Central-edge asymmetry as a probe of Higgs-top coupling in t\bar{t}h production at LHC
CCentral-edge asymmetry as a probe of Higgs-top coupling in t ¯ th production at theLHC Jinmian Li, ∗ Zong-guo Si, † Lei Wu,
3, 4, ‡ and Jason Yue § School of Physics, KIAS, Seoul 02455, Korea School of Physics, Shandong University, Jinan, Shandong 250100, China Department of Physics and Institute of Theoretical Physics,Nanjing Normal University, Nanjing, Jiangsu 210023, China ARC Centre of Excellence for Particle Physics at the Terascale,School of Physics, The University of Sydney, NSW 2006, Australia Department 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 ofthe Standard Model (SM). We propose a central-edge asymmetry ( A CE ) to probe the CP violatingHiggs-top coupling in dileptonic channel of t ¯ th ( → b ¯ b ) production at the LHC. We demonstratethat the CP-violating Higgs-top coupling can affect the central-edge asymmetry through distorting∆ y (cid:96) + (cid:96) − distribution because of the contribution of new top charge asymmetric term. Since ∆ y (cid:96) + (cid:96) − distribution is frame-independent and has a good discrimination even in boosted regime, we use thejet substructure technique to enhance the observability of the dileptonic channel of t ¯ th production.We find that (1) the significance of dileptonic channel of t ¯ th production can reach 5 σ for CP phase ξ = 0 , π/ , π/ L = 795 , , − at 14 TeV LHC. (2) the central-edgeasymmetry A CE show a good discrimination power of CP phase of t ¯ th interaction, which are -40.26%, -26.60%, -9.47% for ξ = 0, π/ π/ χ analysis of ∆ y (cid:96) + (cid:96) − distribution, we find that thescalar and pseudo-scalar interactions can be distinguished at 95% C.L. level at 14 TeV HL-LHC. I. INTRODUCTION
After the discovery of the Higgs boson at the LHC[1, 2], precision study of its properties becomes one ofthe most important tasks in theory and experiment. Sofar, the measured Higgs gauge couplings are compati-ble with the SM predictions at 1-2 σ level. However, theHiggs fermion couplings remain obscure. Among them,the Higgs-top coupling is of particular interest.In the SM, the top quark has the strongest couplingwith the Higgs boson. As such, the Higgs-top couplingplays an special role in the hierarchy problem [3] andthe vacuum stability of the SM [4, 5]. Many models forphysics beyond the SM related with these two problemspredict a modified Higgs-top coupling. So, the precisemeasurements of Higgs-top coupling could give an insighton the pattern of fermion mass generation and the energyscale of new physics above the electroweak scale [6].The most general Lagrangian of the t ¯ th interaction canbe parameterised as follows: L ⊃ − y t √ t (cos ξ + iγ sin ξ ) th, (1)where y t takes the value y SM t = √ m t /v and ξ = 0 in theSM [7], with v = 246 GeV being the vacuum expectationvalue of the Higgs field. ∗ Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: corresponding author:[email protected] § Electronic address: [email protected]
