Top interactions beyond the Standard Model can be conveniently described in
the framework of gauge-invariant effective operators. We briefly review the
general form of the fermion-fermion-gauge boson and fermion-fermion-Higgs
interactions arising from dimension-6 operators, focusing on the top quark. We
discuss in detail an expansion in powers of 1/Lambda^2, where Lambda is the new
physics scale, to consistently calculate observables in terms of top anomalous
couplings.Comment: LaTeX 4 pages, 2 PS figures. Presented at ICHEP 2010, Paris, France,
  July 22-28, 2010, to appear in the proceeding

Aguilar-Saavedra, J. A.

English

arXiv

35th International Conference of High Energy Physics. July 22-28, 2010, Paris (France). PoS(ICHEP 2010)378.Top interactions beyond the Standard Model can be conveniently described in the framework of
gauge-invariant effective operators. We briefly review the general form of the fermion-fermiongauge
boson and fermion-fermion-Higgs interactions arising from dimension-6 operators, focusing
on the top quark. We discuss in detail an expansion in powers of 1/L2, where L is the new
physics scale, to consistently calculate observables in terms of top anomalous couplings.†This work has been partially supported by a MICINN Ramón y Cajal contract and by projects FPA2006-05294
(MICINN), FQM 101 and FQM 437 (Junta de Andalucía), CERN/FP/83588/2008 (FCT), and MRTN-CT-2006-035505
(European Union)

