Central-edge asymmetry as a probe of Higgs-top couplings in tt¯h production at LHC Jinmian Li,1,∗ Zong-guo Si,2,† Lei Wu,3,4,‡ and Jason Yue5,§ 1School of Physics, KIAS, Seoul 02455, Korea 2School of Physics, Shandong University, Jinan, Shandong 250100, China 3ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, NSW 2006, Australia 4Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210023, China 5Department of Physics, National Taiwan Normal University, Taipei 116, Taiwan The Higgs-top coupling plays a central role in the hierarchy problem and the vacuum stability of the Standard Model (SM). We study the CP violating Higgs-top couplings in dileptonic channel of tt¯h(→ b¯b) production at the LHC. We find that the CP violating interactions can affect the distributionoftherapiditydifferenceoftwoleptonsfromthetopdecays(∆y )asaresultofthe (cid:96)+(cid:96)− presenceofthetopquarkchargeasymmetricterm. Suchanobservableisframe-independentandhas 7 agooddiscriminationpoweroftheCPviolatingcouplingseveninboostedregime. Then,wedefine 1 a central-edge asymmetry A to numerically distinguish the CP violating Higgs-top couplings, 0 CE 2 which can reach -40.3%, -26.6% and -9.5% for CP phase ξ =0,π/4,π/2, respectively. Besides, we n perform the binned-χ2 analysis of ∆y(cid:96)+(cid:96)− distribution and find that the scalar and pseudo-scalar interactions can be distinguished at 95% C.L. level at 14 TeV HL-LHC. a J 1 I. INTRODUCTION ℓ ] h After the discovery of the Higgs boson at the LHC t ν p [1, 2], precision study of its properties becomes one of b - p the most important tasks in theory and experiment. So t H b e far, the measured Higgs gauge couplings are compati- h ble with the SM predictions at 1-2σ level. However, the b [ t Higgs fermion couplings remain obscure. Among them, 1 the Higgs-top coupling is of particular interest [3]. b t ℓ v In the SM, the top quark has the strongest coupling 4 with the Higgs boson. As such, the Higgs-top coupling ν 2 plays an special role in the hierarchy problem [4] and 2 the vacuum stability of the SM [5, 6]. Many models for FIG.1. RepresentativeFeynmandiagramofdileptonicchan- 0 physics beyond the SM related with these two problems nel of tt¯H production with H →b¯b at the LHC. 0 predict a modified Higgs-top coupling. So, the precise . 1 measurementsofHiggs-topcouplingcouldgiveaninsight 0 onthepatternoffermionmassgenerationandtheenergy colored particles, e.g. scalar tops or composite top part- 7 1 scale of new physics above the electroweak scale. ners. The latter is directly determined by the Higgs-top : ThemostgeneralLagrangianofthett¯hinteractioncan coupling, and thus is golden mode for this measurement v be parameterised as follows: [10–22]. ThehighorderQCDandEWcorrectionstothe i X m tt¯h production have recently been studied [23–28]. With t r L⊃− v t(cosξ+iγ5sinξ)th, (1) the data set of the 7 and 8 TeV runs of the LHC, the a signal strengths in the tt¯h production channel have been where mt is the top quark mass and v is the vacuum ex- measured by both ATLAS [29, 30] and CMS [31] in var- pectation value of the Higgs field. In the SM, cosξ = 1 ious Higgs decay modes: b¯b, τ+τ− and W+W−. Given andsinξ =0atleadingorder[7]. AttheLHC,theHiggs- thelargeboostedcrosssectionoftt¯h[32],theLHCRun-2 