At the LHC, t ¯ th production is the most promising di-rect way to probe the Higgs-top coupling [8–20]. Withthe data set of 7 and 8 TeV runs of LHC, the signalstrengths in the t ¯ th production channel have been mea-sured by both ATLAS [21, 22] and CMS [23] in variousHiggs decay modes: b ¯ b , τ + τ − and W + W − . Given thelarge boosted cross section of t ¯ th [24], the LHC Run-2would be able to pin down t ¯ th production.The favored channel for observing t ¯ th production atthe LHC exploits the dominant Higgs decay mode h → b ¯ b . In Ref. [25], the observability of purely hadronic topdecay channel of t ¯ th ( → b ¯ b ) has been demonstrated. InRef. [26], the matrix element method was used to im-prove the sensitivity of t ¯ th production at the LHC. Onthe other hand, due to the large multiplicity of jets, thefully hadronic top decay channel has the poor abilityto unveil the nature of the Higgs-top coupling in Eq. 1.Therefore, it is necessary to explore the observability of t ¯ th in other decay modes of top quarks. In Refs. [27–32], various spin polarization/correlation observables in t ¯ th production are proposed to probe the Higgs-top cou-pling. However, the discrimination power of those spinobservables is easily reduced by the experimental kine-matical cuts.In this work, we investigate a central-edge asymmetrythat arises from the rapidity difference of two leptons(∆ y (cid:96) + (cid:96) − ) from the top quark decays in the dileptonicchannel of t ¯ th ( → b ¯ b ) production at the LHC. Wedemonstrate the CP-violating Higgs-top coupling canaffect the central-edge asymmetry through distorting∆ y (cid:96) + (cid:96) − distribution because of the contribution of newtop charge asymmetric term. Since ∆ y (cid:96) + (cid:96) − distributionis frame-independent and has a good discrimination a r X i v : . [ h e p - ph ] F e b even in boosted regime, we apply the jet substructuretechnique to enhance the observability of the dileptonicchannel of t ¯ th production without reducing the discrim-ination power of the central-edge asymmetry. II. CALCULATIONS AND RESULTS
At the LHC, the dominant production of t ¯ th is throughthe gluon fusion. The high order QCD and EW correc-tions to the t ¯ th production have recently been studied[33–40]. The presence of the CP violating Higgs-top in-teraction in Eq. 1 will lead to the top quark charge asym-metry term in t ¯ th production. To see this, we take the s -channel gluon fusion subprocess as example. Assumingincoming gluons momenta q and q , outgoing top andantitop momenta p t , p ¯ t , and Higgs momentum p h , theamplitude is given by M = M + M ∝ ¯ u ( t )Γ t ¯ th [( /p t + /p h ) + m t ] γ ρ v (¯ t )(2 q · q )( m h + 2 p t · p h ) J ρµν (cid:15) µ (cid:15) ν , − ¯ u ( t ) γ ρ [( /p ¯ t + /p h ) − m t ]Γ t ¯ th v (¯ t )(2 q · q )( m h + 2 p ¯ t · p h ) J ρµν (cid:15) µ (cid:15) ν (2)where J ρµν denotes the triple gluon interaction and Γ t ¯ th =(cos θ + iγ sin θ ). Its contribution to the cross section of t ¯ th production involves the factor T r ( /p t γ σ /p ¯ t γ τ γ ), whichis asymmetric in the interchange of t and ¯ t and will affectthe kinematics of the decay products of the top/anti-topquark.In Fig. 1, we show the parton level correlations between∆ y (cid:96) + (cid:96) − and ∆ y t ¯ t in dileptonic t ¯ th ( → b ¯ b ) production for ξ = 0 , π/ , π/ y (cid:96) + (cid:96) − indeed has a strong correlation with ∆ y t ¯ t , which indicatesthat the dynamical reason for changing ∆ y distributioncomes from the above top quark charge asymmetric termrather than spin-correlation. For ξ = π/ π/
2, thedistributions of ∆ y spreads towards the large values, asa comparison with ξ = 0.In Fig. 2, we present the parton-level distributions of∆ y (cid:96) + (cid:96) − for ξ = 0 , π/ , π/ p hT >
40 and 150GeV at 14 TeV LHC. We can see that the the SM inter-action ( ξ = 0) has more events than the mixed ( ξ = π/ | ∆ y (cid:96) + (cid:96) − | < .
5, followed bypseudo-scalar interaction ( ξ = π/ | ∆ y (cid:96) + (cid:96) − | > .
