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Production of the charged Higgs bosons at the CERN Large Hadron Collider in the left-right symmetric model

We study the production of the charged Higgs boson at the LHC in the left-right symmetric model. It is shown that there exists a lower bound of the cross section. We investigate that predicted cross sections of this model are generally larger than those of the two Higgs doublet model or the minimal supersymmetric model.

H ± . However, the structure of the Yukawa couplings and potential of the bidoublet Higgs fields are much different from those of the two doublet Higgs fields. Therefore, it leads to different charged Higgs boson phenomenologies from those in the 2HD model. Constraints on the charged Higgs boson parameter space in the LR model with the present experimental data from Tevatron, LEP and Belle has been presented in Ref. [17]. In this work, we explore the production of H ± bosons at the LHC in the LR model. This paper is organized as follows: In section 2, we briefly review the Higgs sector of the LR model. The production cross sections at the LHC are presented in section 3 and we conclude in section 4.

II. THE HIGGS SECTOR OF THE LEFT-RIGHT SYMMETRIC MODEL
The left-right symmetric model involves an additional SU(2) R symmetry which has to be broken at the higher scale than the electroweak scale. Two triplet Higgs fields ∆ L (3, 1, 2) and ∆ R (1,3,2) represented by are introduced to break the additional symmetry of the model. Actually ∆ R breaks the SU(2) R symmetry and another triplet ∆ L is just introduced as a result of manifest left-right symmetry. The kinetic terms for Higgs fields are given by where the covariant derivatives are defined by The spontaneous breaking of gauge symmetries is triggered by the vacuum expectation values (VEV) The SU(2) R breaking scale v R should be higher than the electroweak scale, k 1,2 ≪ v R since W R should be heavier than W L . Note that v L is irrelevant for the symmetry breaking and just introduced in order to manifest the left-right symmetry. The see-saw relation for the neutrino mass m ν ∼ M LL + M 2 LR /M RR tells us that v R is typically very large ∼ 10 11 GeV, where M ij are the matrix elements for the masses in the (W L , W R ) basis. Then the heavy gauge bosons are too heavy to be produced at the accelerator experiments and the SU(2) R structure is hardly probed in the laboratory. Provided that v R is assumed to be only moderately large v R ∼ O(TeV) for the heavy gauge bosons to be studied at LHC, the Yukawa couplings require to be suppressed in order that the neutrino masses are at the eV scale and v L should be very small or close to 0. This is achieved when the quartic couplings of (φφ∆ L ∆ R )-type terms in the Higgs potential are set to be zero [18,19]. This limit is warranted by the approximate horizontal U(1) symmetry [20] as well as the see-saw picture for light neutrino masses. We adopt this limit here. Higgs boson masses are not affected by taking this limit [19].
The general Higgs potential in the LR model has been studied in Refs. [18,19,21]. We define the parameters ξ = k 2 /k 1 and ǫ = k 1 /v R for convenience. The parameter ξ is the ratio of two VEVs for the EWSB which is corresponding to tan β in the 2HD model. Since ǫ ≪ 1, we will present our formulas as powers of ǫ. Taking the limit that the quartic couplings for (φφ∆ L ∆ R ) terms and v L go to 0 as mentioned above, the charged Higgs boson mass matrix is given in the basis of (φ + 1 , φ + 2 , δ + R , δ + L ) by where m 2 + = α 3 v 2 R /2(1 − ξ 2 ) with the quartic coupling α 3 for Tr(φ † φ∆ L ∆ † L ) + Tr(φ † φ∆ R ∆ † R ) term [19]. If ξ > 1, α 3 should be negative to avoid the dangerous negative mass square of scalar fields. Note that δ + L field from the Higgs triplet ∆ L decouples from other three charged Higgs fields with mass m and is irrelevant for our phenomenological discussion here. The mass of the lightest charged Higgs boson is given by after diagonalization. Since m H ± depends on the coupling α 3 , it is an independent observable. Thus the charged Higgs phenomenologies are expressed in terms of two parameters ξ and m H ± . Note that the mass of W R boson does not appear at the charged Higgs phenomenology. No CP violation in the Higgs sector is assumed for simplicity. Violating the lepton numbers and baryon numbers, the triplet Higgs fields do not allow the ordinary Yukawa coupling terms for Dirac fermions. Thus quark and lepton masses are derived from the Yukawa couplings in terms of the bidoublet Higgs fields, given by where Ψ i = (Û ,D) † is the flavour eigenstates,φ = τ 2 φ * τ 2 , and F , G are 3 × 3 Yukawa coupling matrices. We rotateÛ andD into the mass eigenstates by unitary transforms, The Yukawa coupling matrices F and G are given in terms of where k 2 − = |k 1 | 2 − |k 2 | 2 and M U and M D are diagonal mass matrices for U -type and D-type quarks respectively. Note that these solutions for the Yukawa coupling matrices no longer hold for ξ = 1 we have to treat the ξ = 1 case in a separate way. We do not consider that case in this work. Although small ξ is preferred in order to generate the ratio m b /m t , ξ > 1 region cannot be excluded in general.

