Top Charge Asymmetry -- Theory Status Fall 2013
TTop Charge Asymmetry – Theory Status Fall 2013
Susanne Westhoff
PITTsburgh Particle physics, Astrophysics & Cosmology Center (PITT PACC) ∗ Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA
I review the current status of the charge asymmetry in hadronic top-quark pair productionfrom a theory perspective. The standard-model predictions for the observables at theTevatron and LHC are being discussed, as well as possible explanations of the Tevatronexcess in terms of new physics. I give an outlook for future investigations of the top-quarkcharge asymmetry, focussing on novel observables at the LHC.
The charge asymmetry in top-antitop production provides us with a test of Quantum Chromo-dynamics (QCD) beyond leading-order (LO) interactions. It manifests itself in differing angulardistributions of top and antitop quarks, A C = σ A σ S , σ S,A = (cid:90) d cos θ (cid:18) d σ t ¯ t d cos θ ± d σ ¯ tt d cos θ (cid:19) , (1)where θ is the scattering angle of the top quark ( σ t ¯ t ) or antitop quark ( σ ¯ tt ) off of the incidentquark in the parton center-of-mass frame. Experimentally, the charge asymmetry is measuredin terms of top-antitop rapidity differences, A exp C = σ (∆ y > − σ (∆ y < σ (∆ y >
0) + σ (∆ y < . (2)In proton-antiproton collisions, the total charge asymmetry is closely related to a top-quarkforward-backward asymmetry in the laboratory system, which is measured through the rapiditydifference ∆ y = y t − y ¯ t (yielding A exp C = A yC = A C ). In proton-proton collisions, the chargeasymmetry induces a forward-central asymmetry, which is measured through the difference ofabsolute rapidities ∆ y = | y t | − | y ¯ t | (yielding A exp C = A | y | C (cid:28) A C ). The sensitivity of A | y | C to thepartonic charge asymmetry is reduced due to | y t | − | y ¯ t | not being invariant under boosts alongthe beam axis. At the LHC, A | y | C is further suppressed by a large background from symmetricgluon-gluon initial states.The results of asymmetry measurements at the Tevatron and LHC experiments are sum-marized in Figure 1 [1] and discussed in detail in the contribution of Viatcheslav Sharyy inthese proceedings. Here it shall suffice to mention the observation of an excess in A yC at theTevatron, while measurements of A | y | C at the LHC are consistent with their standard-model(SM) prediction (and with zero) within uncertainties. ∗ preprint PITT-PACC-1310 a r X i v : . [ h e p - ph ] N ov symmetry, % Inclusive AsymmetryttLepton+jets Asymmetry η Lepton qLepton+jetsDileptons Asymmetry η Lepton dDileptons -1 D0 5.4 fb 6.5 % ± -1 D0 9.7 fb |<1.5) η ± ± ± -1 CDF 9.4 fb 4.7 % ± -1 CDF 9.4 fb % (extr.) -2.9+3.2
Bernreuther & Si, Phys.Rev., D86 (2012) 034026
Asymmetry, %
Bernreuther & Si, Phys.Rev., D86 (2012) 034026: ± -1 CMS 19.7 fb 1.5 % ± ± ± -1 CMS 5.0 fb , 7 TeV -1 CMS 5.0 fb 1.0 % ± ± ± -1 ATLAS 4.7 fb , 7 TeV -1 ATLAS 4.7 fb Inclusive AsymmetryttLepton+jetsDileptonsLepton+jetsDileptons Asymmetry η Lepton dDileptons
Figure 1: Charge asymmetry measurements at the Tevatron (left panel) and the LHC (rightpanel). Shown are the inclusive t ¯ t asymmetries A yC and A | y | C in lepton+jets and dilepton finalstates, as well as the lepton asymmetries A (cid:96)C ( qη , Tevatron) and A (cid:96)(cid:96)C (d η ), defined in Eqs. 8 and9. SM predictions including scale uncertainties are displayed in gray.This write-up covers the current theoretical status of the SM prediction for the chargeasymmetry (Section 2), as well as potential contributions of new physics (Section 3). I discussthe limitations to observe A | y | C at the LHC and suggest new observables involving an additionalhard jet as an alternative way of measuring the charge asymmetry in proton-proton collisions(Section 4). I conclude in Section 5 with an outlook and comments on related observables thatallow a more complete picture of the charge asymmetry. In QCD, the charge asymmetry is generated at next-to-leading order (NLO) by additionalvirtual and real gluon radiation [2], as illustrated in Figure 2. Normalized to the symmetriccross section, the perturbative expansion of the charge asymmetry reads A QCD C = α s σ (1) A + α s σ (2) A + . . .