5. Sucha behavior will give a small (large) asymmetry A CE for ξ = π/ ξ = 0). Besides, it can seen that the differ-ence among ξ = 0 , π/ , π/ y (cid:96) + (cid:96) − distribution is notsensitive to the increase of p hT . This indicates that thevariable ∆ y (cid:96) + (cid:96) − has a good discriminating power for thedifferent CP phases even in boosted phase space.To quantitatively describe the difference in ∆ y distri-butions for different CP phase, we define a central-edge ∆ y tt ∆ y ‘‘ parton level ξ =0 p hT > GeV N d Nd ∆ y tt d ∆ y ‘‘ ∆ y tt ∆ y ‘‘ parton level ξ =0 . πp hT > GeV N d Nd ∆ y tt d ∆ y ‘‘ ∆ y tt ∆ y ‘‘ parton level ξ =0 . πp hT > GeV N d Nd ∆ y tt d ∆ y ‘‘ FIG. 1: Parton level correlation between ∆ y (cid:96) + (cid:96) − and ∆ y t ¯ t in dileptonic t ¯ th ( → b ¯ b ) production for ξ = 0 (upper), π/ π/ asymmetry, A CE ≡ σ | ∆ y (cid:96) + (cid:96) − | > | ∆ y (cid:96) + (cid:96) − | − σ | ∆ y (cid:96) + (cid:96) − | < | ∆ y (cid:96) + (cid:96) − | σ | ∆ y (cid:96) + (cid:96) − | > | ∆ y (cid:96) + (cid:96) − | + σ | ∆ y (cid:96) + (cid:96) − | < | ∆ y (cid:96) + (cid:96) − | , (3)where ∆ y is the critical value of ∆ y (cid:96) + (cid:96) − and is deter-mined from the crossing point of ∆ y (cid:96) + (cid:96) − distributionsfor the different CP phases. The prediction of A CE sig-nificantly different from the SM value of t ¯ th productionwould strongly indicate the the non-standard CP violat-ing Higgs-top interaction in Eq. 1.In Table I, we numerically give the parton-level val-ues of A CE ( (cid:96) + (cid:96) − ) for ξ = 0 , π/ , π/ p hT >
40 (150) GeV, we can see that the value of A CE ( (cid:96) + (cid:96) − ) predicted by the SM is about -52%(-49%), −4 −2 0 2 4 ∆y (cid:6) + (cid:6) − N d N d ∆ y (cid:6) + (cid:6) − parton levelp hT >40 GeV ℓ=0ℓ=π/4ξ=π/2 −4 −2 0 2 4 ∆y (cid:6) + (cid:6) − N d N d ∆ y (cid:6) + (cid:6) − parton levelp hT >150 GeV ℓ=0ℓ=π/4ξ=π/2 FIG. 2: Normalized parton-level ∆ y (cid:96) + (cid:96) − distribution in t ( → b(cid:96) + ν (cid:96) )¯ t ( → ¯ b(cid:96) − ν ¯ (cid:96) ) h production with p hT >
40 GeV (upperpanel) and p hT >
150 GeV (lower panel) at 14 TeV LHC. ξ A CE ( (cid:96) + (cid:96) − )(%) p hT >
40 GeV p hT >
150 GeV0 -52.00 -48.92 π/ π/ A CE ( (cid:96) + (cid:96) − ) with p hT > ,
150 GeV for ξ = 0 , π/ , π/ while it becomes about -41%(-36%) and -17%(-17%) forthe mixed and pseudo-interactions, respectively.In the following, we study the observability of thedileptonic channel of t ¯ th production with the sequent de-cay h → b ¯ b and the charge asymmetry A CE ( (cid:96) + (cid:96) − ) for CPphases ξ = 0 , π/ , π/ t ¯ tb ¯ b and t ¯ tZ ( → b ¯ b ) productions. Since the signal and back-grounds have good discrimination in the high p hT regime,we apply the jet substructure technique to reconstructingthe Higgs boson.We use MadGraph5 aMC@NLO [41] to generate theparton-level signal and background events, in which thetop quark and Higgs boson are further decayed with
Mad-spin [42]. The signal t ¯ th and background t ¯ tZ is matchedup to 1 jets by using MLM matching scheme [43] with xqcut = 30 GeV. We take qcut to max ( xqcut + 5 , xqcut ∗ .
2) [44] in our simulation. The CTEQ6M parton distri- bution functions (PDF) [45] are chosen for our calcula-tion. We set the renormalisation scale µ R and factori-sation scale µ F to be µ R = µ F = ( m h + 2 ∗ m t ) /
2. Weuse
PYTHIA6 [46] for implementing parton showering andhadronization.
