Advances in High Energy Physics
Volume 2015 (2015), Article ID 980687, 12 pages
http://dx.doi.org/10.1155/2015/980687

Research Article

The Higgs Sector of the Minimal SUSY Model

Lorenzo Basso1,2

¹Universitè de Strasbourg, IPHC, 23 rue du Loess, 67037 Strasbourg, France
²CNRS, UMR7178, 67037 Strasbourg, France

Received 23 April 2015; Revised 17 June 2015; Accepted 25 June 2015

Academic Editor: Kai Schmidt-Hoberg

Copyright © 2015 Lorenzo Basso. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP³.

Abstract.

I review the Higgs sector of the extension of the minimal supersymmetric standard model (MSSM). I will show that the gauge kinetic mixing plays a crucial role in the Higgs phenomenology. Two light bosons are present, a MSSM-like one and a -like one, which mix at one loop solely due to the gauge mixing. After briefly looking at constraints from flavour observables, new decay channels involving right-handed (s)neutrinos are presented. Finally, how model features pertaining to the gauge extension affect the model phenomenology, concerning the existence of R-Parity-conserving minima at loop level and the Higgs-to-diphoton coupling, will be reviewed.

1. Introduction

The recently discovered Higgs boson is considered as the last missing piece of the standard model (SM) of particle physics. Nonetheless, several firm observations univocally call for its extension, mainly, but not limited to, the presence of dark matter, the neutrino masses and mixing pattern, the stability of the SM vacuum, and the hierarchy problem. Supersymmetry (SUSY) has long been considered as the most appealing framework to extend the SM. Its minimal realisations (MSSM and its constrained versions (for a review, see [1])) start however to feel considerable pressure to accommodate the recent findings, especially the measured Higgs mass of  GeV. Despite not in open contrast with the MSSM, the degree of fine tuning required to achieve it is more and more felt as unnatural. In order to alleviate this tension, nonminimal SUSY realisations can be considered. One can either extend the MSSM by the inclusion of extra singlets (e.g., NMSSM [2]) or by extending its gauge group. Concerning the latter, one of the simplest possibilities is to add an additional Abelian gauge group. I will focus here on the presence of group which can be a result of an heterotic string theory (and hence M-theory) [3–5]. This model, the minimal -Parity-conserving supersymmetric standard model (BLSSM in short), was proposed in [6, 7] and neutrino masses are obtained via a type I seesaw mechanism. Furthermore, it could help to understand the origin of -Parity and its possible spontaneous violation in supersymmetric models [6–8] as well as the mechanism of leptogenesis [9, 10].

It was early pointed out that the presence of two Abelian gauge groups in this model gives rise to kinetic mixing terms of the form

which are allowed by gauge and Lorentz invariance [11], as and are gauge-invariant quantities by themselves; see, for example, [12]. Even if these terms are absent at tree level at a particular scale, they will in general be generated by RGE effects [13, 14]. These terms can have a sizable effect on the mass spectrum of this model, as studied in detail in [15], and on the dark matter, where several scenarios would not work if kinetic mixing is neglected, as thoroughly investigated in [16]. In this work, I will review the properties of the Higgs sector of the model. Two light states exist, a MSSM-like boson and a -like boson. After reviewing the model, I will show that a large portion of parameter space exists where the SM-like Higgs boson has a mass compatible with its measure, both in a “normal” ( GeV) and in an “inverted” hierarchy ( GeV), also in agreement with bounds from low energy observables and dark matter relic abundance. The phenomenological properties of the two lightest Higgs bosons will be systematically investigated, where once again the gauge mixing is shown to be fundamental. The presence of extra D-terms arising from the new sector, as compared to models based on the SM gauge symmetry, has a large impact on the model phenomenology. They affect both the vacuum structure of the model and the Higgs sector, in particular enhancing the Higgs-to-diphoton coupling. Both of these issues will be reviewed here, although the latter is disfavoured by recent data [17], to show model features beyond the MSSM.