α s σ (0) S + α s σ (1) S + α s σ (2) S + . . . . (3)Currently, the charge-asymmetric piece is known at NLO QCD ( σ (1) A ), whereas the symmet-ric cross section has recently been calculated up to NNLO ( σ (2) S ) [3]. The strong remnantdependence on the factorization and renormalization scales has been significantly reduced bythe resummation of large logarithms close to the partonic threshold [4, 5, 6]. The leadingcontribution to A QCD C is dominated by the lowest-order expansion of the threshold-resummedcross section, and the asymmetry proves stable under higher-order threshold corrections. The2 q ¯ q ¯ qt ¯ t q q qtt ¯ tg g Figure 2: Charge asymmetry in QCD from quark-antiquark annihilation (left) and quark ex-citation (right). Shown are representative diagrams for inclusive t ¯ t production (dashed anddotted cuts, qg contribution negligible) and t ¯ t + j production (dotted cuts).numerical impact of fixed-order NNLO contributions ( σ (2) A ) on the asymmetry is not known todate, but is an important ingredient for a precise prediction of A QCD C .Electroweak (EW) contributions to the charge asymmetry turn out to be significant. Fixed-order EW corrections increase the Tevatron asymmetry A yC by about 23% [7]. Their effect onthe LHC asymmetry A | y | C is smaller due to the different parton distributions in the initial state.The resummation of EW Sudakov logarithms yields an additional enhancement of 5% (apartfrom a minor double-counting with fixed-order corrections) [8]. Including the leading QCDand EW fixed-order contributions, the SM predictions for the asymmetries at the Tevatron andthe LHC are given by [9] A yC (1 .
96 TeV) = 8 . +0 . − . % , A | y | C (7 TeV) = 1 . ± .
05 % , (4)where the errors are scale uncertainties. Notice that A C decreases, if higher-order QCD cor-rections to σ S are included. This approach presumably underestimates the charge asymmetry,due to an incomplete cancellation of higher-order effects affecting both σ S and σ A .Since the results of charge asymmetry measurements are compared to predictions fromMonte Carlo event generators, a precise understanding of their features is crucial for a correctinterpretation. State-of-the-art Monte Carlo generators such as SHERPA and HERWIG++with NLO matching to parton showers reproduce the qualitative features of the charge asym-metry in QCD: a decline with increasing t ¯ t transverse momentum p t ¯ tT , as well as an increasewith M t ¯ t and ∆ y [10, 11]. However, the substantial dependence of Monte Carlo predictions onthe functional scale in the hard process indicates that the observed excess of the asymmetry athigh M t ¯ t and ∆ y may be due to higher-order QCD and EW corrections not taken into accountby Monte Carlo generators. Beyond the SM, a charge asymmetry can be generated at tree level by the interference of a new q ¯ q → t ¯ t process with the QCD amplitude, as illustrated in Figure 3. Light new particles cangenerate an asymmetry as well through self-interference, if their quantum numbers prohibit aninterference with the SM amplitude. Possible contributions can be classified into three kinematiccategories: a massive color octet with axial-vector couplings to quarks in the s-channel, a vectorboson with flavor-changing couplings in the t-channel, or a new scalar in the u-channel. Such Notice that EW Sudakov logarithms significantly reduce the invariant mass spectrum in t ¯ t production,d σ t ¯ t / d M t ¯ t , which affects constraints on potential new-physics contributions to A C . u ¯ u t ¯ t u ¯ u t ¯ t u ¯ u ¯ tt u ¯ u t ¯ tgSZ ′ Gg uA g tA g ut g u ¯ t g s g s Figure 3: New-physics contributions to the charge asymmetry at tree level.new