Anomalous Top-Higgs Couplings and Top Polarisation in Single Top and Higgs Associated Production at the LHC

In this paper, we put constraints on anomalous $\mathcal{CP}$-violating top-Higgs couplings using the currently available Higgs data and explore the prospect of measuring these couplings at 240 GeV TLEP. We find that the $\mathcal{CP}$-violating phase $\xi$ is currently limited in the range $|\xi|<0.6\pi$ at 95\% C.L. and may be further constrained to $|\xi|<0.07\pi$ at TLEP. Under this consideration, we further investigate the observability of the scalar ($\xi =0$), pseudoscalar ($\xi =0.5\pi$) and mixed ($\xi =0.25\pi$) top-Higgs interactions through the channel $pp \to t(\to \ell^+\nu_\ell b)h(\to b\overline{b})j$. We find that it is most promising to observe pure pseudoscalar interactions with $y_t=y_t^{SM}$, although this will be challenging due to a low signal to background ratio. We also find that the anomalous top-Higgs couplings can lead to sizeable differences in lepton forward-backward asymmetries and can be distinguished by measuring the lepton angular distributions from polarised top quarks at 14 TeV LHC.


I. INTRODUCTION
The discovery of the Higgs boson at the Large Hadron Collider (LHC) [1,2] is a major step towards elucidating the electroweak symmetry breaking (EWSB) mechanism. To ultimately establish its nature, a precise measurement of the Higgs couplings to fermions and gauge bosons, and Higgs self-coupling is an important task of experiments at LHC and future colliders [3,4]. Although the observed Higgs signals are still plagued with large uncertainties, they have at least firmly established the key Higgs production and decay channels predicted by the Standard Model (SM). In turn, the Higgs main production channel gg → h indirectly indicates the existence of top-Higgs interactions.
In the SM, top quark is the most massive fermion and hence has the strongest coupling to the Higgs boson. As such, it plays an important role in the EWSB and in various cosmological phenomena, such as electroweak phase transition and baryogenesis. The associated production of the top pair with Higgs boson have been widely investigated at the LHC [5,6] as a direct probe of the top-Higgs Yukawa coupling. Based on an integrated luminosity of L = 20.3 fb −1 , the ATLAS collaboration has analysed pp → tth, with h → bb, and set a 95% C.L. limit [7] on the tth cross section, σ tth < 4.1σ SM tth . The determination of the dominant background, tt + jets, is expected to be improved by the copious production of top quarks at the LHC [8]. However, even if the tth coupling can be measured with sufficient accuracy, information on the relative phase between the top-Higgs Yukawa coupling and gauge-Higgs coupling will still be lacking.
In this regard, the search for Higgs boson production in association with a single top have proposed in Refs. [9]. Like single top productions, there are three different production modes characterised by the virtuality of the W boson [10]. The t channel process pp → thj with a space-like W has the largest cross section amongst these production mode, reaching ∼ 88.2 fb (14 TeV) at NLO QCD in the SM [11]. The most important feature of thj production is that the interference between the contributing processes with htt and hW W couplings allows direct examination both the modulus (y t ) and the CP violating phase (ξ) of the top-Higgs Yukawa coupling [10][11][12][13][14][15]. Such anomalous top-Higgs couplings may result from various new physics models [16][17][18][19][20][21]. The CMS collaboration has very recently presented the result on thj searches in the h → γγ channel, and obtained a weak bound on the cross section of events with inverted top-Higgs coupling [22]. An equally important feature is that the top quark produced via the weak interaction in thj is left-handed in the SM. It is therefore expected that non-standard top-Higgs couplings will affect the polarisation states of top quark and change the angular distributions of the top quark decay products [13]. Such a polarisation asymmetry has been widely used to probe the anomalous top quark interactions at the LHC [23]. The precise measurement of thj channel opens a new window to probe the top quark Yukawa couplings and new physics at the LHC.
