We study the top forward-backward asymmetry (FBA $\equiv A_{\rm FB}$)
reported by CDF and D0 Collaborations in the effective lagrangian approach.
Using dimension-6 effective largrangians for $q \bar{q} \rightarrow t \bar{t}$,
we study the $t\bar{t}$ production cross section and the $A_{\rm FB}$, and a
few observables: the FB spin-spin correlation that is strongly correlated with
the $A_{\rm FB}$, and longitudinal top polarization as a new probe of chiral
structures for possible new physics scenarios.Comment: To appear in Top 2011 Proceeding (Sant Feliu de Guixols, Spain

Ko, P.

English

arXiv

We study the top forward-backward asymmetry (FBA ≡ AFB)

reported by CDF and D0 Collaborations in the effective Lagrangian approach. Using dimension-6 effective Largrangians for q¯q → t¯t, we study the t¯t production cross section and the AFB, and a few observables: the FB spin-spin correlation that is strongly correlated with the AFB, and longitudinal top polarization as a new probe of chiral structures for possible new physics scenarios

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2012-11218-5Colloquia: TOP2011IL NUOVO CIMENTO Vol. 35 C, N. 3 Maggio-Giugno 2012Effective field theory for top physicsP. KoSchool of Physics, KIAS - Seoul 130-722, Korearicevuto l’ 1 Marzo 2012pubblicato online il 28 Maggio 2012Summary. — We study the top forward-backward asymmetry (FBA ≡ AFB)reported by CDF and D0 Collaborations in the effective Lagrangian approach. Usingdimension-6 effective Largrangians for qq¯ → tt¯, we study the tt¯ production crosssection and the AFB, and a few observables: the FB spin-spin correlation that isstrongly correlated with the AFB, and longitudinal top polarization as a new probeof chiral structures for possible new physics scenarios.PACS 14.65.Ha – Top quarks.PACS 12.60.-i – Models beyond the standard model.1. – IntroductionTop quark is the heaviest particle observed so far, and could be sensitive to theunderlying physics of electroweak symmetry breaking. So far there is no clear deviationfrom the SM predictions, possibly except for the AFB observed at the Tevatron(1) AFB(CDF) = (0.158± 0.074), AFB(D0) = (0.196± 0.065),compared with the SM prediction AFB ∼ 0.078 [1]. This ∼ 1–2σ deviation and themass-dependent AFB might be due to some new physics. On the other hand, search fora new resonance decaying into tt¯ pair has been carried out at the Tevatron. As of now,there is no clear signal for such a new resonance. And the tt¯ production cross sectionis well described by the SM. Therefore, in this paper, I will consider the case where anew physics scale relevant to AFB is large enough so that production of a new particle isbeyond the reach of the Tevatron [2-4]. Then it is adequate to integrate out the heavyfields, and use the resulting effective Lagrangian in order to study new physics effectson σtt¯ and AFB in a model independent way. At the Tevatron, the tt¯ production isdominated by qq¯ → tt¯, and it would be sufficient to consider dimension-6 four-quarkoperators (the so-called contact interaction terms) to describe the new physics effects onthe tt¯ production at the Tevatron. Note that a similar approach was adopted for thedijet production to constrain the composite scale of light quarks for long time. Beforeproceeding to the main topics of this paper, let us recall that similar approaches werec© Societa` Italiana di Fisica 4950 P. KOtaken in refs. [5-7]. Also, there are effective field theory approaches for the same-sign toppair production [8].2. – Effective field theory for top physics and new physical observablesOur starting point is the effective Lagrangian with dimension-6 operators relevant tothe tt¯ production at the Tevatron [2](2) L6 = g2sΛ2∑A,B[CAB1q (q¯AγμqA)(t¯BγμtB) + CAB8q (q¯ATaγμqA)(t¯BT aγμtB)],where T a = λa/2, {A,B} = {L,R}, and L,R ≡ (1 ∓ γ5)/2 with q = (u, d)T , (c, s)T .Using this effective Lagrangian, we calculate the cross section up to O(1/Λ2), keepingonly the interference term between the