Singlet Boson in Supersymmetric Model as a Mimic of the Standard Model Higgs at the LHC

We show that the gauge singlet scalar boson in low-energy supersymmetric model may behave as the standard model (SM) Higgs boson if the singlet couples to (heavy) vector-like colored particles. In this case, the SM-Higgs-like signal at the LHC can be mimicked by the singlet production process for wide range of the singlet mass.

In the field of particle physics, Higgs boson is the most important particle which should be experimentally found. Discovery of the Higgs boson itself is of course a great progress because it confirms the Higgs mechanism as the origin of electroweak symmetry breaking.
Once discovered, in addition, we will also be able to acquire information about the physics beyond the standard model (SM) by detailed study of the Higgs boson. This is because the properties of Higgs, in particular the Higgs mass, are strongly dependent on how the SM is embedded into the new physics model.
The most prominent example of physics beyond the SM is the low-energy supersymmetry (SUSY); the minimal SUSY SM (MSSM) predicts the existence of "light" Higgs boson. At the tree level, the MSSM predicts the Higgs mass to be smaller than the Z-boson mass. Even if loop corrections are taken into account, the upper bound on the Higgs mass is ∼ 135 GeV assuming that the stop mass is lighter than ∼ 2 TeV [1]. In many extended SUSY models, there still exists light Higgs boson. For example, in the next-to-the MSSM (NMSSM), which is the model with gauge-singlet superfield, the lightest Higgs mass is predicted to be smaller than 140 GeV as far as the perturbativity of coupling constants up to the grand unified theory (GUT) scale is assumed [2]. Thus, the existence of the light Higgs boson is a crucial check point of low-energy SUSY.
The LHC experiment is about to discover the Higgs boson if its mass is within the accessible range. Even if a Higgs-like object is found, however, it would be still a question whether it is really the Higgs boson which is responsible for the electroweak symmetry breaking. In the study of low-energy SUSY, this is an important question because some class of SUSY models may be discriminated based on the properties of the observe Higgslike object. Thus we should clarify if there is any possibility of a particle which may mimic SM-Higgs-like signals at the LHC.
In non-SUSY case, there are such possibilities [3,4]. In particular, the Higgs-like signal may show up at the LHC if there exists a singlet boson s which couples to vector-like colored fermions (or directly couples to gluon via the dimension 5 interaction of sG µν G µν , with G µν being the field strength of the gluon field) [4]. Because a singlet chiral multiplet appears in various SUSY models, including the NMSSM, we pursue this possibility in the framework of SUSY model .
In this letter, we will show that the SM-Higgs-like signal at the LHC can be easily mimicked if there exists a singlet field which couples to a new vector-like colored chiral supermultiplets. Thus, even if the LHC experiment finds a SM-Higgs-like signal at the mass region above the SUSY Higgs mass bound, low-energy SUSY is still a possibility. For this mechanism to work, we also show that there should exist colored particles with their masses smaller than 500 − 600 GeV.
First let us briefly summarize the basic idea how the SM-Higgs-like signal is mimicked in the SUSY model with singlet. As is well-known, the most efficient process of producing Higgs boson at the LHC is the gluon fusion process, which is induced by the top-loop diagram.
Thus, if the singlet field couples to colored particles, then we expect a significant production cross section for the singlet field due to the gluon fusion. In addition, in SUSY models with singlet (as in the case of NMSSM), the singlet mixes with the SM-like Higgs boson due to the superpotential and SUSY breaking interactions. Consequently, if the singlet dominantly decays via the mixing, then the LHC signal of the singlet production is like that of the SM-Higgs production.
To see this can really happen in SUSY model, we adopt the simplest set up. We introduce the gauge-singlet superfield S as well as the following vector-like chiral multiplets: one of the strong motivation to consider SUSY, we have introduced L andL so that the newly introduced fields can be embedded into the complete multiplet of SU (5) GUT . As we will show below, L andL are not important for the enhancement of the singlet-boson production at the LHC. In our analysis, we introduce N 5 -pairs of vector-like multiplets; the index i runs from 1 to N 5 . Notice that the perturbativity of the gauge coupling constant breaks down at high-energy scale if N 5 is too large. Requiring the perturbativity up to the GUT scale, we require N 5 ≤ 4 in our analysis.
Motivated by the NMSSM, we adopt the following form of the superpotential for the singlet field: where H d and H u are down-and up-type Higgses, respectively. For simplicity, the Yukawa coupling constants for the SD i D i and SL i L i terms are taken to be i-independent; this may be due to SU (N 5 ) flavor symmetry. We have checked that our conclusion does not significantly change even if we do not adopt this assumption. In addition, the relevant part of the soft-SUSY breaking term is given by In our analysis, for simplicity, we fix some of the parameters as The Higgs potential is also sensitive to some of the parameters in the MSSM Lagrangian.