Delphes3 [47] with input of default AT-LAS detector card is used for simulating detector effects.In this simulation, we take the b -jet tagging efficiency as70% with the other light quark and gluon mis-taggingprobability 1% [48].Events which contain exactly two opposite sign lep-tons and at least four jets will be selected in our follow-ing analysis. These two leptons should have p T > | η | < . Delphes3 output other than isolated leptons are thenused for jet clustering with
Fastjet [49]. We adopt theBDRS method for tagging Higgs jet substructure: (1) re-constructing the fat jets using C/A algorithm [50] withradius R = 1 . p hT >
150 GeV; (2) breaking each fatjet by undoing the clustering procedure. Higgs jet can-didate is taken as the leading fat jet that has large massdrop µ < .
67 and not too asymmetric mass splitting y > .
09 at certain step during the de-clustering; (3) fil-tering the Higgs neighbourhood by re-running the C/Aalgorithm with a finer angle R filt = min(0 . , R j ,j / b -tagon the two leading subjects. The Higgs jet candidateis required to have both subjects being b -tagged. Thepileup effects on the Higgs mass can be controlled by theBDRS filtering. For event that contains the Higgs jetcandidate, we proceed further to reconstruct narrow jets.The constituents of the Higgs jet candidate are removedfrom those particle-flow objects. The remnants are clus-tered with the anti- k T jet clustering algorithm [51] withthe cone radius of R = 0 . b -tagged.In Table II, the cut-flow of cross sections of the signaland background events is presented for 14 TeV LHC. Thecross sections of t ¯ th are normalized to their NLO QCDvalues [36]. After the cut p BDRST ( b ¯ b ) >
150 GeV, the t ¯ tb ¯ b background is reduced by almost O (10 − ), while thesignals only by O (10 − ). The Higgs mass window cut | m B DRSb ¯ b − | <
10 GeV will further suppress t ¯ tb ¯ b and t ¯ tZ backgrounds by one order. After all cuts, we findthat the significance S/ √ B of ξ = 0 , π/ , π/ σ when the luminosity L = 795 , , − . Thetypical values of S/B are about 30%. The correspondingvalues of A CE ( (cid:96) + (cid:96) − ) are -40.26%, -26.60% and -9.47%,which are mildly diminished by the event selections. • Cut p BDRST ( b ¯ b ) >
150 GeV, the t ¯ tb ¯ b background isreduced by almost O (10 − ), while the signals onlyby O (10 − ). • Cut | m B DRSb ¯ b − | <
10 GeV will further suppress t ¯ tb ¯ b and t ¯ tZ backgrounds by one order.A straightforward Gaussian estimate of the significance cut t ¯ th ( ξ = 0) t ¯ th ( ξ = π/ t ¯ th ( ξ = π/ t ¯ tb ¯ b t ¯ tZ ( → b ¯ b )2 (cid:96) , p (cid:96)T >
25 GeV, | η (cid:96) | < . p BDRS T ( b ¯ b ) >
150 GeV 2.02 1.47 0.97 19.24 0.252 non-Higgs b ’s 0.28 0.21 0.15 1.41 0.04 p bT (non- h ) >
30 GeV, | η b (non- h ) | < . (cid:12)(cid:12) m BDRS bb − (cid:12)(cid:12) <
