A Heavy Scalar at the LHC from Vector Boson Fusion

A hypothetical scalar mixed with the standard model Higgs appears in few contexts of new physics. This study addresses the question what mass range is in the reach of $14$ TeV LHC given different magnitudes of mixing angle $\alpha$, where event simulations are based on production from vector boson fusion channel and decays into SM leptons through ${\rm WW}$ or ${\rm ZZ}$. It indicates that heavy scalar mass up to $539$ GeV and $937$ GeV can be excluded by integrated luminosity of $300$ $\rm{fb}^{-1}$ and $3000$ $\rm{fb}^{-1}$ respectively for $\sin^{2}\alpha$ larger than $0.04$.

≤ m H ≤ 1000 GeV in model-independent way. This is achieved in terms of the measured production cross section [7,8] and decay [9] for the SM-like Higgs. While the background for SM diboson signal is reconstructed by using the data of 20.3 f b −1 at the 8 TeV LHC 1 .
Given different integrated luminosity the mass ranges for 5σ discovery at 8 TeV LHC will be explicitly work out for small, moderate and large mixing effect, respectively.
Section IV is devoted to the application to new physics models. We show that in two interesting examples, i.e., the next-to-minimal supersymmetric model (NMSSM) and the scalar singlet extension of SM, some part of the parameter space is exactly covered by the phenomenological study of Sec. II and III. Finally, we conclude in Sec.V.

II. PRODUCTION CROSS SECTION AT THE LHC
When there is a new scalar state H which has the same spin, parity and quantum numbers as the SM-like Higgs h they probably mix with each other. In this section we discuss the production and decay of such scalar in the case of weak mixing as allowed by the precise measurement on the SM Higgs couplings. We focus on the discovery of this scalar through the SM diboson excess at the LHC, which will shed light on the W W and Z Z excesses at ∼ 3σ level reported by the ATLAS collaboration.
Let us define the mass squared matrix for state vector (H, h) in the decoupling limit as, In the next section such realization will be shown to cover much of parameter space of new physics models. Because of small ∆m 2 the mass eigenvalues will be slightly modified as, Remarkably, the strengths of SM-like couplings h − X i − X i , where X i refers to the SM vector bosons and fermions, are reduced in compared with the SM expectation, and conversely those of couplings H − X i − X i are enhanced. Note that their tree-level values are zero in the decoupling limit. In the presence of the mixing effect these couplings are given by in normalized to what the SM expects, where The present LHC experiments on the precise measurement of SM-like Higgs coupling leads to an upper bound on the small quantity sin 2 α ≤ 0.04 [5].
The production cross section σ (pp → H) can be obtained through that of the SM-like Higgs,   The property among the couplings H − X − X may be violated in some specific situation, e.g., in the parameter space of minimal supersymmetric SM model with tan β = 1. As in the large tan β-region the b-quark fusion process will dominate the production cross section for H instead of gluon fusion [10], as a result of enhanced Since the mixing effect is rather small, the branching ratio Br(H → V i V i ) is mildly dependent on the mixing effect through the possible decay H → hh. Take the approximation in which this channel is ignored, we show in Fig.2 and Fig.3 the production cross sections of SM dibosons through the intermediate scalar H. We have not shown the bi-quark and bi-lepton channels, as they are so tiny in compared with the W W and Z Z channels. We refer the reader to HEDCAY [9] for more details about the branching ratios for each H decay channel. See also [8].
Among diboson decay chanels, H → g g and H → γγ are bounded by the LHC Run I searches on dijet [11] and γγ [12] signal, respectively, In the light of Fig.2, we find that H with mass below ∼ 200 GeV has been excluded. In what follows, we mainly focus on the range 300 GeV ≤ m H ≤ 1000 GeV.
Very recently, the ATLAS collaboration reported both W W and Z Z excesses at 3σ level [6] at the 8 TeV LHC.

III. PROSPECT FOR DISCOVERY
In order to discuss the prospect for 5σ discovery for H, the SM background for diboson production at the LHC should be reconstructed. In terms of the data of 20.3 fb −1 collected by the LHC Run I data for Z Z production [13] and W W production [14], the production cross sections σ SM (pp → Z Z) and σ SM (pp → W W ) can be reproduced accordingly. See [15,16] for other diboson channels.
By combining Fig.2 we show in Fig.4 and Fig.5  • for moderate mixing 0.02 ≤ sin 2 α < 0.04, m H below 1 TeV can be fully detected with data of 200 fb −1 through the Z Z decay.
• for small mixing effect sin 2 α < 0.01, there is no chance for the discovery in the whole mass range 100 GeV ≤ m H ≤ 1000 GeV except that we have significantly larger integrated luminosity.
The analysis can be performed for the 14 TeV LHC similarly. Once σ SM (pp → Z Z) and σ SM (pp → W W ) are measured at the 14 TeV LHC, it can be completed in terms of Fig.3.