topcouplingcanbeprobedthroughthegluonfusionpro- would be able to pin down tt¯h production very soon. duction (gg h) [8] and the associated production of In order to enhance the observability of tt¯h produc- the top pair→with Higgs boson (tt¯h) [9]. The former has tion, the dedicated reconstruction approaches of the top asizablecrosssection. However, itisnotonlyalteredby quark and Higgs boson have been proposed [33–35]. On a modified Higgs-top coupling but also by new possible the other hand, it is obvious that the measurement of the signal strength of tt¯h production alone is not suffi- cient to unveil the nature of the Higgs-top coupling in ∗ [email protected] Eq. 1. Therefore, it is essential to investigate the kine- † [email protected] matical distributions of tt¯h production at the LHC. In ‡ [email protected] previousstudies,thespinpolarization/correlationeffects § [email protected] of top quarks were used to probe the Higgs-top interac- 2 tions in tt¯h production at the LHC. However, the sen- 1 d2N sitivity of the spin observables usually depends on the Nd∆yttd∆y‘0‘.200 specific reference frames, the reconstruction efficiency of 4 parton level 0.175 thetopquarkmomentaandthekinematicalcuts[36–40]. ξ=0 pTh>40 GeV 0.150 In this work, we propose to use the difference of 2 rapidity of two leptons (∆y ) from the top decays to 0.125 (cid:96)+(cid:96)− diagnosetheCPpropertyofHiggs-topcouplingsthrough ∆y‘‘ 0 0.100 the dileptonic channel of tt¯h( b¯b) production at the 0.075 → LHC. Such an observable is boosted invariant and can 2 0.050 be distorted by the CP violating tt¯h interaction because of the appearance of top quark charge asymmetric term. 4 0.025 0.000 4 2 0 2 4 ∆ytt 1 d2N II. CALCULATIONS AND RESULTS Nd∆yttd∆y‘‘ 0.16 4 parton level AttheLHC,thedominantproductionoftt¯histhrough ξpT=h0>.2450π GeV 0.14 the gluon fusion (c.f. Fig. 1). The presence of the CP 2 0.12 violating Higgs-top interaction in Eq. 1 will lead to the 0.10 top quark charge asymmetry term in tt¯h production. To ∆y‘‘ 0 0.08 see this, we take the s-channel gluon fusion subprocess 0.06 as example. Assuming incoming gluons momenta q and 2 1 0.04 q2, outgoing top and antitop momenta pt, pt¯, and Higgs momentum p , the amplitude is given by 4 0.02 h 0.00 4 2 0 2 4 = 1+ 2 ∆ytt M M M ∝ u¯(t)(Γ2tqt¯h[(qp/t)(+mp/2h+)+2pmt]pγρ)v(t¯)Jµρν(cid:15)µ1(cid:15)ν2, N1d∆ydt2tdN∆y‘‘ 1· 2 h t· h 0.105 u¯(t)γρ[(p/t¯+p/h)−mt]Γtt¯hv(t¯)Jρ (cid:15)µ(cid:15)ν (2) 4 pξ=ar0t.o5n0π level 0.090 − (2q1·q2)(m2h+2pt¯·ph) µν 1 2 2 pTh>40 GeV 0.075 w(choesrθe+Jµρiνγdseinnoθt)e.sItthsectorniptrleibgultuioonnitnotetrhaectciroonssansedctΓitot¯nho=f ∆y‘‘ 0 0.060 5 0.045 tt¯hproductioninvolvesthefactorTr(p/tγσp/t¯γτγ5),which 2 isasymmetricintheinterchangeoftandt¯andwillaffect 0.030 the kinematics of the decay products of the top/anti-top 0.015 4 quark. 