10 GeV 0.053 0.048 0.042 0.09 0.0013TABLE II: Cut flow of the cross sections of the signal t ¯ th for ξ = 0 , π/ , π/ t ¯ tb ¯ b and t ¯ tZ at 14 TeV LHC.The cross section is in unit fb. ξ = ξ = πξ = π ℒ [ fb - ] S FIG. 3: The significance of A CE in dileptonic t ¯ tH ( → b ¯ b ) pro-duction versus the integrated luminosity L for the CP phase ξ = 0 , π/ , π/ of A CE is given by S = A CE δA CE (cid:39) | ∆ σ ∆ y (cid:96) + (cid:96) − |L√ σ tot L . (4)In Fig. 3, we show the significance of A CE versus the lu-minosity L at 14 TeV LHC. We find that the SM predic-tion of A CE can be observed at 3 σ level when L = 1500fb − , while for the mixed and pseudo-scalar interactions,their significance is less than 3 σ in the run of 14 TeVLHC. − −
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
95% CL − −
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
95% CL p - v a l u e L [fb − ] ξ : 0 VS π/ ξ : π/ π/ ξ : 0 VS π/ p - v a l u e L [fb − ] ξ : 0 VS π/ ξ : π/ π/ ξ : 0 VS π/ FIG. 4: The significance of A CE ( (cid:96) + (cid:96) − ) in dileptonic t ¯ tH ( → b ¯ b ) production versus the integrated luminosity L for the CPphase ξ = 0 , π/ , π/ Finally, we estimate the CP discrimination in Higgs-top couplings by calculating the binned- χ of the ∆ y (cid:96) + (cid:96) − histogram at reconstructed level. In Fig. 4, we can seethat the 14 TeV LHC will be able to distinguish ξ = 0 and ξ = π/ L (cid:39) − . III. CONCLUSIONS
In this work, we investigate the CP violating Higgs-top couplings in dileptonic channel of t ¯ th ( → b ¯ b ) produc-tion at the LHC. We find that the CP violating inter-action can distort the distribution of the rapidity differ-ence of two leptons from the top decays because of thepresence of the top quark charge asymmetric term. Wealso find that such an observable has a good discrimi-nation power of the CP violating couplings in boostedregime. To numerically show the difference in ∆ y (cid:96) + (cid:96) − distributions, we define a central-edge asymmetry A CE ,which can reach -40.3%, -26.6% and -9.5% for CP phase ξ = 0 , π/ , π/
2, respectively. Besides, we simply performthe binned- χ analysis of ∆ y (cid:96) + (cid:96) − distribution and findthat the scalar interaction and the pseudo-interactioncan be distinguished at 95% level at 14 TeV LHC with L (cid:39) − of integrated luminosity. Acknowledgments
We thanks the valuable discussions with MengchaoZhang, Archil Kobakhidze, J. M. Yang and C. R. Chen.This work is partly supported by the Australian ResearchCouncil (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. Aad et al. [ATLAS Collaboration], Phys. Lett.B , 1 (2012) doi:10.1016/j.physletb.2012.08.020[arXiv:1207.7214 [hep-ex]].[2] S. Chatrchyan et al. [CMS Collaboration], Phys. Lett.B , 30 (2012) doi:10.1016/j.physletb.2012.08.021[arXiv:1207.7235 [hep-ex]].[3] G. ’t Hooft, NATO Sci. Ser. B , 135 (1980).[4] M. Sher, Phys. Rept. , 273 (1989). doi:10.1016/0370-1573(89)90061-6[5] G. Degrassi, S. Di Vita, J. Elias-Miro, J. R. Es-pinosa, G. F. Giudice, G. Isidori and A. Strumia,JHEP , 098 (2012) doi:10.1007/JHEP08(2012)098[arXiv:1205.6497 [hep-ph]].