Searching for Heavy Charged Higgs Bosons through Top Quark Polarization
Abdesslam Arhrib Adil Jueid Stefano Moretti





aarhrib@gmail.com
Département de Mathématiques, 
Faculté des Sciences et Techniques,
Université Abdelmalek Essaadi, B. 416, Tangier, Morocco.


adil.jueid@sjtu.edu.cn

INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology,
Department of Physics and Astronomy, Shanghai Jiao Tong University,
Shanghai 200240, China.


s.moretti@soton.ac.uk
School of Physics and Astronomy, University of Southampton,

Southampton, SO17 1BJ, United Kingdom.


We study the production of a heavy charged Higgs boson at the Large Hadron Collider (LHC) in gb → H^- t within a 2-Higgs Doublet Model (2HDM). 
The chiral structure of the H^+ t̅ b coupling can trigger a particular spin state of the top quark produced
 in the decay of a charged Higgs boson and, therefore, is sensitive to the underlying mechanism of the Electro-Weak Symmetry 
 Breaking (EWSB). Taking two benchmark models (2HDM type-I and 2HDM type-Y) as an example, we show that inclusive 
 rates, differential distributions as well as forward-backward asymmetries of the top quark’s 
 decay products can be used to search for heavy charged Higgs bosons as well as a model discriminators.


Searching for Heavy Charged Higgs Bosons through Top Quark Polarization
    Stefano Moretti
    
=======================================================================






§ INTRODUCTION
	


The top quark is believed to play an important role in  new phenomena beyond the Standard Model (SM).
It was discovered at the  Tevatron by the D0 <cit.> 
and CDF <cit.> collaborations about two decades ago. It is the heaviest
elementary particle we know of with a mass close to the EW scale (m_t = 172.5 GeV). The implications of this are manifold. (i) The top quark has a very short lifetime compared to hadronization time scales. (ii) It strongly couples to the SM Higgs boson and therefore can affect its phenomenology in a significant way. (iii) Its mass is an important input for  studies related to the vacuum stability of the universe. However, the large mass of the top quark also implies that it can be produced in reasonable numbers only at high energy accelerators, such as the Large Hadron Collider (LHC). Further, the short lifetime of the top quark (τ_t ≃ G_F^-1 m_t^-3≪ m_t/Λ_QCD^2) implies that all its fundamental properties can be pinned down by studying its decay products (for a review, see, e.g., <cit.> and references therein). 

The 2-Higgs Doublet Model (2HDM) is one of the  simplest extensions of the SM proposed four decades ago (for a review, see, e.g.,  <cit.>). In this model, two complex doublets 
are introduced to break the EW gauge symmetry and give rise to fermion and gauge boson masses. After Electroweak Symmetry Breaking (EWSB), there are five physical Higgs states (which can be regarded as mediators of mass generation dynamics): two neutral CP-even ones (h^0 and H^0, with m_h^0<m_H^0), one CP-odd neutral one (A^0) and a pair of charged ones (H^±). The top quark couples to all of these particles. Hence, top quark processes have been studied extensively within the 2HDM  because  the structure of the new Yukawa couplings can  reveal the properties of the underlying 2HDM <cit.>. 


The purpose of this short report is to discuss the polarization effects of the top quark in studies of the charged Higgs bosons at the LHC taking the 2HDM as a benchmark model. We discuss two  Yukawa realizations of the 2HDM:  i.e.,  the 2HDM Type-I (2HDM-I) and  2HDM Type-Y (2HDM-Y). The spin observables (which consist of angular and energy distributions of the decay products) of the top quark can improve the sensitivity of searches for charged Higgs bosons so long that the chiral structure of the H^+ t̅ b vertex is non-trivial.




§ PRODUCTION OF CHARGED HIGGS BOSONS IN ASSOCIATION WITH TOPS





For details about the model and the constraints used in this study, we refer the interested reader to <cit.>. It is customary to study H^± production in association with a top quark (bg→ tH^- + c.c.) <cit.> so that the cross section is controlled by the H^+t̅ b coupling. It is  convenient to write the aforementioned vertex in the form