0.000 InFig.2,weshowthepartonlevelcorrelationsbetween 4 2 0 2 4 ∆y(cid:96)+(cid:96)− and ∆ytt¯in dileptonic tt¯h( b¯b) production for ∆ytt → ξ =0,π/4,π/2 at 14 TeV LHC. We can see that ∆y indeedhasastrongcorrelationwith∆ytt¯,whichindic(cid:96)a+t(cid:96)e−s FinIGd.ile2p.toPnaicrtott¯nh(le→velb¯bc)orprreoladtuiocntiobnetfworeeξn=∆y0(cid:96)+((cid:96)u−ppaenrd),∆πy/t4t¯ that the dynamical reason for changing ∆y distribution (middle), π/2 (lower) at 14 TeV LHC. comesfromtheabovetopquarkchargeasymmetricterm rather than spin-correlation. For ξ = π/4 and π/2, the distributions of ∆y spreads towards the large values, as variable ∆y has a good discriminating power for the (cid:96)+(cid:96)− a comparison with ξ =0. different CP phases even in boosted phase space. In Fig. 3, we present the parton-level distributions of To quantitatively describe the difference in ∆y distri- ∆y(cid:96)+(cid:96)− forξ =0,π/4,π/2inEq.1withphT >40and150 butions for different CP phase, we define a central-edge GeV at 14 TeV LHC. We can see that the the SM inter- asymmetry, action(ξ =0)hasmoreeventsthanthemixed(ξ =π/4) σ σ bipnusteteuirodanoct-isisocnarleaivnreritsnheteeirnraactnthgioeenroa(fnξ|g∆e=yo(cid:96)πf+/(cid:96)−2∆)|y.<W1.h5i,l>efot1lhl.o5ew.deSidsutbrcihy- ACE ≡ σ||∆∆yy(cid:96)(cid:96)++(cid:96)(cid:96)−−||>>||∆∆yy(cid:96)(cid:96)00++(cid:96)(cid:96)−−||−+σ||∆∆yy(cid:96)(cid:96)++(cid:96)(cid:96)−−||<<||∆∆yy(cid:96)(cid:96)00++(cid:96)(cid:96)−−||, (3) (cid:96)+(cid:96)− a behavior will give a small (large|) asymm|etry A for where ∆y0 is the critical value of ∆y that is deter- CE (cid:96)+(cid:96)− ξ = π/2 (ξ = 0). Besides, it can seen that the differ- mined from the crossing point of ∆y distributions (cid:96)+(cid:96)− ence among ξ =0,π/4,π/2 in ∆y distribution is not for the different CP phase. The prediction of A sig- (cid:96)+(cid:96)− CE sensitive to the increase of ph. This indicates that the nificantly different from the SM value of tt¯h production T 3 weapplythejetsubstructuretechniquetoreconstructing 0.35 the Higgs boson. ℓ=0 0.30 parton level ℓ=π/4 We use MadGraph5 aMC@NLO [41] to generate the pTh>40 GeV ξ=π/2 parton-level signal and background events, in which the 0.25 topquarkandHiggsbosonarefurtherdecayedwithMad- spin [42]. The signal tt¯h and background tt¯Z is matched 0.20 dN∆y+(cid:6)(cid:6)− up to 1 jets by using MLM matching scheme [43] with 1Nd0.15 xqcut=30GeV.Wetakeqcuttomax(xqcut+5,xqcut ∗ 1.2) [44] in our simulation. The CTEQ6M parton distri- 0.10 bution functions (PDF) [45] are chosen for our calcula- 0.05 tion. We set the renormalisation scale µ and factori- R sation scale µ to be µ = µ = (m +2 m )/2. We 0.00 −4 −2 ∆y(cid:6)0+(cid:6)− 2 4 usePYTHIA6[F46]forimpRlemenFtingparhtonsh∗owetringand hadronization. Delphes3 [47] with input of default AT- 0.35 LASdetectorcardisusedforsimulatingdetectoreffects. ℓ=0 In this simulation, we take the b-jet tagging efficiency as 0.30 parton level ℓ=π/4 pTh>150 GeV ξ=π/2 70% with the other light quark and gluon mis-tagging 0.25 probability 1% [48]. Events which contain exactly two opposite sign lep- 0.20 dN∆y+(cid:6)(cid:6)− tons and at least four jets will be selected in our follow- 1Nd0.15 ing analysis. These two leptons should have pT > 15 GeV, η < 2.5 and be isolated. Particle-flow objects 0.10 | | in Delphes3 output other than isolated leptons are then 0.05 used for jet clustering with Fastjet [49]. We adopt the BDRSmethodfortaggingHiggsjetsubstructure: (1)re- 0.00 −4 −2 0 2 4 constructing the fat jets using C/A algorithm [50] with ∆y(cid:6)+(cid:6)− radius R=1.5 and ph >150 GeV; (2) breaking