[6] F. Bezrukov and M. Shaposhnikov, J. Exp. Theor. Phys. , 335 (2015) [Zh. Eksp. Teor. Fiz. , 389 (2015)]doi:10.1134/S1063776115030152 [arXiv:1411.1923 [hep-ph]].[7] J. A. Aguilar-Saavedra, Nucl. Phys. B , 215 (2009)doi:10.1016/j.nuclphysb.2009.06.022 [arXiv:0904.2387[hep-ph]].[8] W. J. Marciano and F. E. Paige, Phys. Rev. Lett. ,2433 (1991). doi:10.1103/PhysRevLett.66.2433[9] J. Ellis, D. S. Hwang, K. Sakurai and M. Takeuchi,JHEP , 004 (2014) doi:10.1007/JHEP04(2014)004[arXiv:1312.5736 [hep-ph]].[10] A. Kobakhidze, L. Wu and J. Yue, JHEP , 100(2014) doi:10.1007/JHEP10(2014)100 [arXiv:1406.1961[hep-ph]].[11] F. Boudjema, R. M. Godbole, D. Guadagnoli andK. A. Mohan, Phys. Rev. D , no. 1, 015019 (2015)doi:10.1103/PhysRevD.92.015019 [arXiv:1501.03157[hep-ph]].[12] H. L. Li, P. C. Lu, Z. G. Si and Y. Wang, Chin.Phys. C , no. 6, 063102 (2016) doi:10.1088/1674-1137/40/6/063102 [arXiv:1508.06416 [hep-ph]].[13] S. Khatibi and M. Mohammadi Najafabadi,Phys. Rev. D , no. 7, 074014 (2014)doi:10.1103/PhysRevD.90.074014 [arXiv:1409.6553[hep-ph]].[14] J. Yue, Phys. Lett. B , 131 (2015)doi:10.1016/j.physletb.2015.03.044 [arXiv:1410.2701[hep-ph]].[15] M. R. Buckley and D. Goncalves, Phys.Rev. Lett. , no. 9, 091801 (2016)doi:10.1103/PhysRevLett.116.091801 [arXiv:1507.07926[hep-ph]].[16] Q. H. Cao, S. L. Chen and Y. Liu, arXiv:1602.01934 [hep-ph].[17] A. V. Gritsan, R. Rontsch, M. Schulze andM. Xiao, Phys. Rev. D , no. 5, 055023 (2016)doi:10.1103/PhysRevD.94.055023 [arXiv:1606.03107[hep-ph]].[18] M. J. Dolan, M. Spannowsky, Q. Wang andZ. H. Yu, Phys. Rev. D , no. 1, 015025 (2016)doi:10.1103/PhysRevD.94.015025 [arXiv:1606.00019[hep-ph]].[19] J. Chang, K. Cheung, J. S. Lee and C. T. Lu,arXiv:1607.06566 [hep-ph].[20] A. Kobakhidze, N. Liu, L. Wu and J. Yue,arXiv:1610.06676 [hep-ph].[21] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B , 222 (2015) doi:10.1016/j.physletb.2014.11.049[arXiv:1409.3122 [hep-ex]].[22] G. Aad et al. [ATLAS Collaboration], Eur. Phys. J. C , no. 7, 349 (2015) doi:10.1140/epjc/s10052-015-3543-1 [arXiv:1503.05066 [hep-ex]].[23] V. Khachatryan et al. [CMS Collaboration],JHEP , 087 (2014) Erratum: [JHEP , 106 (2014)] doi:10.1007/JHEP09(2014)087,10.1007/JHEP10(2014)106 [arXiv:1408.1682 [hep-ex]].[24] D. de Florian et al. [LHC Higgs Cross Section WorkingGroup Collaboration], arXiv:1610.07922 [hep-ph].[25] M. R. Buckley, T. Plehn, T. Schell and M. Takeuchi,JHEP , 130 (2014) doi:10.1007/JHEP02(2014)130[arXiv:1310.6034 [hep-ph]].[26] P. Artoisenet, P. de Aquino, F. Maltoni and O. Mat-telaer, Phys. Rev. Lett. , no. 9, 091802 (2013)doi:10.1103/PhysRevLett.111.091802 [arXiv:1304.6414[hep-ph]].[27] J. Bramante, A. Delgado and A. Martin,Phys. Rev. D , no. 9, 093006 (2014)doi:10.1103/PhysRevD.89.093006 [arXiv:1402.5985[hep-ph]].