In this work, we will examine the current and future constraints on the non-standard top quark Yukawa couplings from the Higgs data at the LHC and TLEP. We investigate the observability of pp → thj with h → bb for the scalar, pseudoscalar and mixed interactions of top-Higgs. The potential to discriminate such anomalous top-Higgs couplings will be studied by performing reconstructed level Monte Carlo simulations at 14 TeV LHC. This paper is organised as follows: In section II, we present the Higgs data constraints on the anomalous top quark Yukawa coupling. In section III, we discuss its observability by analysing the process pp → thj. Conclusions will be drawn in section IV.

II. HIGGS DATA CONSTRAINTS
In some new physics models, the top quark Yukawa coupling can be different from the SM prediction. The new physics effects on tth coupling can be parameterised by a minimal set of the gauge invariant dimension-six operators [16]. The most general Lagrangian of the tth interaction in the broken phase can be parameterised as follows: where y t takes the value y SM t = √ 2m t /v and ξ = 0 in the SM, with v ≈ 246 GeV being the vacuum expectation value of the Higgs field. It is useful to define the scalar and pseudoscalar components of the anomalous top-Higgs interaction normalised to the tree-level SM coupling as C S = y t cos ξ/y SM t and C P = y t sin ξ/y SM t respectively. It should be noted that such CPviolating interactions contribute to the electric dipole moment (EDM). However, the bounds on the coupling C P depend on the assumption of Higgs couplings to other light fermions [24,25]. Since these couplings are practically unobservable at the LHC, we do not impose EDM constraints in this work. Other constraints from low-energy physics observables, such as B s −B s and B → X s γ, remain relatively weak [25].
An obvious consequence of non-standard top-Higgs interaction is that the production rate of gg → h and decay width of h → γγ will deviate from those in the SM. We impose the latest Higgs data constraints on the anomalous couplings C S and C P by calculating χ 2 with the public package HiggsSignals-1.2.0 [26], which includes all the available data sets from the ATLAS, CMS, CDF and DØ collaborations. In Fig. 1, we present the Higgs data constraints on the anomalous couplings C S and C P using current Higgs data and the prospect of improving the bounds at TLEP with √ s = 240 GeV. We find that reduced pseudoscalar couplings in the range |C P | > 0.6 have been excluded at 95% C.L by the current Higgs data and that positive scalar couplings C S > 0.5 are strongly favoured. As the CP-phase ξ increases from 0 to π/2, the 95% C.L.
allowed region for y t /y SM t reduces from 0.7 -1.2 to 0.4 -0.6. The expected measurement of C S at 14 TeV HL-LHC (3000 fb −1 ) will further constrain C P to the range |C P | < 0.4. To estimate the bounds at TLEP, all measured Higgs couplings are assumed to be the same as the SM predictions, and the expected measurement uncertainties are taken from Table 1-16 of Ref. [27]. The main constraints come from the precise determinations of loop induced, reduced C hgg and C hγγ couplings at TLEP. From Fig. 1, we see that the allowed range of C P at 95% C.L. shrinks to |C P | < 0.2, and C S is very close to one. In Fig. 2, we project the samples in the above 95% C.L. range allowed by the current Higgs data on the plane of the Higgs-diphoton reduced coupling C hγγ versus the CP phase ξ. From

III. ANOMALOUS tth COUPLINGS AND thj PRODUCTION
In the numerical calculations we take the SM input parameters as follows [28]: By performing the Monte Carlo simulation, we investigate the observability of the anomalous top-Higgs couplings through the single top and Higgs associated production at the LHC where j denotes the light jets and ℓ + = e + , µ + . Our signal is characterised by multi-jets (1 forward jet + 3 b-jets) + 1 lepton + missing energy (due to the neutrinos) in the final states.
Although the h → bb decay mode suffers a loss of efficiency in Higgs mass reconstruction, this shortcoming is mildly compensated by the large branching ratio of h → bb. Such a signature resembles the tth topology analysed by ATLAS and CMS collaborations at the LHC Run-I, where at least 3 b-jets are required [29].
