Central-edge asymmetry as a probe of Higgs-top coupling in $t\bar{t}h$ production at LHC

The Higgs-top coupling plays a central role in the hierarchy problem and the vacuum stability of the Standard Model (SM). We propose a central-edge asymmetry ($A_{CE}$) to probe the CP violating Higgs-top coupling in dileptonic channel of $t\bar{t}h(\to b\bar{b})$ production at the LHC. We demonstrate that the CP-violating Higgs-top coupling can affect the central-edge asymmetry through distorting $\Delta y_{\ell^+\ell^-}$ distribution because of the contribution of new top charge asymmetric term. Since $\Delta y_{\ell^+\ell^-}$ distribution is frame-independent and has a good discrimination even in boosted regime, we use the jet substructure technique to enhance the observability of the dileptonic channel of $t\bar{t}h$ production. We find that (1) the significance of dileptonic channel of $t\bar{t}h$ production can reach $5\sigma$ for CP phase $\xi=0,\pi/4,\pi/2$ when the luminosity ${\cal L}=795,993,1276$ fb$^{-1}$ at 14 TeV LHC. (2) the central-edge asymmetry $A_{CE}$ show a good discrimination power of CP phase of $t\bar{t}h$ interaction, which are -40.26\%, -26.60\%, -9.47\% for $\xi=0$, $\pi/4$, $ \pi/2$ respectively and are hardly affected by the event selections. Besides, by performing the binned-$\chi^2$ analysis of $\Delta y_{\ell^+\ell^-}$ distribution, we find that the scalar 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 of the most important tasks in theory and experiment. So far, the measured Higgs gauge couplings are compatible with the SM predictions at 1-2σ level. However, the Higgs fermion couplings remain obscure. Among them, the Higgs-top coupling is of particular interest.
In the SM, the top quark has the strongest coupling with the Higgs boson. As such, the Higgs-top coupling plays an special role in the hierarchy problem [3] and the vacuum stability of the SM [4,5]. Many models for physics beyond the SM related with these two problems predict a modified Higgs-top coupling. So, the precise measurements of Higgs-top coupling could give an insight on the pattern of fermion mass generation and the energy scale of new physics above the electroweak scale [6].
The most general Lagrangian of the tth interaction can be parameterised as follows: where y t takes the value y SM t = √ 2m t /v and ξ = 0 in the SM [7], with v = 246 GeV being the vacuum expectation value of the Higgs field.
The favored channel for observing tth production at the LHC exploits the dominant Higgs decay mode h → bb. In Ref. [25], the observability of purely hadronic top decay channel of tth(→ bb) has been demonstrated. In Ref. [26], the matrix element method was used to improve the sensitivity of tth production at the LHC. On the other hand, due to the large multiplicity of jets, the fully hadronic top decay channel has the poor ability to unveil the nature of the Higgs-top coupling in Eq. 1. Therefore, it is necessary to explore the observability of tth in other decay modes of top quarks. In Refs. [27][28][29][30][31][32], various spin polarization/correlation observables in tth production are proposed to probe the Higgs-top coupling. However, the discrimination power of those spin observables is easily reduced by the experimental kinematical cuts.
In this work, we investigate a central-edge asymmetry that arises from the rapidity difference of two leptons (∆y + − ) from the top quark decays in the dileptonic channel of tth(→ bb) production at the LHC. We demonstrate the CP-violating Higgs-top coupling can affect the central-edge asymmetry through distorting ∆y + − distribution because of the contribution of new top charge asymmetric term. Since ∆y + − distribution is frame-independent and has a good discrimination arXiv:1701.00224v2 [hep-ph] 4 Feb 2018 even in boosted regime, we apply the jet substructure technique to enhance the observability of the dileptonic channel of tth production without reducing the discrimination power of the central-edge asymmetry.

II. CALCULATIONS AND RESULTS
At the LHC, the dominant production of tth is through the gluon fusion. The high order QCD and EW corrections to the tth production have recently been studied [33][34][35][36][37][38][39][40]. The presence of the CP violating Higgs-top interaction in Eq. 1 will lead to the top quark charge asymmetry term in tth production. To see this, we take the s-channel gluon fusion subprocess as example. Assuming incoming gluons momenta q 1 and q 2 , outgoing top and antitop momenta p t , pt, and Higgs momentum p h , the amplitude is given by where J ρ µν denotes the triple gluon interaction and Γ tth = (cos θ + iγ 5 sin θ). Its contribution to the cross section of tth production involves the factor T r( / p t γ σ / ptγ τ γ 5 ), which is asymmetric in the interchange of t andt and will affect the kinematics of the decay products of the top/anti-top quark.
In Fig. 1, we show the parton level correlations between ∆y + − and ∆y tt in dileptonic tth(→ bb) production for ξ = 0, π/4, π/2 at 14 TeV LHC. We can see that ∆y + − indeed has a strong correlation with ∆y tt , which indicates that the dynamical reason for changing ∆y distribution comes from the above top quark charge asymmetric term rather than spin-correlation. For ξ = π/4 and π/2, the distributions of ∆y spreads towards the large values, as a comparison with ξ = 0.
In Fig. 2, we present the parton-level distributions of ∆y + − for ξ = 0, π/4, π/2 in Eq. 1 with p h T > 40 and 150 GeV at 14 TeV LHC. We can see that the the SM interaction (ξ = 0) has more events than the mixed (ξ = π/4) interaction in the range of |∆y + − | < 1.5, followed by pseudo-scalar interaction (ξ = π/2). While the distribution is reverse in the range of |∆y + − | > 1.5. Such a behavior will give a small (large) asymmetry A CE for ξ = π/2 (ξ = 0). Besides, it can seen that the difference among ξ = 0, π/4, π/2 in ∆y + − distribution is not sensitive to the increase of p h T . This indicates that the variable ∆y + − has a good discriminating power for the different CP phases even in boosted phase space.
To quantitatively describe the difference in ∆y distributions for different CP phase, we define a central-edge