each fat T jet by undoing the clustering procedure. Higgs jet can- FIG. 3. Normalized parton-level ∆y distribution in (cid:96)+(cid:96)− t(→b(cid:96)+ν(cid:96))t¯(→¯b(cid:96)−ν(cid:96)¯)hproductionwithphT >40GeV(upper didate is taken as the leading fat jet that has large mass panel) and ph >150 GeV (lower panel) at 14 TeV LHC. drop µ < 0.67 and not too asymmetric mass splitting T y >0.09 at certain step during the de-clustering; (3) fil- tering the Higgs neighbourhood by re-running the C/A algorithm with a finer angle R = min(0.3,R /2) would strongly indicate the the non-standard CP violat- filt j1,j2 andtakingthethreehardestsubjects; (4)applyingb-tag ing Higgs-top interaction in Eq. 1. on the two leading subjects. The Higgs jet candidate A ((cid:96)+(cid:96)−)(%) is required to have both subjects being b-tagged. The ξ ph >40 GecV ph >150 GeV pileupeffectsontheHiggsmasscanbecontrolledbythe T T BDRS filtering. For event that contains the Higgs jet 0 -52.00 -48.92 π/4 -41.13 -35.58 candidate,weproceedfurthertoreconstructnarrowjets. π/2 -16.53 -16.73 The constituents of the Higgs jet candidate are removed from those particle-flow objects. The remnants are clus- TABLE I. Parton-level values of Ac((cid:96)+(cid:96)−) with phT >40,150 tered with the anti-kT jet clustering algorithm [51] with GeV for ξ=0,π/4,π/2 at 14 TeV LHC. the cone radius of R = 0.4 and are required to give at least two narrow jets, in which exactly two are b-tagged. In Table II, the cut-flow of cross sections of the signal In Table I, we numerically give the parton-level val- andbackgroundeventsispresentedfor14TeVLHC.The ues of A ((cid:96)+(cid:96)−) for ξ = 0,π/4,π/2 at 14 TeV LHC. cross sections of tt¯h are normalized to their NLO QCD CE For ph > 40 (150) GeV, we can see that the value of values [26]. After the cut pBDRS(b¯b) > 150 GeV, the T T A ((cid:96)+(cid:96)−) predicted by the SM is about -52%(-49%), tt¯b¯bbackgroundisreducedbyalmost (10−2),whilethe whCiEle it becomes about -41%(-36%) and -17%(-17%) for signals only by (10−1). The HiggsOmass window cut the mixed and pseudo-interactions, respectively. mBDRS 125 <O10 GeV will further suppress tt¯b¯b and In the following, we study the observability of the t|t¯Zb¯bbackg−round|s by one order. After all cuts, the signif- dileptonicchanneloftt¯hproductionwiththesequentde- icance S/√B of ξ = 0,π/4,π/2 can reach 5σ when the cayh b¯bandthechargeasymmetryA ((cid:96)+(cid:96)−)forCP luminosity = 795,993,1276 fb−1. The typical values phases→ξ =0,π/4,π/2byincludingthedCeEtectoreffectsat of S/B areLabout 30%. 14TeVLHC.ThedominantSMbackgroundsarethett¯b¯b In Table III, we present the values of A ((cid:96)+(cid:96)−) at CE and tt¯Z( b¯b) productions. Since the signal and back- the reconstructed level after all above cuts. It can be grounds h→ave good discrimination in the high ph regime, seenthatthevaluesofA ((cid:96)+(cid:96)−)aremildlydiminished T CE 4 cut tt¯h(ξ=0) tt¯h(ξ=π/4) tt¯h(ξ=π/2) tt¯b¯b tt¯Z(→b¯b) 2(cid:96), p(cid:96) >25 GeV, |η |<2.5 13.31 9.14 5.31 2424.73 1.56 T (cid:96) pBDRS(b¯b)>150 GeV 2.02 1.47 0.97 19.24 0.25 T 2 non-Higgs b’s 0.28 0.21 0.15 1.41 0.04 pb(non-h)>30 GeV, |η (non-h)|<2.5 0.22 0.17 0.13 1.13 0.03 T b (cid:12)(cid:12)mBDRS−125(cid:12)(cid:12)<10 