SM and new physics contributions.We make one comment: the chromomagnetic operators of dim-5 would be generatedat one loop level, whereas the qq¯ → tt¯ operators can be induced at tree level. Thereforethe chromomagnetic operators will be suppressed further by gs/(4π)2 × (loop function),compared with the dim-6 operators we consider in this paper. Therefore we will ig-nore chromomagnetic operators in this paper. (See refs. [5-7] for the discussion on thisoperator.)Neglecting the transverse polarizations, the squared amplitude summed (averaged)over the final (initial) colors is given by(3) |M|2 = g4ssˆ2{D0 +D1(PL + P¯L) +D2(PL − P¯L) +D3PLP¯L},where PL and P¯L are the longitudinal polarizations of t and t¯ [3].The unpolarized coefficient D0 leads to the total cross section σtt¯ and the forward-backward asymmetry AFB. On the other hand, the coefficient D3 gives the spin-spincorrelations C and CFB considered and suggested beforeD0  49{2m2t sˆ[1 +sˆ2Λ2(C1 + C2)]s2θˆ(4)+sˆ22[(1 +sˆ2Λ2(C1 + C2))(1 + c2θˆ) + βˆt(sˆΛ2(C1 − C2))cθˆ]},where sˆ = (p1 + p2)2, βˆ2t = 1 − 4m2t/sˆ, and sθˆ ≡ sin θˆ and cθˆ ≡ cos θˆ, with θˆ beingthe polar angle between the incoming quark and the outgoing top quark in the tt¯ restframe. And the couplings are defined as: C1 ≡ CLL8q + CRR8q and C2 ≡ CLR8q + CRL8q .Since we have kept only up to the interference terms, there are no contributions fromthe color-singlet operators with coupling CAB1q . The term linear in cos θˆ could generatethe forward-backward asymmetry which is proportional to ΔC ≡ (C1 − C2). Note thatboth light quark and top quark should have chiral couplings to the new physics in orderto generate AFB at the tree level (namely ΔC = 0). This parity violation, if large,could be observed in the nonzero (anti)top spin polarization [3]. The allowed region inthe (C1, C2) plane that is consistent with the Tevatron data at the 1σ level is around0.15  C1  0.97 and −0.67  C2  −0.15 for Λ = 1TeV. The positive C1 and thenegative C2 are preferred at the 1σ level [2, 3].EFFECTIVE FIELD THEORY FOR TOP PHYSICS 51-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 300  400  500  600  700  800AFBMtt [GeV]C1LC1USM+INTFR. TOTAL     CDF data    -0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 300  400  500  600  700  800AFBMtt [GeV]C2LC2USM+INTFR. TOTAL     CDF data    Fig. 1. – (Color online) Top FB asymmetry as functions of Mtt¯. In the left frames we are takingC1 in the range between C1L = 0.15 and C1U = 0.97 with C2 = 0. In the right frames, wevary C2 in the range between C2L = −0.15 and C2U = −0.67 with C1 = 0. In each frame, thetwo bands are for AFB in the lower and higher Mtt¯ bins varying C1 (left) and C2 (right) in theranges delimited by C1L,1U and C2L,2U , respectively, and the dots for the CDF data with errors.In the solid (red) lines, we include only the SM contribution and the one from the interferencebeween the SM and NP amplitudes while the effects of (NP )2 term have been added in thedotted (blue) lines.Another interesting observable which is sensitive to the chiral structure of new physicsaffecting qq¯ → tt¯ is the top quark spin-spin correlation [2](5) C =σ(tLt¯L + tRt¯R)− σ(tLt¯R + tRt¯L)σ(tLt¯L + tRt¯R) + σ(tLt¯R + tRt¯L).Since new physics must have chiral couplings both to light quarks and top quark, the spin-spin correlation defined above will be affected. In ref. [2], we proposed a new spin-spin FBasymmetry CFB defined as CFB ≡ C(cos θ ≥ 0)−C(cos θ ≤ 0), where C(cos θ ≥ 0(≤ 0))implies that the cross sections in the numerator of eq. (5) are obtained for the forward(backward) region: cos θ ≥ 0(≤ 0). In ref. [2], it was noticed that there is a clear strongcorrelation between CFB and AFB . This correlation must be observed in the futuremeasurements if the AFB anomaly is real and a new particle is too heavy to be producedat the Tevatron.One can also make predictions of the AFB as functions of Mtt¯ [9], which are shown infig. 