A sizeable difference in the differential production cross section of top and
antitop quarks, respectively, is predicted for hadronically produced heavy
quarks. It is of order $\alpha_s$ and arises from the interference between
charge odd and even amplitudes respectively. For the TEVATRON it amounts to
approximately 5-10% in the region where the cross section is large and could
therefore be measured in the next round of experiments. At the LHC the
asymmetry can be studied by selecting appropriately chosen kinematical regions.Comment: LaTeX, 5pp, 5 figures, uses revtex. The complete paper, including
  figures, is also available via anonymous ftp at
  ftp://ttpux2.physik.uni-karlsruhe.de/ , or via www at
  http://www-ttp.physik.uni-karlsruhe.de/cgi-bin/preprints/ Final version as
  published in Phys.Rev.Let

A. D. Martin

F. A. Berends

F. Halzen

G. Marchesini

G. Rodrigo

J. H. Kühn

P. Nason

P. Tipton

R. K. Ellis

T. Sjöstrand

W. Beenakker

English

arXiv

A sizable difference in the differential production cross section of top and antitop quarks, respectively, is predicted for hadronically produced heavy quarks. It is of order αs and arises from the interference between charge odd and even amplitudes, respectively. For the Fermilab Tevatron it amounts to up to 15% for the differential distribution in suitable chosen kinematical regions. The resulting integrated forward-backward asymmetry of 4%¿5% could be measured in the next round of experiments. At the CERN Large Hadron Collider the asymmetry can be studied by selecting appropriately chosen kinematical regions

Kühn, Johann H.