GeV 0.053 0.048 0.042 0.09 0.0013 bb TABLE II. Cut flow of the cross sections of the signal tt¯h for ξ = 0,π/4,π/2 and backgrounds tt¯b¯b and tt¯Z at 14 TeV LHC. The cross section is in unit fb. N their significance is less than 3σ in the run of 14 TeV ξ events ACE((cid:96)+(cid:96)−)(%) LHC. ∆η>1.5 ∆η<1.5 0 2653 6230 -40.26 110000 π/4 4239 7312 -26.60 π/2 7774 9400 -9.47 TABLE III. Reconstructed level values of A ((cid:96)+(cid:96)−) at 14 CE TeV LHC. ee uu valval 1100−−11 p-p- 9955%%CCLL by the event selections, but are still obviously different ξξ:: 00VVSSππ//44 ξξ::ππ//44VVSSππ//22 for ξ =0,π/4,π/2. ξξ:: 00VVSSππ//22 1100−−22 5 550000 11000000 11550000 22000000 22550000 33000000 33550000 44000000 44550000 55000000 ξ= 0 LL[[ffbb−−11]] 4 ξ=0.25π FIG. 5. The significance of A ((cid:96)+(cid:96)−) in dileptonic tt¯H(→ CE ξ=0.50π b¯b)productionversustheintegratedluminosityLfortheCP phase ξ=0,π/4,π/2 at 14 TeV LHC. 3 S Finally, we estimate the CP discrimination in Higgs- 2 topcouplingsbycalculatingthebinned-χ2 ofthe∆y(cid:96)+(cid:96)− histogram at reconstructed level. In Fig. 5, we can see thatthe14TeVLHCwillbeabletodistinguishξ =0and 1 ξ = π/2 interactions at 95% C.L. level if the luminosity 3200 fb−1. L(cid:39) 0 0 500 1000 1500 2000 2500 3000 ℒ[fb-1] III. CONCLUSIONS FIG.4. ThesignificanceofA indileptonictt¯H(→b¯b)pro- CE In this work, we investigate the CP violating Higgs- duction versus the integrated luminosity L for the CP phase top couplings in dileptonic channel of tt¯h( b¯b) produc- ξ=0,π/4,π/2 at 14 TeV LHC. → tion at the LHC. We find that the CP violating inter- action can distort the distribution of the rapidity differ- AstraightforwardGaussianestimateofthesignificance ence of two leptons from the top decays because of the of A is given by CE presence of the top quark charge asymmetric term. We S = ACE |∆σ∆y(cid:96)+(cid:96)−|L. (4) anlastoiofinnpdotwheartosfucthheaCnPobvsieorlvaatibnlge hcoauspalinggosodindbisocorsimteid- δACE (cid:39) √σtot L regime. To numerically show the difference in ∆y(cid:96)+(cid:96)− In Fig. 4, we show the significance of A versus the lu- distributions, we define a central-edge asymmetry A , CE CE minosity at 14 TeV LHC. We find that the SM predic- which can reach -40.3%, -26.6% and -9.5% for CP phase L tion of A can be observed at 3σ level when =1500 ξ =0,π/4,π/2, respectively. Besides, wesimplyperform CE fb−1,whileforthemixedandpseudo-scalarinteLractions, the binned-χ2 analysis of ∆y distribution and find (cid:96)+(cid:96)− 5 that the scalar interaction and the pseudo-interaction ACKNOWLEDGMENTS can be distinguished at 95% level at 14 TeV LHC with 3200 fb−1 of integrated luminosity. We thanks the valuable discussions with Mengchao L(cid:39) Zhang, Archil Kobakhidze, J. M. Yang and C. R. Chen. ThisworkispartlysupportedbytheAustralianResearch Council (LW), by the National Natural Science Foun- dation of China (NNSFC) under grants Nos. 11325525 (ZS), by National Research Foundation of Korea (NRF) Research Grant NRF-2015R1A2A1A05001869 (JL). [1] G.Aadetal.(ATLASCollaboration),Phys.Lett.B710, doi:10.1103/PhysRevLett.116.091801 [arXiv:1507.07926 49 (2012). [hep-ph]]. [2] S. 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