    g_t̅ bH^+ = i (C_L P_L + C_R P_R ),

with C_L = 1/√(2) v m_t κ_u^A and 
C_R = 1/√(2) v m_b κ_d^A, wherein κ_u,d^A are the Yukawa couplings (please see, e.g., <cit.> from more details about the phenomenology of the Yukawa sector in the 2HDM). The nature of the chiral structure of the H^+ t̅ b coupling depends on tanβ. First, in the 2HDM-I (and 2HDM-X), both the R- and L-handed components are proportional to 1/tanβ and hence, given that C_L ∝ m_t while C_R ∝ m_b, the H^+t̅ b coupling is dominated by the L-handed component. In contrast, in the 2HDM-II (and 2HDM-Y), the L- and R-handed components of  the H^+t̅ b coupling behave differently depending on tanβ: (i) for tanβ < √(m_t/m_b)(tanβ>√(m_t/m_b)) the coupling is dominated by the L(R)-handed component;  (ii) for tanβ≈√(m_t/m_b), the coupling is purely scalar (with no γ_5 structure). 
We display in Fig. <ref> the dependence of the chiral components C_L,R of the H^+t̅b vertex and the production cross section upon tanβ. We can see that the cross section in the 2HDM-Y falls to a dip around  tan^2β≈ m_t/m_b  and then increases for large tanβ. In the 2HDM-I, however, it decreases always for increasing tanβ. As for the H^+t̅b vertex,  we notice first that C_L is decreasing as a function of tanβ  in both types of 2HDM (the corresponding lines in fact overlap). However, in the 2HDM-Y, C_R can be about two orders of magnitude larger than C_L for large tanβ values. 

For definiteness, in what follows,  we will choose our benchmark scenarios with tanβ=1 for the 2HDM-I and tanβ=50 
 for the 2HDM-Y which give:

    
  * (C_L,C_R) = (0.94, -0.025) for 2HDM-I;
    
  * (C_L,C_R) = (0.019, 1.3) for 2HDM-Y.

 Before closing this section, we briefly discuss Next-to-Leading Order (NLO) QCD corrections to the production cross section. It was shown that corrections to kinematical quantities (such as the b-jet transverse momentum) imply an almost constant K-factor <cit.>. These corrections also improve the agreement between the 4-Flavor scheme (4FS) and 5-Flavor Scheme (5FS)[We notice that the gg→b̅ t H^- process is the 4FS equivalent of the bg→ tH^- channel in the 5FS <cit.>.]. The authors of <cit.> have found that spin observables used in this paper are mildly dependent on the perturbative order used in the calculations: specifically, (i) no substantial corrections to angular observables and (ii) constant corrections to observables based on the b-jet energy distribution. 




§ PHENOMENOLOGICAL SETUP



In this section, we discuss the observables that we have used to study the sensitivity of this production process to
top polarization effects, as a function of tanβ and m_H^±. We believe that these observables are important to pursue two goals: (i) distinguish the signal from the SM backgrounds and (ii) disentangle different Yukawa realizations of the 2HDM from each other (or different BSM models from each other).
 
First, one can study the 
 differential distribution 
 in cosθ_ℓ^a of the emerging lepton which is 100% correlated to the top quark producing it

    1/σdσ/dcosθ_ℓ^a = 
       1/2(1 + α_ℓ^± P_t,t̅cosθ_ℓ^a),

wherein α_ℓ^± is the so-called spin analyzing power of the  charged lepton and θ_ℓ^a = ∡ (ℓ̂^±, Ŝ_a), with ℓ̂^± being the direction of flight of the charged lepton in the top quark rest frame and Ŝ_a the spin quantization axis in the basis a. In this work, we focus on the helicity basis where the spin quantization axis is defined to be the direction of motion of the top quark in the so-called (tt̅) Zero Momentum Frame (ZMF). It was found that energy distributions of the decay products (and their ratios) in the laboratory frame are excellent probes of top quark polarization. These observables were proposed by <cit.> as a probe of new physics and used as a way to probe anomalous W^+t̅b couplings in <cit.>. They are given by 

    u = E_ℓ/E_ℓ+E_b,     
    z = E_b/E_t,     
     x_ℓ = 2 E_ℓ/m_t,

where E_ℓ, E_b and E_t are the energies of the charged lepton, 
b-jet and  the top quark in the pp center-of-mass frame, respectively. 

We use Madgraph5_aMC@NLO <cit.>, MadSpin <cit.> and Pythia8 <cit.> for the generation of the hard-scattering processes at LO, decay of heavy-resonances and showering/hadronization, respectively. Then, Rivet 2.5.4 <cit.> was used for particle-level analysis where jets are clustered with the help of FastJets <cit.> using the  anti-k_⊥ algorithm with jet radius D=0.5. Top quark candidates were reconstructed using the PseudoTop definition <cit.> used widely by the ATLAS and CMS collaborations. We finally use a Rivet analysis for the validation of the CMS measurement of the tt̅ differential cross section at √(s)=8 TeV <cit.>. 




§ RESULTS



Events are selected if they contain exactly one isolated charged lepton (electron or muon not from tau decays), at least 5 jets (where at least 3 of these are b-tagged) and missing transverse energy (which corresponds to the SM neutrinos from W^± boson decays). We require the presence of one electron(muon) with p_T > 30 GeV(p_T > 27 GeV) and |η|< 2.5(|η| < 2.4. The missing transverse energy  is required to satisfy E_T^miss > 20 GeV. We first require p_T > 30 GeV and |η| < 2.4 for all the jets in an event. We then refine our selection criteria by vetoing events which do not have a leading jet with p_T > 50 GeV.  This set of cuts will be denoted by Cuts1. We impose two additional cuts, denoted by Cuts2(Cuts3) on the scalar sum of the jet transverse momenta: i.e. we impose H_T > 500 GeV(1000 GeV). 