particles and their embedding into specific models have been studied in great detail andfound to be strongly constrained by correlated effects on charge-symmetric observables. Inparticular, the asymmetry excess at the Tevatron has stimulated a large effort to test possiblenew contributions at the LHC, with beneficial effects on general new-physics searches.Among color octets with axial-vector couplings to quarks, dubbed “axigluons”, two speciesyield a positive contribution to A C : light axigluons ( M G (cid:46) m t ) with flavor-universal couplings, g qA · g tA > M G (cid:38) m t ) with opposite-sign couplings, g qA · g tA < t ¯ t and dijet production, by the LHC asymmetry A | y | C , as well as electroweakprecision observables [15, 16]. Light axigluons are thus required to be broad in order to hidein the t ¯ t and dijet distributions measured at Tevatron and LHC. They can still account forthe Tevatron excess in a mass window 200 GeV < M G <
450 GeV, which may be closed byexamining the tail of angular distributions in dijet production at the LHC. Heavy axigluonsare highly challenged by a recent model-independent measurement by the CMS collaboration,which confines new-physics effects in the high-energy tail of the cross section, σ t ¯ t ( M t ¯ t > t ¯ t invariant mass spectrum. They areexcluded by measurements of atomic parity violation [18].Further asymmetry candidates are new vector bosons with masses around 300 GeV andflavor-changing neutral couplings in the t-channel, often referred to as Z (cid:48) bosons [19]. Strongconstraints from flavor observables require a highly non-trivial flavor structure of their cou-plings, confined to right-handed up and top quarks. Such structures can be arranged for bymeans of flavor symmetries [20], which also protect the new bosons from inducing undesiredsame-sign top production. Additional strong constraints on Z (cid:48) candidates arise, as for theu-channel contributions, from the t ¯ t and dijet invariant mass distributions and from atomicparity violation. At the LHC, a kinematic angular asymmetry in associated Z (cid:48) t productionreconciles t-channel bosons with the measured charge asymmetry A | y | C [21]. Searches for thecorresponding Z (cid:48) t resonances with Z (cid:48) → ¯ tu , however, rule out an explanation of the Tevatronexcess unless alternative Z (cid:48) decay channels dominate [22]. Since many of these constraints aremodel-dependent, t-channel explanations of the asymmetry are not conclusively ruled out yet.However, the search for Z (cid:48) bosons in top-like final states at the LHC has a high exclusion po-tential. Along the lines described in [23] for a W (cid:48) model, t-channel explanations of the Tevatronexcess may be completely ruled out by scanning existing LHC event samples from top-quarkanalyses for Z (cid:48) effects.4 Charge asymmetry observables at the LHC
Due to the smallness of A | y | C , achieving a high significance for a measurement of the chargeasymmetry in inclusive t ¯ t production at the LHC is difficult. With more luminosity during the14 TeV run, the ultimate sensitivity to the asymmetry will be limited by systematic uncertain-ties. A dedicated study [24] shows that a significance of 95% may eventually be achieved, ifat least 50% of the systematic errors scale with the luminosity. Given these limitations, it isadvisable and maybe indispensable to consider alternative strategies to measure the top chargeasymmetry at the LHC.An interesting route to be pursued is top-antitop production in association with a hardjet in the final state. In this process, the charge asymmetry is generated already at treelevel by real gluon exchange (see Figure 2). As a first approach, the charge asymmetry canbe defined analogously to A | y | C in inclusive t ¯ t production. In QCD, this observable has beencalculated up to NLO [25, 26]. The resulting asymmetry at the LHC at 7 TeV is extremelysmall, A | y | C = 0 . ± .