2. The Model

For a detailed discussion of the masses of all particles as well as of the corresponding one-loop corrections, we refer to [15]. Attention will be paid to the main aspects of the kinetic mixing since it has important consequence for the scalar sector. For the numerical investigations that will be shown, we used the SPheno version [22, 23] created with SARAH [24–28] for the BLSSM. For the standardised model definitions, see [29], while for a review of the model implementation in SARAH, see [30]. This spectrum calculator performs a two-loop RGE evaluation and calculates the mass spectrum at one loop. In addition, it calculates the decay widths and branching ratios (BRs) of all SUSY and Higgs particles as well as low energy observables like . We will discuss the most constrained scenario with a universal scalar mass , a universal gaugino mass , and trilinear soft-breaking couplings proportional to the superpotential coupling () at the GUT scale. Other input parameters are , , , , and . They will be defined in the following section. The numerical study here presented has been performed by randomly scanning over the independent input parameters above described via the SSP toolbox [31], while low energy observables such as BR() and BR() have been evaluated with the FlavourKit package [32]. Furthermore, during the scans, all points have been checked with HiggsBounds-4.1.1 [33–36], both in the “normal” hierarchy and in the “inverted” hierarchy case.

2.1. Particle Content and Superpotential

The model consists of three generations of matter particles including right-handed neutrinos which can, for example, be embedded in 16-plets. Moreover, below the GUT scale, the usual MSSM Higgs doublets are present as well as two fields and responsible for the breaking of . The field is also responsible for generating a Majorana mass term for the right-handed neutrinos and thus we interpret its charge as its lepton number. The same goes for , and we call these fields bileptons since they carry twice the lepton number of (anti)neutrinos. The quantum numbers of the chiral superfields with respect to are summarised in Table 1.

Table 1: Chiral superfields and their quantum numbers under , where .

Superfield
Spin-0
Spin-
Generations

3

3

3

3

3

3

1

1

1

1

The superpotential is given by

and we have the additional soft SUSY-breaking terms:

where , are generation indices. Without loss of generality, one can take and to be real. The extended gauge group breaks to as the Higgs fields and bileptons receive vacuum expectation values ():

We define in analogy to the ratio of MSSM ().

2.2. Gauge Kinetic Mixing

As already mentioned in the Introduction, the presence of two Abelian gauge groups in combination with the given particle content gives rise to a new effect absent in any model with just one Abelian gauge group: gauge kinetic mixing. This can be seen most easily by inspecting the matrix of the anomalous dimension, which for our model at one loop reads

with typical GUT normalisation of the two Abelian gauge groups, that is, for and for [7]. Therefore, even if at the GUT scale the kinetic mixing terms are zero, they are induced via RGE evaluation at lower scales. It turns out that it is more convenient to work with noncanonical covariant derivatives rather than with off-diagonal field-strength tensors as in (1). However, both approaches are equivalent [37]. Therefore, in the following, we consider covariant derivatives of the form , where is a vector containing the charges of the field with respect to the two Abelian gauge groups, is the gauge coupling matrix

and contains the gauge bosons .

As long as the two Abelian gauge groups are unbroken, we have still the freedom to perform a change of basis by means of a suitable rotation. A convenient choice is the basis where , since in this case only the Higgs doublets contribute to the gauge boson mass matrix of the sector, while the impact of and is only in the off-diagonal elements. Therefore, we choose the following basis at the electroweak scale [38]:

When unification at some large scale ( GeV) is imposed, that is, and , at SUSY scale, we get [15]

2.3. Tadpole Equations

The minimisation of the scalar potential is here described in the so-called tadpole method. We can solve the tree-level tadpole equations arising from the minimum conditions of the vacuum with respect to , , ,  and . Using and , we obtain

, and, thus, we find an approximate relation between and

For the numerical results, the one-loop corrected equations are used, which lead to a shift of the solutions in (9)–(12).

2.4. The Scalar Sector

In this model, MSSM complex doublets and bilepton complex singlets are present, yielding -even, -odd, and charged physical scalars.