For the production of a charged Higgs boson in association with a top quark followed by the H^±→ t b decay, where one top decays hadronically and the other one leptonically, there are many background contributions. The most important ones are the exclusive production of a top (anti)quark pair in association with a b-quark (i.e., tt̅ b + c.c.),  top quark pair production in association with a light jet and tt̅ inclusive production. The first one is completely irreducible while the second one might contribute since the associated light jet can be mis-tagged as a b-jet, then, the third background is partially reducible since the production of additional b-quarks is possible from the parton shower, notably in g→ bb̅ splitting, but it is not a leading effect. There are further possible background processes, such as single top, di-boson and W^± + jet production, but these are generally negligible compared to the previous ones. 

Using  a standard top (anti)quark reconstruction procedure on both heavy flavor states combined with  the requirements on jet activity and the cuts in H_T will reduce substantially the background. To enable the possible observation of a signal, we compute its significance defined as <cit.>

    𝒮 = √(2 ((N_s+N_b) log(1+N_s/N_b) - N_s)),

where N_s(N_b) is the number of signal(background) events 
after a given selection. We finally compute these for ℒ = 200 and 1000 fb^-1 of  integrated LHC luminosity. The obtained values are  displayed in Tab. <ref>. 






   

In the left panel of Fig. <ref>, we show the cosθ_ℓ^k spectrum for the irreducible SM background (denoted by Sm) as well as the 2HDM-I and 2HDM-Y after applying the basic selections. We can see clearly that the Sm curves exhibit almost no dependence on cosθ_ℓ^k except for some negative values of it. The interesting observation is that the 2HDM-I and 2HDM-Y have opposite slopes and hence different polarization with different sign. We can see that, in 2HDM-Y, the cosθ_ℓ^k is not able to distinguish between the different masses of the charged Higgs. The u-variable is displayed in the right panel of Fig. <ref> for the Sm plus the 2HDM-I and 2HDM-Y for m_H^± = 500 GeV. We can see that u is more sensitive and can efficiently separate between the three different models[For more details about the results, please see <cit.>.]. 

To quantify the sensitivity of the spin observables on the modelling paradigm, we suggest the use 
of forward-backward asymmetries constructed from the observables defined in Eqs. (<ref>)–(<ref>). Asymmetries are  resilient to NLO QCD corrections and  the choice of flavor scheme. We define an asymmetry A_X as 

    A_X = σ(X > X_c) - σ(X < X_c)/σ(X > X_c) + σ(X < X_c),

with X = cosθ_ℓ^k, x_ℓ, u and where X_c is a reference point for the asymmetry A_X. In the present study, we choose
the following references points: cosθ_ℓ,c^k = 0, x_ℓ,c = 0.6 and u_c = 0.5. In Tab. <ref>, we show the values of the three 
asymmetries in the SM and the two usual 2HDM types. It is clear that A_θ_ℓ can distinguish between the SM and the two realizations of the 
2HDM considered here. Furthermore, this asymmetry can even distinguish between 
the different masses for the 2HDM-I case. Further, for the 2HDM-Y,  A_θ_ℓ is insensitive to the mass of the charged Higgs boson. However, 
A_x_ℓ is able to remove this degeneracy for the 2HDM-Y.





§ CONCLUSIONS


We studied the sensitivity to spin observables in charged Higgs boson searches at the LHC. We have shown that these observables (both angles and energies of the H^± decay products) may improve the sensitivity of the LHC upon charged Higgs boson signals which can be further improved if forward-backward asymmetries are used. Further, we found out that these observables can be used for characterization analyses as post-discovery tools. We would expect that a fully-fledged signal-to-background selection should be attempted now by ATLAS and CMS, possibly in conjunction with machine learning methods trained to acquire the  spin dynamics affecting differently an H^± induced signal and SM background. We illustrated that these kinematical variables (and the asymmetries constructed out of them) are resilient to NLO QCD corrections and the choice of the flavor scheme inside the proton. Finally, we should close by remarking that our approach can be exploited for a variety of other new physics frameworks containing such (pseudo)scalar charged states so long that they induce chiral structures in the H^+t̅b vertex that are predominantly L- or R-handed.



§ ACKNOWLEDGMENTS



The work of AJ is supported by CEPC theory program and by the National Natural Science Foundation of China 
under the Grants No. 11875189 and No.11835005.
SM is supported in part through the NExT Institute and the STFC CG ST/L000296/1.  AA  and SM acknowledge funding via the H2020-MSCA-RISE-2014 grant no. 645722 (NonMinimalHiggs). 

JHEP