Rodrigo García, Germán Vicente

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:hep-ph/9802268v2  20 Jul 1998Charge asymmetry in hadroproduction of heavy quarksJ.H. Ku¨hn and G. RodrigoInstitut fu¨r Theoretische Teilchenphysik, Universita¨t KarlsruheD-76128 Karlsruhe, Germany(February 12, 1998)A sizeable difference in the differential production cross section of top and antitop quarks, re-spectively, is predicted for hadronically produced heavy quarks. It is of order αs and arises from theinterference between charge odd and even amplitudes respectively. For the TEVATRON it amountsup to 15% for the differential distribution in suitable chosen kinematical regions. The resulting inte-grated forward-backward asymmetry of 4–5% could be measured in the next round of experiments.At the LHC the asymmetry can be studied by selecting appropriately chosen kinematical regions.12.38.Bx, 12.38.Qk, 13.87.Ce, 14.65.HaTop quark production at hadron colliders has become one of the central issues of theoretical [1] and experimental [2]research. The investigation and understanding of the production mechanism is crucial for the determination of the topquark couplings, its mass and the search for new physics involving the top system. A lot of effort has been investedin the prediction of the total cross section and, more recently, of inclusive transverse momentum distributions [1].In this work we will point to a different aspect of the hadronic production process, which can be studied witha fairly modest sample of quarks. Top quarks produced through light quark-antiquark annihilation will exhibit asizeable charge asymmetry – an excess of top versus antitop quarks in specific kinematic regions – induced throughthe interference of the final-state with initial-state radiation (Fig. 1 a, b) and the interference of the box with thelowest-order-diagram (Fig. 1 c, d). The asymmetry is thus of order αs relative to the dominant production process.In suitable chosen kinematical regions it reaches up to 15%, the integrated forward-backward asymmetry amountsto 4–5%. Top quarks are tagged through their decay t → b W+ and can thus be distinguished experimentally fromantitop quarks through the sign of the lepton in the semileptonic mode and eventually also through the b-tag. Asample of hundred to two hundred tagged top quarks should in fact be sufficient for a first indication of the effect.(c) (d)(b)(a)qqQQFIG. 1. Origin of the QCD charge asymmetry in hadroproduction of heavy quarks: interference of final-state (a) withinitial-state (b) gluon bremsstrahlung plus interference of the box (c) with the Born diagram (d).Top production at the TEVATRON is dominated by quark-antiquark annihilation, hence the charge asymmetrywill be reflected not only in the partonic rest frame but also in the center of mass system of proton and antiproton.The situation is more intricate for proton-proton collisions at the LHC, where no preferred direction is at hand in thelaboratory frame. Nevertheless it is also in this case possible to pick kinematical configurations which allow the studyof the charge asymmetry.The charge asymmetry has also been investigated in [3] for a top mass of 45 GeV. There, however, only thecontribution from real gluon emission was considered requiring the introduction of a physical cutoff on the gluonenergy and rapidity to avoid infrared and collinear singularities. Experimentally, however, only inclusive top-antitop1production has been studied to date, and the separation of an additional soft gluon will in general be difficult. Inthis work, we will therefore include virtual corrections and consider inclusive distributions only. We will see below,that the sign of the asymmetry for inclusive production is opposite to the one given for the tt¯g process in [3]. Thecharge asymmetry of heavy flavour production in quark-antiquark annihilation to bottom quarks was also discussedin [4–6] where its contribution to the forward-backward asymmetry in proton-antiproton collisions was shown to bevery small. In addition there is also a slight difference between the distribution of top and antitop quarks in thereaction gq → tt¯q. At the TEVATRON its contributions is bellow 10−4. (This effect should not be confused with thelarge asymmetry in the top quarks’ angular or rapidity distribution in this reaction which is a trivial consequence ofthe asymmetric partonic initial state and vanishes after summing over the incoming parton beams.)In a first step the charge asymmetry will be evaluated at the partonic level for the quark-antiquark induced reaction.The calculation proceeds in analogy to the corresponding QED process [7,8]. The interference terms correspondingto real emission (Fig. 1 a∗b) and virtual radiation (Fig. 1 c∗d) are evaluated separately with an appropriate infraredregulator. Soft radiation up to a cutoff Egcut is then combined with the virtual correction leaving the hard radiationwith Eg > Egcut which can be evaluated numerically. The asymmetric part does not exhibit a light quark masssingularity, whence mq can be set to zero throughout; in other words, no collinear singularities arise. The virtual plussoft radiation on one hand and the real hard radiation on the other contribute with opposite signs, with the formeralways larger than the later which explains the difference in sign between our result and [3].-20-15-10-505101520-1 -0.5 0 0.5 1cos q∧Asymmetry (%)tb Qq q–q∧FIG. 2. Differential charge asymmetry in top quark pair production for fixed partonic center of mass energy√sˆ = 400 GeV(solid), 600 GeV (dashed) and 1 TeV (dotted). We also plot the differential asymmetry for a b-quark with√sˆ = 400 GeV(dashed-dotted).4.555.566.577.588.5500 1000 1500√s∧ (GeV)Asymmetry (%)tbFIG. 