We implement the CP-violating interaction of tth in (1) by using the package FeynRules is the lower bound for ξ = π/2. We can see that the maximal value of the cross section occurs at |ξ| = π, due to the constructive interference of the contributions involving the hW W and htt couplings.
Parton showering and fast detector simulations are subsequently performed by PYTHIA [32] and Delphes [33]. Jets are clustered by using the anti-k t algorithm with a cone radius ∆R = 0.7 [34]. We keep the default cuts setting when generating the parton level events and set both the renormalisation (µ R ) and factorisation (µ F ) scale to the default event-by-event value and take CTEQ6L as the parton distribution function [35]. We adopt the b-jet tagging efficiency (ǫ b ) formula [36] that is a function of the transverse momentum and rapidity of the jets, with ǫ b = 0 in the forward region (|η| > 2.5). We also include a misidentification probability of 10% and 1% for c-jets and light jets respectively. The mis-tag of QCD jets is assumed to be the default value as in Delphes. The number of events generated for both the signals and backgrounds in our calculations is 1.2 × 10 6 .
The main SM backgrounds are: (B1) pp → ttj, this channel can fake the signal when one light jet from the (anti-)top quark hadronic decay is misidentified as a b-jet and the other one is lost in the detector. Due to an extra hard jet with tt, such a process will be the largest background after all the cuts listed in Tab. I; (B2) pp → tt, it is similar to the ttj background and can mimic the signal if a light jet is mis-tagged; (B3) pp → tZ(→ bb)j, which is an irreducible background but with a pair of b-jets coming from Z boson; and (B4) the irreducible QCD process pp → tbbj. Since the last two backgrounds have been demonstrated to be small [11,15], we will focus on backgrounds (B1) and (B2). We impose the basic cuts on the final states as follows: In Fig. 4, we plot the pseudorapidity distributions of the leading jet in the signals and backgrounds. It can be observed that most events of tt and ttj have a leading jet in the central region, which differs significantly from the signal, where a forward spectator jet accompanies the top quark and Higgs boson. The pseudorapidity of the leading jet is therefore required to satisfy 2.5 < |η j 1 | < 4.7 in order to reduce the backgrounds of tt and ttj.
[GeV]   Another cut which further suppresses the tt and ttj backgrounds is the invariant mass cut on the two b-jets from the Higgs boson decay. As proposed in Ref. [15], the b-jet from the top quark decay can be tagged by selecting the minimal one among the invariant masses of each b-jet and the lepton, which should also satisfy M min bℓ < 200 GeV. The remaining two b-jets are the considered as possible daughters of the Higgs boson for the signal. Given that the third b-jet in the backgrounds of tt and ttj comes mainly from the misidentification of the jets in the top quark hadronic decay, the invariant mass M rej bbj and the two b-jets rejected by the minimisation of M bℓ should have a peak around m t for the tt and ttj, as is evident in Fig. 5. We further find that the signal M rej bb invariant mass peaks are more narrow than those of the backgrounds but are still relatively broad around the Higgs mass, reducing the effectiveness of the cut |M rej bb − m h | < 15 GeV in enhancing the observability of the signals. Similar to Fig. 5, we display M rej bbj and M rej bb distributions with a forward jet cut 2.5 < |η j 1 | < 4.7 in Fig. 6. Comparing with Fig. 5, we can find that the peak of M rej bbj moves towards the high invariant mass region. This indicates that the selected forward jets in tt and ttj events are not from the top quark hadronic decay. We claim that the M rej bbj cut will not be very effective in improving the significance of the signal after the forward jet cut.