1. Our results based on the effective Lagrangian approach are significantly smallerthan the CDF and D0 data. If this deviation is confirmed in the future analysis, it wouldimply that the effective Lagrangian approach is not adequate to describe the top FBasymmetry at the Tevatron, and one has to consider various explicit models one by one,and investigate which model describes all the data in a consistent way.The other P -violating coefficient D2 could be observable at the Tevatron, revealinggenuine features of new physics responsible for AFB. Explicitly, we have obtained(6) D2  sˆ9Λ2[(C ′1 + C′2)βˆt(1 + c2θˆ) + (C ′1 − C ′2)(5− 3βˆ2t )cθˆ],52 P. KOwith C ′1 ≡ CRR8q − CLL8q , C ′2 ≡ CLR8q − CRL8q . Therefore D2 will provide additional infor-mation on the chiral structure of new physics in qq¯ → tt¯. For definiteness, we considerthe two new observablesD ≡ σ(tRt¯L)− σ(tLt¯R)σ(tRt¯R) + σ(tLt¯L) + σ(tLt¯R) + σ(tRt¯L),(7a)DFB ≡ D(cos θˆ ≥ 0)−D(cos θˆ ≤ 0),(7b)which involve the sum and difference of the coefficients C ′1 and C′2, respectively. Wefound that |D| and |DFB| could be as large as 0.1 in the region |C ′1,2 (1TeV/Λ)2|  1 [3].Note that there are no experimental constraints on the D and DFB observables yet.3. – Possible underlying physics?Now we study specific new physics that could generate the relevant dim-6 operatorswith corresponding Wilson coefficients (please refer to refs. [2,3] for the definitions of theinteraction Lagrangians). It is impossible to exhaust all the possibilities, and we considerthe following interactions of quarks with spin-1 flavor-conserving (FC) color-octet V a8Avectors, spin-1 flavor-violating (FV) color-singlet V˜1A and color-octet V˜ a8A vectors, andspin-0 FV color-singlet S˜1 and color-octet S˜a8A scalars (A = L,R). After integrating outthe heavy vector and scalar fields, we obtain the Wilson coefficients CAB8q with A,B =L,R, explicit expressions of which could be found in refs. [2, 3].Table I. – New particle exchanges and the signs of induced couplings CAB (A,B = R,L),C1 − C2, C′1 + C′2, and C′1 − C′2.Resonance CRR CLL CLR CRL C1 − C2 C′1 + C′2 C′1 − C′2 AFBV˜1R − 0 0 0 − − − ×V˜1L 0 − 0 0 − + + ×V˜8R + 0 0 0 + + +√V˜8L 0 + 0 0 + − − √S˜1R 0 0 0 − + + − √S˜1L 0 0 − 0 + − + √S˜8R 0 0 0 + − − + ×S˜8L 0 0 + 0 − + − ×Sα2 − 0 0 0 − − − ×Sαβ13 + 0 0 0 + + +√V8R ± 0 0 0 ± ± ± √(+)or×(−)V8L 0 ± 0 0 ± ∓ ∓ √(+)or×(−)V8R, V8L indef. indef. indef. indef. indef. indef. indef. indef.EFFECTIVE FIELD THEORY FOR TOP PHYSICS 53-0.1-0.075-0.05-0.025 0 0.025 0.05 0.075 0.1-0.1 -0.075-0.05-0.025  0  0.025 0.05 0.075  0.1DFBD~V8R, V8R, Sαβ13~S1R~V8L, V8L~S1L-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5-0.5 -0.4 -0.3 -0.2 -0.1  0  0.1  0.2  0.3  0.4  0.5DFBDg L8q g L8t  (Λ 2 / mV 2 )= 2g L8q g L8t  (Λ 2 / mV 2 )= 1g L8q g L8t  (Λ 2 / mV 2 )=-1g L8q g L8t  (Λ 2 / mV 2 )=-2Fig. 2. – (Color online) (a) The predictions for D and DFB of the models under consideration,being consistent with the σtt¯ and AFB measurements at the 1-σ level. We assume that onlyone resonance exists or dominates. (b) The predictions for D and DFB, being consistent withthe σtt¯ and AFB measurements at the 1-σ level, for several values of gL8qgL8t (1TeV/mV 8)2 =+2 (magenta), +1 (green), −1 (blue), and −1 (sky blue), from the upper-right corner to thelower-left one. The general model with flavor-conserving color-octet V8R and V8L vectors isconsidered.Let us first consider the FV cases. Among the FV interactions with vector or scalarbosons, V˜8R,8L, S˜1R,1L, and Sαβ13 can give the correct sign for (C1 − C2) ∝ AFB [2]. Butone cannot discriminate one model from another only with the AFB measurement. Fromtable I, we observe that each of the four cases with V˜8R, V˜8L, S˜1R, and S˜1L gives adifferent sign combination of C ′1 + C′2 and C′1 − C ′2. In fig. 2, we show the prediction ofeach model for D and DFB varying the model parameters which are consistent with thecurrent measurements of σtt¯ and AFB at the 1-σ level. We observe that D and DFB takethe same (+,+) and (−,−) signs for V˜8R and V˜8L, respectively, while they