Aguilar-Saavedra, Juan Antonio

Institutional Repository of the University of Granada

Effective operators in top physics

Aguilar Saavedra, Juan Antonio

Repositorio Institucional Universidad de Granada

PoS(ICHEP 2010)378Effective operators in top physicsJuan Antonio Aguilar-Saavedra∗†University of GranadaE-mail: jaas@ugr.esTop interactions beyond the Standard Model can be conveniently described in the framework ofgauge-invariant effective operators. We briefly review thegeneral form of the fermion-fermion-gauge boson and fermion-fermion-Higgs interactions arising from dimension-6 operators, focus-ing on the top quark. We discuss in detail an expansion in powers of 1/Λ2, whereΛ is the newphysics scale, to consistently calculate observables in terms of top anomalous couplings.35th International Conference of High Energy PhysicsJuly 22-28, 2010Paris, France∗Speaker.†This work has been partially supported by a MICINN Ramón y Cajal contract and by projects FPA2006-05294(MICINN), FQM 101 and FQM 437 (Junta de Andalucía), CERN/FP/83588/2008 (FCT), and MRTN-CT-2006-035505(European Union).c© Copyright owned by the author(s) under the terms of the CreativCommons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(ICHEP 2010)378Effective operators in top physics Juan Antonio Aguilar-Saavedra1. IntroductionOne of the main motivations for detailed studies of the top quark properties is to search forindirect effects of new physics not directly observable. Heavy physics above the electroweak scalecan be parameterised using an effective LagrangianLeff = ∑ CxΛ2Ox + . . . , (1.1)whereOx are dimension-6 operators invariant under the Standard Model (SM) gauge symmetry,Λ the new physics scale and the dots stand for dimension-8 and higher-order operators, usuallyignored. Dimension-6 operators were classified in [1] and an operator bsis was given, whichcan be used to parameterise any new physics contribution up to higher orders. Later, it has beenfound [2, 3] that some of these operators are actually redundant and can be dropped from the list.This simplification is very useful for phenomenology, because it implies that (i) the most generalfermion-fermion-gauge boson interactions arising from dimension-6 operators contains at mostγµandσ µνqν terms, whereq is the boson momentum; (ii) the most general fermion-fermion-Higgsinteractions only contain scalar and pseudo-scalar terms. In the particularcase of the top quark wehave, for example, the most generalWtbvertexLWtb = −g√2b̄γµ (VLPL +VRPR) t W−µ−g√2b̄iσ µνqνMW(gLPL +gRPR) t W−µ +h.c. , (1.2)whereVL = Vtb +C(3,3+3)∗φqv2Λ2 , VR =12C33∗φφv2Λ2 , gL =√2C33∗dWv2Λ2 , gR =√2C33uWv2Λ2 , being the gauge-invariant operatorsO(3,3+3)φq =i2[φ†(τ I Dµ −←−D µτ I )φ](q̄L3γµτ I qL3) , O33φφ = i(φ̃†Dµφ)(t̄RγµbR) ,O33dW = (q̄L3σµντ I bR)φ WIµν , O33uW = (q̄L3σ µντ I tR)φ̃ WIµν , (1.3)in standard notation. Were it not for this simplification, theWtbvertex would contain 6 additionalLorentz structures, with 6 more parameters arising from 5 (redundant) operat rs. Additional detailscan be found in Refs. [3].One may always ask about precision electroweak data and constraints onthese operators be-cause, being the top quark the SU(2)L partner of theb quark, gauge invariant operators containingthetL field automatically involvebL. For example, theZbLbL vertex, well measured at LEP, receivescorrections from effective operatorsLZbLbL =−g2cWb̄Lγµ[−1+(C(3,3+3)φq +C(1,3+3)φq) v2Λ2+23s2W]bLZµ , (1.4)whereO(3,3+3)φq is the operator producing a deviationδVL≡VL−Vtb in theWtbvertex, andO(1,3+3)φq =i2 (φ†←→Dµφ)(q̄L3γµqL3). Does this imply thatC(3,3+3)φq is small, because fine-tuning withC(1,3+3)φq (soas to keep agreement with LEP data) is unnatural? The answer is no. For exampl , mixing with aheavy charge 2/3 isosingletT, when integrated out, precisely givesC(3,3+3)φq =−C(1,3+3)φq [4]. And2PoS(ICHEP 2010)378Effective operators in top physics Juan Antonio Aguilar-Saavedrait is clear that itmustbe so, because the mixing ofT with the SM charge 2/3 mass eigenstates doesnot affect the down sector, where the GIM mechanism is still at work. When written in the lan-guage of effective operators, this is just the relationC(3,3+3)φq =−C(1,3+3)φq . Detailed analyses of theeffects onB physics ofWtbanomalous couplings imply thatVR andgL (that is,C33φφ andC33dW) arevery constrained if no other new physics is present [5]. But discarding operators merely becausethey contain terms with twob fields is, as we can see, too naive and restrictive.2. The leading order approximationThe anomalous couplingsδVL, VR, gL, gR in Eq. (1.2) are proportional to the scale ratiov2/Λ2,and thus some expansion in powers of 1/Λ2 seems adequate. In general, the interference terms be-tween SM amplitudes and dimension-6 operators are proportional to 1/Λ2, and the pure dimension-6 operator