) (cid:68) A FB (cid:68) D (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:68) A FB (cid:68) C o ff (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:45) (cid:68) A FB (cid:68) C b ea m (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:68) A FB (cid:68) C h e l (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:68) A FB B b ea m (cid:72) L H C (cid:76) G' Φ (cid:68)(cid:83) (cid:45) (cid:45) (cid:45) (cid:45) (cid:68) A FB B h e l (cid:72) L H C (cid:76) FIG. 8: Correlations between the NP contributions to the inclusive FBA at the Tevatron and various spin observables at the7 TeV LHC (see text for details and definitions). The present experimental results (68% C.L. regions) are shaded in horizontaland vertical bands. For ∆ C hel we also show the 95% C.L. contour in thin dashed line. The NP model predictions are determinedfrom the global fit as specified in Sec. IV and are bounded by full (axigluon G in the low ( m G .
450 GeV in black) and high( m G &
700 GeV in gray) mass regions), dashed (scalar color triplet ∆), dotted (scalar color sextet Σ) and dot-dashed (neutralcomponent of the scalar isodoublet φ in the low ( m φ . m t in darker shade) and high ( m φ >
200 GeV in lighter shade) massregion) contours. els. Some sensitivity to the light scalar isodoublet model is exhibited by the recent beamline axis spin correlationmeasurement by DØ [39] as seen in the center left plot in Fig. 7. On the other hand (anti)top polarization ( B i both in the beamline and in the helicity basis) offers a very powerful probe of scalar t -channel models and a O (20%)precision measurement (in helicity basis) could already test (and discriminate between) the scalar color triplet (∆)and isodoublet ( φ ) model explanations of the FBA. Finally, the axigluon ( G ) models in general give very smallcontributions to the chosen spin observables. For example, at the Tevatron, spin correlation measurements at O (2%)precision would be required to probe such FBA explanations.The results for the relevant spin observables at the 7 TeV LHC are shown in Fig. 8. Among these, presently themost powerful probe of FBA inspired models is the helicity basis spin correlation as measured recently by ATLAS [41].In particular it already represents a non-trivial constraint for the scalar isodoublet and heavy axigluon models. Inthe light scalar isodoublet scenario, the large negative deviation in ∆ C hel can be traced to sizable non-standard The results for ∆ D , ∆ C i and B i at the 7 TeV and 8 TeV LHC are almost identical and we do not show the later separately. Figure 9.
Left: experimental measurements of spin observables. Right (taken from Ref. [47]):theoretical predictions within several new physics models. The horizontal axis represents theincrease in A F B from new physics sources and the vertical axis the increase in the corresponding( B or C ) coefficient, with respect to the SM value. The legends ∆, Σ correspond to ω , Ω inour notation. C at the LHC has little effect on the allowed parameter space for models reproducing theTevatron A F B (Fig. 9, middle right panel). More restrictive is the measurement of the toppolarisation, i.e. the B t parameter [50, 51] (Fig. 9, lower left panel). The average of the ATLASand CMS measurements, B = − . ± .
04, disfavours at the ∼ σ level the explanation of theasymmetry by colour sextet and triplet scalars, which couple to t R and predict a positive topquark polarisation (Fig. 9, lower right panel).For completeness, it is worth mentioning that lepton-based FB asymmetries have also beenmeasured at the Tevatron [2, 52], A (cid:96)F B = N ( Q · η > − N ( Q · η < N ( Q · η >
0) + N ( Q · η < ,A (cid:96)(cid:96) = N (∆ η > − N (∆ η < N (∆ η >
0) + N (∆ η < , (8)with η the rapidity of the charged leptons and Q their charge. These asymmetries includeinformation from the t ¯ t FB asymmetry and the top polarisation [53, 54] —the latter is foundin agreement with the SM— and provide a complementary experimental handle to probe newcontributions to t ¯ t production. The measurements of A (cid:96)F B (see Fig. 10) are more precise andexhibit a positive excess with respect to SM predictions, whereas the only measurement of thedilepton asymmetry, A (cid:96)(cid:96) = 0 . ± . A (cid:96)(cid:96) SM = 0 .