[28] W. Bernreuther and Z. G. Si, Nucl. Phys. B , 90 (2010) doi:10.1016/j.nuclphysb.2010.05.001[arXiv:1003.3926 [hep-ph]].[29] W. Bernreuther and Z. G. Si, Phys. Rev. D , 034026 (2012) doi:10.1103/PhysRevD.86.034026[arXiv:1205.6580 [hep-ph]].[30] W. Bernreuther, D. Heisler and Z. G. Si, JHEP , 026(2015) doi:10.1007/JHEP12(2015)026 [arXiv:1508.05271[hep-ph]].[31] J. A. Aguilar-Saavedra, D. Amidei, A. Juste andM. Perez-Victoria, Rev. Mod. Phys. , 421 (2015)doi:10.1103/RevModPhys.87.421 [arXiv:1406.1798 [hep-ph]].[32] R. M. Godbole, G. Mendiratta and S. Rin-dani, Phys. Rev. D , no. 9, 094013 (2015)doi:10.1103/PhysRevD.92.094013 [arXiv:1506.07486[hep-ph]].[33] S. Dawson, S. Dittmaier and M. Spira, Phys. Rev.D , 115012 (1998) doi:10.1103/PhysRevD.58.115012[hep-ph/9805244].[34] R. Frederix, S. Frixione, V. Hirschi, F. Mal-toni, R. Pittau and P. Torrielli, Phys. Lett. B , 427 (2011) doi:10.1016/j.physletb.2011.06.012[arXiv:1104.5613 [hep-ph]].[35] Y. Zhang, W. G. Ma, R. Y. Zhang, C. Chenand L. Guo, Phys. Lett. B , 1 (2014)doi:10.1016/j.physletb.2014.09.022 [arXiv:1407.1110[hep-ph]].[36] F. Demartin, F. Maltoni, K. Mawatari, B. Page andM. Zaro, Eur. Phys. J. C , no. 9, 3065 (2014)doi:10.1140/epjc/s10052-014-3065-2 [arXiv:1407.5089[hep-ph]].[37] S. Frixione, V. Hirschi, D. Pagani, H.-S. Shao and M. Zaro, JHEP , 184 (2015)doi:10.1007/JHEP06(2015)184 [arXiv:1504.03446 [hep-ph]].[38] S. Frixione, V. Hirschi, D. Pagani, H. S. Shaoand M. Zaro, JHEP , 065 (2014)doi:10.1007/JHEP09(2014)065 [arXiv:1407.0823 [hep- ph]].[39] F. Maltoni, E. Vryonidou and C. Zhang, JHEP , 123(2016) doi:10.1007/JHEP10(2016)123 [arXiv:1607.05330[hep-ph]].[40] A. Broggio, A. Ferroglia, B. D. Pecjak and L. L. Yang,arXiv:1611.00049 [hep-ph].[41] J. Alwall et al. , JHEP , 079 (2014)doi:10.1007/JHEP07(2014)079 [arXiv:1405.0301 [hep-ph]].[42] P. Artoisenet, R. Frederix, O. Mattelaer and R. Rietkerk,JHEP , 015 (2013) doi:10.1007/JHEP03(2013)015[arXiv:1212.3460 [hep-ph]].[43] F. Caravaglios, M. L. Mangano, M. Moretti and R. Pit-tau, Nucl. Phys. B , 215 (1999).[44] https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/Matching[45] P. M. Nadolsky, H. -L. Lai, Q. -H. Cao, J. Huston,J. Pumplin, D. Stump, W. -K. Tung and C. -P. Yuan,Phys. Rev. D , 013004 (2008), arXiv:0802.0007 [hep-ph]. [46] T. Sjostrand, S. Mrenna and P. Z. Skands, JHEP , 026 (2006) doi:10.1088/1126-6708/2006/05/026[hep-ph/0603175].[47] J. de Favereau et al. [DELPHES 3 Collaboration],JHEP , 057 (2014) doi:10.1007/JHEP02(2014)057[arXiv:1307.6346 [hep-ex]].[48] G. Aad et al. [ATLAS Collaboration], JINST , no.04, P04008 (2016) doi:10.1088/1748-0221/11/04/P04008[arXiv:1512.01094 [hep-ex]].[49] M. Cacciari, G. P. Salam and G. Soyez, Eur. Phys. J.C , 1896 (2012) doi:10.1140/epjc/s10052-012-1896-2[arXiv:1111.6097 [hep-ph]].[50] Y. L. Dokshitzer, G. D. Leder, S. Moretti andB. R. Webber, JHEP , 001 (1997) doi:10.1088/1126-6708/1997/08/001 [hep-ph/9707323].[51] M. Cacciari, G. P. Salam and G. Soyez, JHEP0804