take different(+,−) and (−,+) signs for S˜1L and S˜1R, respectively. The color-sextet scalar Sαβ13 givesthe same (+,+) sign as the V˜8R case. Therefore, a simple sign measurement of D andDFB can endow us with the model-discriminating power.Unlike the FV cases, the FC color-octet vectors can always accommodate the positivesign of (C1 − C2). For the case of V8R (V8L), the couplings gR8q (gL8q) and gR8t (gL8t)must have different signs to accommodate the positive AFB. In fig. 2, we also show thepredictions of the model with V8R or V8L vector for D and DFB.4. – Beyond the effective field theory: the case of light Z ′Before closing this paper, let me make a few comments on the new physics scenarioswith spin-1 objects, such as axigluon, Z ′, W ′ or SU(3)uR flavor gauge bosons. Wheneverthese new spin-1 particles have chiral couplings to the SM quarks, it is important toextend the SM Higgs sector too, in order that we can write (renormalizable) Yukawacouplings for all the SM fermions. One has to introduce new Higgs doublets that arecharged under new gauge group, and they can affect the top FBA and the same-sign toppair production rate in general. Also the new Higgs doublets can contribute to the Wjj54 P. KOsignals. These points were first noticed in refs. [10,11], and was presented by ChaehyunYu in the poster session [12] at this workshop. It is important to make sure that allthe minimal ingredients for the minimal consistent model are included before one startsphenomenological analysis.5. – ConclusionsIn this paper, we considered the tt¯ productions at the Tevatron using dimension-6contact interactions relevant to qq¯ → tt¯, mainly concentrating on the top FBA, (FB) spin-spin correlation, and the P -odd longitudinal (anti)top polarization of PL and P¯L. TheP -odd top-quark longitudinal polarization observables Both PL and P¯L can be nonzeroin many new physics scenarios for the top FBA, in sharp contrast to the case of pureQCD, and can give another important clue for the chiral structure of new physics, whichis completely independent of σtt¯ or AFB. Our results in table I and fig. 2 encode thepredictions for the P -odd observables corresponding to the polarization difference (PL−P¯L) in various new physics scenarios in a compact and an effective way, when those newparticles are too heavy to be produced at the Tevatron but still affect AFB. If these newparticles could be produced directly at the Tevatron or at the LHC, we cannot use theeffective Lagrangian any more. We have to study specific models case by case includingthe new particles explicitly, and anticipate rich phenomenology at colliders as well as atlow energy [13].∗ ∗ ∗I am grateful to Dong Won Jung, Jae Sik Lee, Yuji Omura and ChaehyunYu for enjoyable collaborations on the subjects presented in this paper.REFERENCES[1] Antunano O., Kuhn J. H. and Rodrigo G., Phys. Rev. D, 77 (2008) 014003.[2] Jung D.-W., Ko P., Lee J. S. and Nam S.-h., Phys. Lett. B, 691 (2010) 238.[3] Jung D.-W., Ko P. and Lee J. S., Phys. Lett. B, 701 (2011) 248.[4] Jung D.-W., Ko P. and Lee J. S., Phys. Rev. D, 84 (2011) 055027.[5] Aguila-Saavedra J. A., Nucl. Phys. B, 843 (2011) 638; 851 (2011) 443(R).[6] Zhang C. and Willenbrock S., Phys. Rev. D, 83 (2011) 034006.[7] Degrande C., Gerard J. M., Grojean C., Maltoni F. and Servant G., JHEP, 1103(2011) 125.[8] Degrande C., Gerard J. M., Grojean C., Maltoni F. and Servant G., Phys. Lett.B, 703 (2011) 306.[9] Jung D.-W., Ko P. and Lee J. S., preprint arXiv:1111.3180 [hep-ph].[10] Ko P., Omura Y. and Yu C., preprint arXiv:1108.0350 [hep-ph].[11] Ko P., Omura Y. and Yu C., preprint arXiv:1108.4005 [hep-ph].[12] Ko P., Omura Y. and Yu C., these proceedings, preprint arXiv:1201.1352 [hep-ph].[13] Ko P. et al., in preparation.

Effective field theory for top physics

http://eprints.bice.rm.cnr.it/17822/1/ncc10234.pdf

Effective field theory for top physics

Abstract

Similar works

Full text

Available Versions

Scientific Open-access Literature Archive and Repository