III. PRODUCTION OF THE CHARGED HIGGS BOSON AT THE LHC
The relevant interaction lagrangian of the charged Higgs boson production is given by where the couplings are defined by The light charged Higgs boson such that m H ± < m t − m b can be produced through the top quark decay t → bH ± sequentially after the top quark pair production at the LHC. The cross section of top quark pair production σ(pp → tt) = O(1 nb) implies that 10 8 pairs of top quarks will be produced with expected integrated luminosity of 100 fb −1 at the LHC. We show the light charged Higgs boson production defined by the cross section times branching ratio, σ(pp → tt) · Br(t → bH + ) in Fig. 1. We use the total cross section for tt production as 833 pb for next-to-leading order (NLO) QCD corrections including next-to-leading-log (NLL) resummation [23]. The branching ratio of the top quark decay is constrained by the measurement at the Tevatron, Br(t → W b) = 0.94 +0.31 −0.24 [22]. The decay of the top quark into a light H ± boson has been examined by the CDF collaboration at Tevatron to obtain the exclusion region on the model parameter space with the absence of the observed charged Higgs boson in the MSSM [1] and in the LR model [17]. The parameter space (ξ, m H ± ) of the LR model is severely constrained by the Tevatron data, even there is a conservative lower bound of m H ± > 145 GeV. The solid parts of the plots are predictions with allowed parameters in the LR model. As a benchmark, the productions of H ± in the MSSM are also plotted with varying tan β. Yukawa couplings of the LR model have a definite lower bound as ξ varies, so do the production cross sections. We may consider the graph for ξ = 0.01 to be the lower bound since the Yukawa couplings are saturated as xi becomes smaller. The cross section with ξ = 0.01 is almost same as that of the 2HD model with tan β ≈ 35. Thus we find that the productions in the LR model are generically larger than those in the 2HD model unless tan β is large.
If H ± is heavier than the top quark, the gb → tH ± process is the most promising channel for direct production of H ± boson at the LHC. We write the scattering amplitude as iM(gb →tH + ) = ig sb T c ab ǫ(p g ) in terms of the Yukawa couplings given in Eq. (11) and obtain the partonic cross section aŝ where the colliding energy is kinematically allowed ifŝ > (m t + m H ) 2 . The hadronic cross section is given by where f g and f b are the parton distribution functions (PDF) for gluon and b-quark respectively. We use the leading order CTEQ6 functions for a gluon and a b-quark PDF in a proton [24]. The QCD factorization and renormalization scales Q are set to be the gb invariant mass, i.e., √ŝ . The NLO QCD corrections to gb → tH − process in the MSSM has been calculated in Refs. [25,26] and the next-to-next-to-leading order (NNLO) soft-gluon corrections calculated in Ref. [27]. They are shown to be substantial contributions to the production cross section and we include them.
Since the QCD corrections are model-independent, we can use the K-factors for the cross section given in Ref. [27] in order to include the QCD corrections for our work. The cross sections including NNLO corrections are depicted in Fig. 2. As a benchmark, the cross sections in the MSSM are also plotted. The running masses for top quark and bottom quark at the scale of m H ± have been used in the formula, e.g. m t ≈ 170 GeV and m b ≈ 2.9 Gev for m H ± = 200 GeV. The supersymmetric NLO QCD corrections calculated in Ref. [26] are relatively small and depends on the SUSY parameters and we do not include them here. Contribution from the 2 → 3 process, gg → tbH − is not considered in this paper. This is considerable, but essentially common process which shows the same trends with a factor two or three smaller than the gb → tH − process in both models. The ξ-dependence of the cross section is shown in Fig. 3. Near ξ = 1, the cross section drastically increases and it is saturated as ξ goes far off. As in the case of the light H ± , there is a lower bound for the production cross section σ(pp → gb →tH + ) in the LR model. The lower bound value of the cross section of the LR model is close to that of the 2HD model with tan β = 57. Thus the cross section of the LR model is generally larger than that in the 2HD model except for large tan β region. We estimate that when tan β < ∼ 50. The cross section in the 2HD model increases as tan β increases but suppressed by m 2 b and the m 2 t term is suppressed by 1/ tan 2 β. In the LR model, the Yukawa couplings involve the factors of 2ξ/|1 − ξ 2 | or (1 + ξ 2 )/|1 − ξ 2 | instead of tan β or 1/ tan β, and they are of order O(1) or more. Thus the m 2 t terms in the cross section dominate and the cross section is larger than that in the 2HD model unless tan β is large enough.