3. Integrated charge asymmetry as a function of the partonic center or mass energy for top and bottom quark pairproduction.2The QCD asymmetry is related to the corresponding QED asymmetry through the replacement of αQEDQQ′ bythe factor 12αs(dabc/4)2 = αs · 5/12. Let us define the differential asymmetry throughAˆ(cos θˆ) =Nt(cos θˆ)−Nt¯(cos θˆ)Nt(cos θˆ) +Nt¯(cos θˆ), (1)where θˆ denotes the top quark production angle in the qq¯ restframe and N(cos θˆ) = dσ/dΩ(cos θˆ). Since Nt¯(cos θˆ) =Nt(− cos θˆ) as a consequence of charge conjugation symmetry, Aˆ(cos θˆ) can also be interpreted as a forward-backwardasymmetry of top quarks. In Fig 2, Aˆ(cos θˆ) is displayed for√sˆ = 400 GeV, 600 GeV and 1 TeV for Mt = 175 GeV.For completeness we also display the result for bb¯ production at√sˆ = 400 GeV with Mb = 4.6 GeV. The strongcoupling constant is evaluated at the scale µ =√sˆ/2 from αs(MZ) = 0.118.The integrated charge asymmetry¯ˆA =Nt(cos θˆ ≥ 0)−Nt¯(cos θˆ ≥ 0)Nt(cos θˆ ≥ 0) +Nt¯(cos θˆ ≥ 0), (2)is shown in Fig 3 as a function of√sˆ. With a typical value around 6− 8.5% it should be well accessible in the nextrun of the TEVATRON.-15-10-5051015-1 -0.5 0 0.5 1cos qAsymmetry (%)tp p–q(a)00.511.522.533.544.550 0.5 1 1.5 2|ytop | < ycutAsymmetry (%)(b)FIG. 4. a) Differential charge asymmetry in the proton-antiproton restframe using the MRS96-1 structure function. Weconsider also two different choices of the factorization scale: µ =√sˆ (solid) and µ =√sˆ/2 (dashed). b) Integrated asymmetryfor (anti-)top quarks with rapidities less than ycut.The asymmetry can in principle be studied experimentally in the partonic restframe, as a function of sˆ, by measuringthe invariant mass of the tt¯ system plus an eventually radiated gluon. It is, however, also instructive to study the3asymmetry in the laboratory frame by folding the angular distribution with the structure functions [9]. The differentialasymmetry is displayed in Fig. 4a, where qq¯ and gg initiated processes are included in the denominator. For the totalcharge asymmetry we predictA¯ =Nt(cos θ ≥ 0)−Nt¯(cos θ ≥ 0)Nt(cos θ ≥ 0) +Nt¯(cos θ ≥ 0)= 4.3− 4.6% , (3)where different choices of the structure function and different choices of the factorization scale, µ =√sˆ and µ =√sˆ/2,have been considered.10-610-510-4q–qggqq–pp–ds0 /dx ds∧ (pb GeV-2 )(a)0255075100qq–ggrel (%)(b)10-710-610-510-410-310-2q–qggqq–ppds0 /dx ds∧ (pb GeV-2 )(c)0255075100-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1qq–q–q ggx=x1-x2rel (%)(d)FIG. 5. Differential cross sections (Fig. a, c) and relative amount (Fig. b, d) of quark-antiquark, antiquark-quark andgluon-gluon initiated processes as functions of x1 − x2 = 2P3(tt¯g)/√s in lowest order, for√s = 1.8 TeV in proton-antiproton(Fig. a, b) and√s = 14 TeV in proton-proton (Fig. c, d) collisions with√sˆ = 400 GeV in both cases.4In principle one might expect that cuts on the top quark or its decay products at large rapidities could affect theasymmetry. In Fig 4b we thus present the asymmetry for the restricted range | ytop |< ycut as a function of ycut.It approaches its maximal value already for ycut = 1, indicating that also cuts on the top decay products W andb jets with rapidities, say, larger than 2 will not lead to a significant reduction of the asymmetry. We would alsolike to mention that event generators which do not include the full NLO matrix elements [10,11] cannot predict theasymmetry.Top-antitop production in proton-proton collisions at the LHC is, as a consequence of charge conjugation symmetry,charge symmetric if the laboratory frame is chosen as the reference system. However, by selecting the invariant massof the tt¯(+g) system and its longitudinal momentum appropriately, one can easily constrain the parton momenta suchthat a preferred direction is generated for quark-antiquark reactions. This last point is illustrated in Fig 5 where wepresent the relative amount of quark-antiquark, antiquark-quark and gluon-gluon initiated processes as functions ofx1 − x2 = 2P3(tt¯g)/√s in lowest order, for√s = 14 TeV and√sˆ = 400 GeV as characteristical example. A detailedstudy of this situation will be presented elsewhere [12].The box diagram, Fig. 1 c, can also give rise to tt¯ in a colour singlet configuration, which in turn interferes withtt¯ production through the photon or Z. A similar consideration applies to interference between initial and final stateradiation. The resulting asymmetry is obtained from the QCD asymmetry through the following replacementαs2(dabc4)2→ αQEDQtQq + (1−83s2W )(2Iq − 4Qqs2W )16s2W c2W11− M2Zsˆ (4)which amounts to an increase of the asymmetry by typically a factor 1.04 and is thus smaller than uncalculated higherorder corrections.To summarize: the charge asymmetry can be used as an important tool to investigate the production dynamics.For the TEVATRON it amounts to roughly 4− 5% and can therefore be studied with a sample of several hundred tt¯pairs expected for the next run. The asymmetry can also be studied at the LHC if one selects appropriate kinematicconfigurations.We would like to acknowledge useful discussions with R.K. Ellis, T. Sjo¨strand and M. Seymour. Work supportedby BMBF under Contract 057KA92P and DFG under Contract Ku 502/8-1.[1] S. Catani, “QCD at high-energies,” hep-ph/9712442.[2] P. Tipton, “Experimental top quark physics,” Proceedings of the ICHEP 96, Warsaw, Poland, pg.123 (1996).[3] F. Halzen, P. Hoyer, and C. S. Kim Phys. Lett. 195B (1987) 74.[4] R. K. Ellis in Strong Interactions and Gauge Theories, ed. J. Tran Thanh Van (Editions Frontie`re, Gif-sur-Yvette)pg.339 (1986).[5] P. Nason, S. Dawson, and R. K. Ellis Nucl. Phys. B327 (1989) 49.[6] W. Beenakker, W. L. van Neerven, R. Meng, G. A. Schuler, and J. Smith Nucl. Phys. B351 (1991) 507.[7] F. A. Berends, K. J. F. Gaemers, and R. Gastmans Nucl. Phys. B63 (1973) 381.[8] F. A. Berends, R. Kleiss, S. Jadach, and Z. Was Acta Phys. Polon. B14 (1983) 413.[9] A. D. Martin, R. G. Roberts, and W. J. Stirling Phys. Lett. B387 (1996) 419, hep-ph/9606345.[10] G. Marchesini et. al. Comput. Phys. Commun. 67 (1992) 465.[11] T. Sjo¨strand Comput. Phys. Commun. 82 (1994) 74.[12] J. H. Ku¨hn and R. Rodrigo In preparation.5

Charge asymmetry in hadroproduction of heavy quarks

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Charge Asymmetry in Hadroproduction of Heavy Quarks

Charge asymmetry in hadroproduction of heavy quarks

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