Here, we take one of the important parameter, the tri-linear coupling for the stop (normalized by the top Yukawa coupling constant), as A t = 2 TeV, while other tri-linear scalar coupling parameters in the MSSM sector are taken to be 0. Here, we have adopted a relatively large value of the A t -parameter in order to satisfy the LEP bound for the lightest Higgs boson mass [8]. Furthermore, the masses of all the MSSM sfermions are taken to be 1 TeV. #1 Then, with other parameters being properly chosen, Higgs bosons acquire vacuum expectation values; rest of the parameters (i.e., λ, κ, m 2 H d , m 2 Hu , m 2 S ) are determined by fixing the following quantities: where · · · denotes vacuum expectation value. Here, µ eff plays the role of SUSY invariant Higgs mass (so-called µ-parameter) in the MSSM. In addition, once the singlet field gets a vacuum expectation value, then the newly introduced vector multiplets also become massive. #2 In the present model, the Higgs bosons are composed of five neutral and two charged scalar bosons: three CP-even Higgs bosons h a (with m h 1 < m h 2 < m h 3 ), two CP-odd Higgs bosons and charged Higgs bosons. #3 Because we are interested in the SM-Higgs-like signal at the LHC, we concentrate on the CP-even Higgs sector in the following.
The mass eigenstates h a are related to the gauge eigenstates using the unitary matrix S aA as follows: where h 0 d , h 0 u , and s are the real scalars in the gauge eigenstates H d , H u , and S, respectively. In the following, we consider the case that h 2 is (almost) the singlet field, so that |S 2s | ≫ |S 1s |, |S 3s |, |S 2d |, |S 2u |. #1 We assume that the gauginos are so heavy that they do not affect the following analysys. #2 One may also introduce a bare mass term for the vector-like multiplets. Extension of our analysis to such a case is straightforward. #3 We assume that the CP violation in the Higgs sector is negligible so that there is no mixing between the CP-even and CP-odd sectors. Now, we are at the position to discuss production and decay processes of the singlet Higgs at the LHC. The gluon fusion cross section for the process pp → h 2 → F (with F denoting the final state of the decay of h 2 ) is given by with where Γ(h 2 → F ), Γ(h 2 → gg) and Γ total are the partial decay widths of the decay processes h 2 → F , h 2 → gg and the total decay width of h 2 , respectively. In Eq. (6), √ s is the center of mass energy and g(x) is the gluon distribution in the proton. In the present set up, the process h 2 → F may be induced by the mixing with H d and H u as well as by the loop diagrams with D i andD i inside the loop.
With a relevant choice of parameters, we found that the process h 2 → gg is dominated by the loop diagrams with D i andD i inside the loop, while the decay processes into the weak boson pairs h 2 → V V (with V V = ZZ or W + W − ) are due to the mixing effect. Thus, and where Γ(h SM → V V ) is the partial decay width of the SM Higgs boson (with the mass of m h 2 ). In Eq. (7), where and [5]. In fact, I D ≃ 1 when x D 1, so we approximate I D = 1 in our numerical calculation. Then the results are insensitive to the choice of y D (as far as m D is assumed to be larger than m h 2 ).
One important point is that the decay width Γ(h 2 → gg) (and hence the gluon fusion cross section) is proportional to N 2 5 ; this is because the amplitude is proportional to the number of particles inside the loop. Thus, as we increase the number of vector-like chiral multiplets, the signal of singlet Higgs production process is enhanced.
Using the formulae given above as well as the numerical package NMSSMtools [6], we calculate the cross sections for the Higgs production processes in the present set up. We have calculated the decay width of the SM Higgs to gluon-gluon mode at the leading order. Decay widths of the SM Higgs (except for the gg mode) are calculated by HDECAY package [7].
First, we show the cross section for the process pp → h 2 → V V normalized by the corresponding SM process: In our analysys, only the gluon fusion process, which is the dominant Higgs production process at the LHC, is taken into account.
In Figs. 1 and 2, we show the contours of constant R ZZ for √ s = 7TeV; we have checked that the behavior of R W + W − is almost identical. In the calculation, we have taken tan β = 3 and µ eff = 250 GeV (Fig. 1) and tan β = 5 and µ eff = 110 GeV (Fig. 2). In Fig. 1, the region with m h 2 195 GeV is excluded because the lightest Higgs becomes lighter than the LEP bound (i.e., 114.4 GeV) [8]. Such a result is partly because the choice of tan β parameter. case, they decay into an up-type light quark and W ± -boson. The current lower bound on the masses of such particles is about 400 GeV for N 5 = 4 [9].
Because the lightest Higgs mass is also an important parameter, we have calculated m h 1 in both cases. The results are shown in Figs. 3 and 4.
Finally, let us comment on the decay mode h 2 → γγ. As in the case of the process h 2 → gg, the decay width for the process h 2 → γγ may be also affected by the loop diagrams with the vector-like fermions inside the loop. Importantly, for h 2 → γγ, the W ± -loop diagram contribution is numerically significant as in the case of SM Higgs boson. Even though such a contribution is suppressed by the mixing factor (S 2d cos β + S 2u sin β), we have checked that the effect of W ± -loop diagram is comparable to that of vector-like-fermion loop in the parameter region we have studied. Thus, the branching ratio Br(h 2 → γγ) may significantly deviate from that of the SM Higgs boson.