062 [7]. -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 A l FB (inclusive) D0 dil 5.4 fb -1 D0 l+j / dil 5.4 fb -1 S M D0 l+j -1 Figure 10.
Measurements of the lepton asymmetry A (cid:96)F B at the Tevatron.
7. Discussion
More than two years after the measurement [8] that trigged the wide interest in the FBasymmetry at the Tevatron, there have been various new measurements, updated SM predictionsand plenty of proposals for new physics explanations. But the question still remains whetherthe Tevatron anomaly corresponds to new physics, an unknown higher-order SM correction, orsome kind of systematic effect.The first possibility, of new physics in t ¯ t production, is certainly exciting, but it is not clearwhich form this new physics could have. Among the six simple models that we considered ascandidates to explain the excess in the Tevatron asymmetry, only two of them (a colour octetand a scalar doublet) have survived after imposing just constraints from other observables in t ¯ t production at the Tevatron and LHC. But, in addition, there are some other measurementsthat put the minimal implementation of these models in trouble. Light gluons mediate dijet pair [55] and four-top production [56], neither observed. Theformer constitute a serious constraint for lighter masses, which can be softened by assuminga large gluon width —due for example to decays into some new particle. The latter maybecome relevant for a wide mass range with increased luminosity. In addition, there areconstraints from low-energy B physics [57, 58] and electroweak precision data [59] that arevery model-dependent. • For scalar doublets there are also stringent constraints from B physics [60], atomic parityviolation [61] and possibly from associated production with a top quark.These difficulties, in any case, may just reflect our current inability to propose a compellingmodel that explains the asymmetry measurements at the Tevatron and the LHC, fulfilling theconstraints from other t ¯ t observables and collider data without ad-hoc assumptions and modelfine-tuning. In this regard, we have stressed that a Tevatron A F B excess and a small A C at theLHC are compatible in general. By using Eqs. (6) and considering A u , A d as free independentparameters ranging between − A F B , A C within each m t ¯ t bin. This is shown in Fig. 11. A positive excess at the Tevatronis compatible with a zero, or even negative, asymmetry at the LHC, provided there is somecancellation between the contributions from A u and A d . -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 A FB -0.20-0.15-0.10-0.0500.050.100.150.20 A C < Figure 11.
Model-independent predictionfor the correlation between A C and A F B in several m t ¯ t bins, based on the collider-independent asymmetries. A FB -0.0200.020.040.060.080.10 A C ATLAS + CMS CD F + D Higher-orders: allowed region
Figure 12.
Estimated correlation between A C and A F B from higher-order QCD effects,based on the collider-independent asymme-tries.Explanations of the Tevatron excess by higher-order QCD effects are unlikely to fit datawell, if the trend of current measurements persists. A simple reckoning indicates that, if therewere large missing QCD corrections that shifted A F B to its Tevatron average, they would alsoshift A C away from the LHC average. In the absence of a proper next-to-next-to-leading ordercalculation, one can give a back-of-the-envelope estimate for this correlation by using againEqs. (6) and varying A u , A d around the NLO SM value. The resulting prediction for A C versus A F B in Fig. 12 shows that one cannot simultaneously fit the central values of Tevatron and LHCasymmetries with this kind of corrections to the SM. A similar type of argument is expected tohold for other QCD-based explanations of the anomalies [62, 63].The third option, of unknown systematic errors in Tevatron or LHC experiments, is hard tounderstand since the two experiments at each collider provide similar results. Still, unknownsystematics are unknown by definition, and little can be said in this direction at the moment. We thank W. Bernreuther and Z.-G. Si for providing us with these data. n summary, the A F B puzzle is far from being solved. There are still good hopes thatthere is some type of new physics in t ¯ t production, which might (or might not) be visible byprecision measurements of the LHC charge asymmetry, the t ¯ t differential distributions and thetop polarisation. Fortunately, the upcoming LHC and D0 measurements will provide importantinformation to help approach a solution. Acknowledgements
This work has been supported by MICINN by projects FPA2006-05294 and FPA2010-17915,Junta de Andaluc´ıa (FQM 101, FQM 03048 and FQM 6552) and Funda¸c˜ao para a Ciˆencia eTecnologia (FCT) project CERN/FP/123619/2011.
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