09 % [27]. An observation of A | y | C in t ¯ t + j production at the LHC thusseems to struggle with even greater difficulties than inclusive t ¯ t production, with additionalexperimental challenges due to the extra jet.However, the definition of the charge asymmetry can be improved by taking the jet kinema-tics into account [28]. Two observables of a charge asymmetry turn out to be complementaryin final-state kinematics and in their sensitivity to initial parton states: The incline asymmetry probes the charge asymmetry from quark-antiquark annihilation, whereas the energy asymmetry is sensitive to the asymmetry from quark excitation.Figure 4: Kinematics for the charge asymmetryin t ¯ t + j production. Definition of the inclinationangle ϕ between the planes ( q, ¯ q, j ) and ( t, ¯ t, j ).The incline asymmetry is defined in termsof the inclination angle ϕ between the planesspanned by the initial- and final-state quarksand the jet, as illustrated in Figure 4. Thedifferential incline asymmetryd σ ϕA d θ j = d σ (cos ϕ > θ j − d σ (cos ϕ < θ j (5)is largely independent of the jet scattering an-gle θ j and therefore maximally sensitive tothe top and antitop quarks’ angular distri-butions. To make the incline asymmetry aviable observable for proton-proton collisions,the direction of the incoming quark needs tobe determined by focussing on boosted eventswith large rapidities y t ¯ tj of the t ¯ t + j finalstate. The resulting incline asymmetry forthe LHC then reads A ϕC = σ ϕA ( y t ¯ tj > − σ ϕA ( y t ¯ tj < σ S . (6)With appropriate kinematic cuts, the incline asymmetry reaches up to A ϕC = −
4% at the LHCwith 14 TeV collision energy. 5he energy asymmetry is defined through the difference ∆ E = E t − E ¯ t of top and antitopenergies in the parton center-of-mass frame, A EC = σ (∆ E > − σ (∆ E < σ (∆ E >
0) + σ (∆ E < . (7)It probes the charge asymmetry in the partonic quark-gluon channel and is equivalent to theforward-backward asymmetry of the quark-jet in the top-antitop rest frame. The energy asym-metry is well adapted to the LHC environment. It benefits from the high quark-gluon partonluminosity in proton-proton collisions and can be measured without reconstructing the direc-tion of the incident quark. At the 14 TeV LHC, the energy asymmetry reaches values of up to A EC = −
12% in suitable regions of phase space. This new observable thus holds the potential offirst observing the top-quark charge asymmetry at the LHC in t ¯ t + j production. As a caveat,one needs to add that the predictions for A ϕC and A EC quoted here might be significantly changedby NLO corrections. Investigations of these contributions are underway [29].Another alternative measurement of the top asymmetry at the LHC has been suggested forthe LHCb experiment [30]. The good coverage of the forward region by the LHCb detectormay allow to measure top-antitop rapidity differences in the region of large rapidities, wherethe charge asymmetry is maximal. The origin of the asymmetry excess at the Tevatron remains a puzzle. While the measurementof a charge asymmetry at the LHC is valuable on its own, the comparison with the Tevatronasymmetry will always be limited due to the different experimental conditions. To shed lighton the Tevatron anomaly and to gain further insight into various models in connection withthe charge asymmetry, several related observables have been proposed and in some cases beenmeasured.The charge asymmetry in t ¯ t production can be measured via the angular distributions ofleptons from the top decays without reconstructing the top quarks [31, 32]. Two observableshave been probed by experiments, the single-lepton asymmetry A (cid:96)C = σ ( q · η (cid:96) > − σ ( q · η (cid:96) < σ ( q · η (cid:96) >
0) + σ ( q · η (cid:96) < , (8)where q and η (cid:96) are the lepton’s charge and pseudo-rapidity, and the dilepton asymmetry A (cid:96)(cid:96)C = σ (∆ η > − σ (∆ η < σ (∆ η >