IV. DECAY OF THE CHARGED HIGGS BOSON
The produced charged Higgs boson will decay into light particles. The dominant decay channel is H + → tb for m H ± > m t + m b due to large top quark mass. Another interesting channel is H + →τ ν by triggering with a high p T lepton. We consider the ratio of the decay width for H + →τ ν to that for H + → tb in the LR model and 2HD model. In the LR model, we have while the ratio in the 2HD model is given by where m b /m H ± , m τ /m H ± ≪ 1 and QCD corrections are ignored. The ratios are depicted in Fig. 4. We find that the ratio can be sizable in the 2HD model as tan β increases. It is as large as more than 10 % when tan β > 10, while the ratio is always negligible in the LR model by suppression of m 2 τ /m 2 t . Therefore we can discriminate the underlying Higgs structure of the charged Higgs boson by measuring the ratio Γ(H + →τ ν)/Γ(H + → tb) in the most interesting region of parameter space. When m H ± < m t − m b , the tau channel dominates like in the 2HD model.

V. DETECTION OF THE CHARGED HIGGS BOSON
As shown in the previous section, the H ± boson in the LR model mostly decays into tb(tb) when m H ± > m t + m b . The decay product contains two top quarks. We require one of the top quark to decay semileptonically, t → W b → lνb, and the other hadronically, t → W b → jj ′ b, for triggering and reconstruction of the top quark as well as the charged Higgs boson. The promising final states inside the detector are given by which involve three b-jets and an isolated lepton. The main background in the SM is coming from the tt pair production involving another b jet or other jets. The Monte Carlo simulations for the detection of the charged Higgs boson in the MSSM through H ± → tb have been performed by ATLAS [28] and CMS [29] groups to estimate the discovery potentials of H ± . The essential improvement is expected in the signal reconstruction if the b-tagging efficiency increases in the future. Their results show that the charged Higgs can be discovered up to 300 GeV at low luminosity period of the LHC with the integrated luminosity L ∼ 30 fb −1 . The discovery limit can be raised to be 400 GeV for high tan β (> 25). It is hard to discover the charged Higgs of the 2HD model with the mass above 400 GeV. On the other hand, the production cross sections of H ± in the LR model are generically larger than those in the 2HD model. The larger number of produced H ± bosons due to the larger production cross section indicates an improvement of the signal-to-background ratio since the background events are the SM processes. We expect the better visibility of the charged Higgs boson in the LR model, although no Monte Carlo study for H ± has been done yet in the LR model.

VI. CONCLUDING REMARKS
In this work, we have calculated the production cross sections of the charged Higgs boson in the LR model at the LHC. Observation of a charged Higgs boson is a clear evidence of existence of new physics beyond the SM. We see that the production cross sections of H ± in the LR model have lower bounds depending upon the charged Higgs mass. The cross sections in the LR model are generically larger than those of the 2HD model in the most region of tan β and the better visibility of H ± is expected through H ± → tb channel. We find that the decay into τν channel is strongly suppressed in the LR model due to the smallness of m 2 τ /m 2 t . Combining the cross section and the ratio Γ(H + →τ ν)/Γ(H + → tb), therefore, we can discriminate the LR model from the 2HD model as the underlying physics in the charged Higgs sector. If the production cross section of H ± is lower than the minimal value predicted by the LR model shown in Fig. 2, we can conclude that the LR model is not the underlying physics. When the H ± boson is observed with the production cross section large enough, it may be the ingrediant of either the LR model or the 2HD model with large tan β. In that case, the ratio Γ(H + →τ ν)/Γ(H + → tb) close to 0 indicates the LR model and the ratio of 10 % indicates the 2HD model with large tan β.
In conclusion, the charged Higgs sector can be crucially tested in the production and decay at the LHC. We study the LHC phenomenology of the charged Higgs boson in the LR model compared with that in the 2HD model.