IV. EXAMPLES
In this section we apply the phenomenological insights in the previous two sections to two interesting example, i.e., NMSSM and a real scalar singlet extended SM. We show that either the NMSSM with Peccei-Quinn (PQ) symmetry (IV.A), or the scalar singlet extension of SM with only quartic coupling between singlet and Higgs (IV.B), is covered by our scenario in some part of parameter space. These examples indicate that scalar weakly mixed with the SM-like Higgs is the main signal at the LHC.

A. NMSSM with PQ symmetry
The first example is the NMSSM with an approximate U(1) PQ symmetry. The parameter space of such model is composed of only five model parameters {λ, κ, A λ , tan β, m 2 s } 2 , in which λ and κ appear in the Lagrangian as L ∼ λSH µ H d + κ 3 S 3 + · · · , and A λ refers to the A-term. Under the decomposition, we obtain the 3 × 3 squared mass matrix of CP-even neutral scalars can be satisfied in various situations.
• Case I: sin 4β = 0, and λ = 0. In this case the NMSSM is actually not well defined.
• Case III: sin 4β = 0, and x = 0. This case is reasonable for small soft mass m s , which is true in some specific model buildings, e.g., conventional gauge mediation. The decoupling limit in this case correspond to κ = 0, x = 0 and β c = π/4. Introduce a small deviation β = β c + δ, where | δ |<< 1, it gives rise to small mixing between h and H through non-zero M 2 12 , in which the mass matrix in Eq.(8) is reduced to From Eq.(10) we obtain the mass eigenvalues, Here mt denotes the stop scalar mass. The non-zero matrix element M 2 13 contributes to order δ 4 correction to masses m 2 H and m 2 s . For completeness, we outline mass eigenvalues for CP-odd and charged scalars, For the PQ Goldstone mode m A 2 ∼ 0, and µ eff = A λ /2.
Through M 2 13 scalar s indirectly mixes with h through mixing with scalar H. Therefore, the mixing effect between h and s can be ignored in compared with that of h and H. This implies that NMSSM with parameter choices in the case III, is effectively covered by the new physics model discussed in Sec. II and III. In order to explain the observed Higgs mass m h 125.5 GeV [1] mt > 1 TeV is required similar to the MSSM. Take these points into account scalar H might be the main signal at the LHC.

B. SM With Scalar Singlet
Consider the scalar singlet extension of SM with a real scalar s. As a SM singlet, s can directly couple to the SM Higgs. We employ a Z 2 parity 3 under which s is odd for simplifying the potential V , For simplicity, we assume that all dimensionless couplings in Eq.(13) are positive. Whether the mixing between s and h happens depends on the signs of µ 2 s , which corresponds to different vacuum structures. Write the vacuum expectation values (vevs) as s = υ s and H = υ, they must satisfy, Expand the fields as s = υ s + s and H = (υ + h/ √ 2, 0), we obtain the mass squared matrix for the basis (h, s) T , Eq. (15) and Eq. (14) imply that mixing effect occurs only when the signs of µ 2 s and µ 2 are both negative. If so, the magnitude of mixing effect between h and s is controlled by parameter κ.
For small κ the LHC phenomenology of this model is totally covered by the previous discussions in Sec. II and III. If λ s is also small, s can be further constrained by the decay h → ss for m s < m h /2 [20]. Fig.6 shows the value of κ consistent with the present measurement on the Higgs invisible decay branching ratio Br inv ≤ 0.29 [21] .

V. CONCLUSION
In this paper we have considered the prospect for the discovery of SM singlet which weakly mixes with the SM Higgs. Take into account the allowed magnitude of the mixing effect by the precise measurement on the Higgs couplings, we have shown the mass ranges for 5σ discovery at the 8 TeV LHC for different integrated luminosities. This scenario can be applied to many interesting new physics models. For illustration, we explicitly consider the NMSSM and scalar singlet extension of SM, in which we show that our scenario covers much of the parameter space for each case.