corrections to 1/Λ4. One might then naively consider keeping only the linear 1/Λ2terms, which would give the “leading” corrections, and drop the quadratic1/Λ4 ones. But this“1/Λ2” approximation is far too restrictive, and does not allow to explore many newphysics ef-fects. Indeed, operators which do not interfere with the SM are the onesproducing genuine newphysics effects, beyond corrections to SM processes. One well-known example is given by topflavour-changing neutral processes, extremely suppressed in the SM, which are of order 1/Λ4.These processes, absent in the SM, could be visible for this reason even if suppressed by 1/Λ4.For theWtb vertex, in themb = 0 limit (we will consider a non-zerob mass later) only theoperators generatinḡbLtL and b̄LtR terms interfere with the SM amplitude. Then, the 1/Λ2 ap-proximation leads us to keep only the corrections proportional toδVL andgR (see Table 1). Thisis unfortunate, because we lose the possibility of exploringb chirality-breaking effects. It is well1/Λ2 1/Λ4b̄LγµtL δVL (δVL)2 + dim-8 b̄LtLb̄RγµtR – (VR)2b̄Rσ µνtL – (gL)2b̄Lσ µνtR gR (gR)2 + dim-8 b̄LtRTable 1: Corrections to observables fromWtbanomalous couplings, formb = 0.known that in SM top decays the fractionF+ of W bosons produced with helicity+1 is zero in themb = 0 limit. The reason is that for the SMWtbvertex only left-handedb quarks are produced inthe decay, and then angular momentum conservation forbidsW bosons with helicity+1. (Includinga b quark massmb = 4.8 GeV the fraction of positive helicityW bosons isF+ = 0.00359.) How-ever, the anomalous couplingsδVL, gR still involve left-handedb quarks (otherwise they would notinterfere with the SM amplitude) and their presence does not affectF+. This can be seen in Fig. 1,taken from Ref. [6]. The (quadratic) corrections from anomalous couplingsVR, gL lead to dramaticdepartures from the SM prediction while a non-zerogR makes no difference. The sensitivity tothese deviations in top decays at LHC is excellent [7] precisely becauseF+ is tiny within the SM,and in the 1/Λ2 approximation such effects are lost.Let us then discuss how the 1/Λ2 approximation may be refined. As we see from Table 1,for b̄LtL and b̄LtR terms the linear corrections are of order 1/Λ2 while quadratic ones, as well as3PoS(ICHEP 2010)378Effective operators in top physics Juan Antonio Aguilar-Saavedra-0.2 -0.1 0 0.1 0.2coupling-0.0100.010.020.030.040.050.060.07F+Re gRRe gLRe VRSMdependence on gR-0.2 -0.1 0 0.1 0.2coupling-0.0100.010.020.030.040.050.060.07F+Im gRIm gLIm VRSMdependence on gRFigure 1: Dependence of the helicity fractionF+ onWtbanomalous couplings, forVL = 1.those from dimension-8 operators withb̄LtL, b̄LtR fields, are of order 1/Λ4. For b̄RtR, b̄RtL fieldsthe leading corrections are the quadratic 1/Λ4 ones(VR)2, (gL)2, while dimension-8 operatorswould give non-interfering corrections of order 1/Λ8. It is then consistent to keep for eacht,bchirality the lowest-order terms. (Sub-leading(δVL)2, (gR)2 terms cause no harm and may be keptor discarded at will.) This is what we denote as the “leading order approximation”. When thebquark mass is included, interferences ofb̄RtR andb̄RtL operators are suppressed by(mb/mt)1/Λ2,and their effect is of the same order as the quadratic terms [7]. Complete calculations of severaltop decay observables, keeping quadratic terms as well as theb quark mass, have been performedin Refs. [6, 7], and for single top cross sections in Ref. [8].References[1] W. Buchmuller and D. Wyler,Effective Lagrangian analysis of new interactions and flavorconservation, Nucl. Phys. B268 (1986) 621.[2] B. Grzadkowski, Z. Hioki, K. Ohkuma and J. Wudka,Probing anomalous top-quark couplingsinduced by dim.6 operators at photon colliders, Nucl. Phys. B689 (2004) 108[3] J. A. Aguilar-Saavedra,A minimal set of top anomalous couplings, Nucl. Phys. B812 (2009) 181;Aminimal set of top-Higgs anomalous couplings, Nucl. Phys. B821 (2009) 215.[4] F. del Aguila, M. Perez-Victoria and J. Santiago,Effective description of quark mixing, Phys. Lett. B492 (2000) 98;Observable contributions of new exotic quarks to quark mixing, JHEP0009 (2000)011.[5] B. Grzadkowski and M. Misiak,Anomalous Wtb coupling effects in the weak radiative B-mesondecay, Phys. Rev. D78 (2008) 077501.[6] J. A. Aguilar-Saavedra and J. Bernabeu,W polarisation beyond helicity fractions in top quark decays,Nucl. Phys. B840 (2010) 349.[7] J. A. Aguilar-Saavedra, J. Carvalho, N. F. Castro, A. Onofre and F. Veloso,Probing anomalous Wtbcouplings in top pair decays, Eur. Phys. J. C50 (2007) 519;ATLAS sensitivity to Wtb anomalouscouplings in top quark decays, Eur. Phys. J. C53 (2008) 689.[8] J. A. Aguilar-Saavedra,Single top quark production at LHC with anomalous Wtb couplings, Nucl.Phys. B804 (2008) 160.4

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