0) + σ (∆ η < , (9)in terms of the rapidity difference ∆ η = η (cid:96) + − η (cid:96) − between leptons from the top and antitopdecays. The experimental results for these asymmetries are shown in Figure 1. The relationbetween the lepton asymmetry and the top-antitop asymmetry is model-dependent. Leptonasymmetries thus prove particularly useful in distinguishing between models with chiral top-quark couplings [33].Another proposal considers a measurement the forward-backward asymmetry of bottomquarks at the Tevatron [34]. Above the Z pole, the observable asymmetry is dominated byQCD contributions. Beyond the SM, the bottom charge asymmetry allows to probe the flavorstructure of new-physics contributions to the top asymmetry.6 eferences [1] Courtesy of Viatcheslav Sharyy. For details on the individual measurements, see his contribution on theexperimental status of the top charge asymmetry in these proceedings.[2] J. H. K¨uhn and G. Rodrigo, Phys. Rev. D (1999) 054017 [hep-ph/9807420].[3] M. Czakon, P. Fiedler and A. Mitov, Phys. Rev. Lett. (2013) 252004 [arXiv:1303.6254 [hep-ph]].[4] L. G. Almeida, G. F. Sterman and W. Vogelsang, Phys. Rev. D (2008) 014008 [arXiv:0805.1885 [hep-ph]].[5] N. Kidonakis, Phys. Rev. D (2011) 011504 [arXiv:1105.5167 [hep-ph]].[6] V. Ahrens, A. Ferroglia, M. Neubert, B. D. Pecjak and L. L. Yang, Phys. Rev. D (2011) 074004[arXiv:1106.6051 [hep-ph]].[7] W. Hollik and D. Pagani, Phys. Rev. D (2011) 093003 [arXiv:1107.2606 [hep-ph]].[8] A. V. Manohar and M. Trott, Phys. Lett. B (2012) 313 [arXiv:1201.3926 [hep-ph]].[9] W. Bernreuther and Z. -G. Si, Phys. Rev. D (2012) 034026 [arXiv:1205.6580 [hep-ph]].[10] P. Skands, B. Webber and J. Winter, JHEP (2012) 151 [arXiv:1205.1466 [hep-ph]].[11] S. H¨oche, J. Huang, G. Luisoni, M. Sch¨onherr and J. Winter, Phys. Rev. D (2013) 014040[arXiv:1306.2703 [hep-ph]].[12] G. Marques Tavares and M. Schmaltz, Phys. Rev. D (2011) 054008 [arXiv:1107.0978 [hep-ph]].[13] P. H. Frampton and S. L. Glashow, Phys. Lett. B (1987) 157.[14] M. Bauer, F. Goertz, U. Haisch, T. Pfoh and S. Westhoff, JHEP (2010) 039 [arXiv:1008.0742 [hep-ph]].[15] U. Haisch and S. Westhoff, JHEP (2011) 088 [arXiv:1106.0529 [hep-ph]].[16] M. Gresham, J. Shelton and K. M. Zurek, JHEP (2013) 008 [arXiv:1212.1718 [hep-ph]].[17] S. Chatrchyan et al. [CMS Collaboration], arXiv:1309.2030 [hep-ex].[18] M. I. Gresham, I. -W. Kim, S. Tulin and K. M. Zurek, Phys. Rev. D (2012) 034029 [arXiv:1203.1320[hep-ph]].[19] S. Jung, H. Murayama, A. Pierce and J. D. Wells, Phys. Rev. D (2010) 015004 [arXiv:0907.4112 [hep-ph]].[20] B. Grinstein, A. L. Kagan, M. Trott and J. Zupan, Phys. Rev. Lett. (2011) 012002 [arXiv:1102.3374[hep-ph]].[21] E. Alvarez and E. C. Leskow, Phys. Rev. D (2012) 114034 [arXiv:1209.4354 [hep-ph]].[22] J. Drobnak, A. L. Kagan, J. F. Kamenik, G. Perez and J. Zupan, Phys. Rev. D (2012) 094040[arXiv:1209.4872 [hep-ph]].[23] N. Craig, C. Kilic and M. J. Strassler, Phys. Rev. D (2011) 035012 [arXiv:1103.2127 [hep-ph]].[24] A. Jung, M. Schulze and J. Shelton, arXiv:1309.2889 [hep-ex].[25] S. Dittmaier, P. Uwer and S. Weinzierl, Eur. Phys. J. C (2009) 625 [arXiv:0810.0452 [hep-ph]].[26] K. Melnikov and M. Schulze, Nucl. Phys. B (2010) 129 [arXiv:1004.3284 [hep-ph]].[27] S. Alioli, S. -O. Moch and P. Uwer, JHEP (2012) 137 [arXiv:1110.5251 [hep-ph]].[28] S. Berge and S. Westhoff, JHEP (2013) 179 [arXiv:1305.3272 [hep-ph]].[29] S. Berge, S. Alioli, in preparation.[30] A. L. Kagan, J. F. Kamenik, G. Perez and S. Stone, Phys. Rev. Lett. (2011) 082003 [arXiv:1103.3747[hep-ph]].[31] M. T. Bowen, S. D. Ellis and D. Rainwater, Phys. Rev. D (2006) 014008 [hep-ph/0509267].[32] D. Krohn, T. Liu, J. Shelton and L. -T. Wang, Phys. Rev. D (2011) 074034 [arXiv:1105.3743 [hep-ph]].[33] A. Falkowski, M. L. Mangano, A. Martin, G. Perez and J. Winter, Phys. Rev. D (2013) 034039[arXiv:1212.4003 [hep-ph]].[34] B. Grinstein and C. W. Murphy, Phys. Rev. Lett. (2013) 062003 [arXiv:1302.6995 [hep-ph]].(2013) 062003 [arXiv:1302.6995 [hep-ph]].