The M rej bb distribution of the backgrounds becomes slightly more flat than the one in Fig. 5. In Tab. I, we summarise the cut-flow cross sections of the signal and backgrounds for 14 TeV LHC. Considering that the 95% C.L. from the current LHC data still allows the CP-violating phase ξ to vary within |ξ| 0.6π (c.f. Tab. 1), we take three benchmark points ξ = 0, π/4 and π/2 and assume y t = y SM t to demonstrate the observability of our signals. From Tab. I, we can find that: (1) Since there is always a top quark in the signal and backgrounds, the identification procedure of b-jet from top quark using M min bℓ reduces both signal and background slightly; (2) The tt and ttj events can be further reduced by about one order with the forward jet selection. While the signal only loses about 1/3 events; (3) The Higgs mass window cut can further remove 4/5 events of the backgrounds but keep almost 1/2 of events of the signal.
For each signal point, we calculate the statistical significance S/ i B i and systematic significance S/ i B i for the luminosity L = 3000 fb −1 , where B i represents the number of background events of the i-th background process. From Tab. I, we can see the observability of the pure pseudoscalar interaction (ξ = π/2) at 14TeV HL-LHC is the most promising, with a ∼ 4σ level statistical significance but a low systematic significance ∼ 1.5%. Furthermore, it should be noted that consistency with the current Higgs data when ξ = π/2 requires the values of y t /y SM t to be within the range 0.4-0.6. This will cause a reduction of the cross section of thj by a factor ∼ 2/3, making the observation more challenging at the LHC.

Cuts σ [fb]
thj tt ttj ξ = 0 ξ = π/4 ξ = π/2 (C1) ∆R ij > 0.4, i, j = b, j or ℓ 0.3169 0.6700 2.1860 467.09 661.00  Since the CP-violating interaction described by (1) can affect the chirality of tbW coupling through the interference between different Feynman diagrams, we will investigate the top quark polarisation asymmetry in the process pp → t(→ ℓ + ν ℓ b)h(→ bb)j. The angular distribution of the lepton from a polarised top quark is given by: where the lepton spin analysing power κ ℓ is one at tree level in the SM, θ ℓ is the angle between the direction of the top quark and the lepton momenta in the rest frame of the top quark and P t is the spin asymmetry. We reconstruct the top quark rest frame by minimising χ 2 , which is defined as: where ∆m t is taken as the SM top quark decay width [28]. With the on-shell condition of the W boson and the top quark, the longitudinal momentum of the neutrino p νL can be determined as: where A W = m 2 W + 2p ℓT · E T . The ambiguity of the sign in (7) can be removed by the minimal χ 2 requirement [37].
In Fig. 7, we plot the lepton angular distributions cos θ ℓ for the CP phase ξ = 0, π/4 and π/2 in the signal pp → t(→ ℓ + ν ℓ b)h(→ bb)j at parton level and reconstruction level respectively after the cuts (C3) and (C4) (c.f. Tab. I). From Fig. 7, we can see that the direction of the lepton is inclined to be opposite to its parent top quark for ξ = 0, which corresponds to the SM top-Higgs interaction. However, the mixed and pseudoscalar interactions will affect the polarisation state of the top quark and change the slopes such that the number of events with cos θ ℓ > 0 is larger than those with cos θ ℓ < 0. The differences between the slopes are diluted from the parton level to the reconstruction level.

IV. CONCLUSION
In this paper, we have obtained constraints on the CP-violating top-Higgs couplings using the current Higgs data and found that values of CP-violating phase |ξ| > 0.6π are already excluded at 95% C.L.. We expected TLEP to improve this exclusion region to |ξ| > 0.07π. With current constraints on ξ, we further investigate the observability of the scalar, pseudoscalar and mixed top-Higgs interactions through the channel pp → t(→ ℓ + ν ℓ b)h(→ bb)j. We found that the observation of pseudoscalar interaction is the most promising at the HL-LHC but is still very challenging due to a low of S/B ratio. However, the anomalous top-Higgs couplings can lead to sizeable differences in forward-backward asymmetries and can be distinguished by measuring the lepton angular distributions from polarised top quarks at 14 TeV LHC.