asymmetry,
where ∆y 0 is the critical value of ∆y + − and is determined from the crossing point of ∆y + − distributions for the different CP phases. The prediction of A CE significantly different from the SM value of tth production would strongly indicate the the non-standard CP violating Higgs-top interaction in Eq. 1.
In the following, we study the observability of the dileptonic channel of tth production with the sequent decay h → bb and the charge asymmetry A CE ( + − ) for CP phases ξ = 0, π/4, π/2 by including the detector effects at 14 TeV LHC. The dominant SM backgrounds are the ttbb and ttZ(→ bb) productions. Since the signal and backgrounds have good discrimination in the high p h T regime, we apply the jet substructure technique to reconstructing the Higgs boson.
We use MadGraph5 aMC@NLO [41] to generate the parton-level signal and background events, in which the top quark and Higgs boson are further decayed with Madspin [42]. The signal tth and background ttZ is matched up to 1 jets by using MLM matching scheme [43] with xqcut = 30 GeV. We take qcut to max(xqcut + 5, xqcut * 1.2) [44] in our simulation. The CTEQ6M parton distri-bution functions (PDF) [45] are chosen for our calculation. We set the renormalisation scale µ R and factorisation scale µ F to be µ R = µ F = (m h + 2 * m t )/2. We use PYTHIA6 [46] for implementing parton showering and hadronization. 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 as 70% with the other light quark and gluon mis-tagging probability 1% [48].
Events which contain exactly two opposite sign leptons and at least four jets will be selected in our following analysis. These two leptons should have p T > 15 GeV, |η| < 2.5 and be isolated. Particle-flow objects in Delphes3 output other than isolated leptons are then used for jet clustering with Fastjet [49]. We adopt the BDRS method for tagging Higgs jet substructure: (1) reconstructing the fat jets using C/A algorithm [50] with radius R = 1.5 and p h T > 150 GeV; (2) breaking each fat jet by undoing the clustering procedure. Higgs jet candidate is taken as the leading fat jet that has large mass drop µ < 0.67 and not too asymmetric mass splitting y > 0.09 at certain step during the de-clustering; (3) filtering the Higgs neighbourhood by re-running the C/A algorithm with a finer angle R f ilt = min(0.3, R j1,j2 /2) and taking the three hardest subjects; (4) applying b-tag on the two leading subjects. The Higgs jet candidate is required to have both subjects being b-tagged. The pileup effects on the Higgs mass can be controlled by the BDRS filtering. For event that contains the Higgs jet candidate, we proceed further to reconstruct narrow jets. The constituents of the Higgs jet candidate are removed from those particle-flow objects. The remnants are clustered with the anti-k T jet clustering algorithm [51] with 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 • Cut |m BDRS bb − 125| < 10 GeV will further suppress ttbb and ttZ backgrounds by one order.
A straightforward Gaussian estimate of the significance cut tth(ξ = 0) tth(ξ = π/4) tth(ξ = π/2) ttbb ttZ(→ bb) 2 , p T > 25 GeV, |η | < 2. 5 13   of A CE is given by In Fig. 3, we show the significance of A CE versus the luminosity L at 14 TeV LHC. We find that the SM prediction of A CE can be observed at 3σ level when L = 1500 fb −1 , while for the mixed and pseudo-scalar interactions, their significance is less than 3σ in the run of 14 TeV LHC. Finally, we estimate the CP discrimination in Higgstop couplings by calculating the binned-χ 2 of the ∆y + − histogram at reconstructed level. In Fig. 4, we can see that the 14 TeV LHC will be able to distinguish ξ = 0 and ξ = π/2 interactions at 95% C.L. level if the luminosity L 3200 fb −1 .

III. CONCLUSIONS
In this work, we investigate the CP violating Higgstop couplings in dileptonic channel of tth(→ bb) production at the LHC. We find that the CP violating interaction can distort the distribution of the rapidity difference of two leptons from the top decays because of the presence of the top quark charge asymmetric term. We also find that such an observable has a good discrimination power of the CP violating couplings in boosted regime. To numerically show the difference in ∆y + − 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/4, π/2, respectively. Besides, we simply perform the binned-χ 2 analysis of ∆y + − distribution and find that the scalar interaction and the pseudo-interaction can be distinguished at 95% level at 14 TeV LHC with L 3200 fb −1 of integrated luminosity.