Concerning the -even scalars, the MSSM and bilepton sectors are almost decoupled, mixing exclusively due to the gauge kinetic mixing. In first approximation, the mass matrix is block-diagonal and has mass eigenstates that mimic the MSSM case. In practice, it turns out that only two Higgs bosons are light (hereafter called and , one per sector), while the other two are very heavy (above the TeV scale). The lightest scalars are well defined states, being either almost exclusively doublet-like or bilepton-like. It is worth stressing that their mixing is small (see Figure 4) and solely due to the gauge kinetic mixing (see also [39]).

Concerning the physical pseudoscalars and , their masses are given by

For completeness, we note that the mass of charged Higgs boson reads as in the MSSM as

In this model, the -odd and charged Higgses are typically very heavy. In (10), we see that, compared to the MSSM, there is a nonnegligible contribution from the gauge kinetic mixing. LHC searches limit and TeV, since [40, 41]

at C.L. Notice that recent reanalysis of LEP precision data also constrains TeV at C.L. [42]. A consequence of this strong constraint in the BLSSM is that the first terms in (10)–(12) can be large, pushing for -odd and charged Higgs masses in the TeV range.

The very large bound on the mass is in contrast with the non-SUSY version of the model, where the gauge couplings are free parameters and can be much smaller, hence yielding lower mass bounds. The latter need to be evaluated as a function of both gauge couplings [43].

Next, we describe the sneutrino sector, which shows two distinct features compared to the MSSM. Firstly, it gets enlarged by the superpartners of the right-handed neutrinos. Secondly, even more drastically, a splitting between the real and imaginary parts of each sneutrino occurs resulting in twelve states: six scalar sneutrinos and six pseudoscalar ones [44, 45]. The origin of this splitting is the term in the superpotential (see (2)), which is operator after the breaking of . In the case of complex trilinear couplings or -terms, a mixing between the scalar and pseudoscalar particles occurs, resulting in 12 mixed states and consequently in a mass matrix.

To gain some feeling for the behaviour of the sneutrino masses, we can consider a simplified setup: neglecting kinetic mixing as well as left-right mixing, the masses of the R-sneutrinos at the SUSY scale can be expressed as

In addition, we treat the parameters , , , , , and as independent. The different effects on the sneutrino masses can easily be understood by inspecting (17). The first two terms give always a positive contribution whereas the third one gives a contribution that can be potentially large which differs in sign between the scalar and pseudoscalar states, therefore inducing a large mass splitting between the states. Further, this contribution can either be positive or negative depending on the sign of . For example, choosing and positive, one finds that the -even (-odd) sneutrino is the lightest one for (). This is pictorially shown in Figure 1, as a function of the GUT-scale input parameter , for a choice of the other parameters. One notices that the -even (-odd) sneutrino is the lightest one when the  GeV Higgs boson is predominantly (). It is worth pointing out here that, as will be described in the following section, when  GeV, the next-to-lightest Higgs boson can decay into pairs of -even sneutrinos, but not into similar channel with -odd sneutrinos. Being predominantly a bilepton field, when this decay is open, it saturates its BRs; see Figure 3. Regarding the decay into -odd sneutrinos, this channel is accessible (i.e., is light enough) only in the region where is the SM-like Higgs boson, that is, mainly coming from the doublets. In this case, however, this decay channel is mitigated by the small scalar mixing and is not overwhelming (unlike for , now mainly from the bileptons).

Figure 1: Masses of -even (, cyan) and -odd (, red) R-sneutrinos as a function of . For comparison, also the masses of the lightest (, black) and next-to-lightest (, blue) Higgs bosons are shown. Configurations when GeV are shown in green.

Depending on the parameters, either type of sneutrinos can get very light. For the LSP, it can be a suitable dark matter candidate [16] and yield extra fully invisible decay channels to the Higgs bosons, thereby increasing their invisible widths. In the case of the decay into the -odd sneutrino, since this can happen mainly for the SM-like Higgs boson, one should account for the constraints on the former [17]. Eventually, the R-sneutrinos could also get tachyonic or develop dangerous -Parity-violating . While the first possibility is taken into account in our numerical evaluation by SPheno, and such points are excluded from our scans, the second case will be reviewed in the following subsection.

The last important sector for considerations that will follow is the one of the charged sleptons. See [46] for further details. New SUSY breaking D-term contributions to the masses appear, which can be parametrised as a function of the mass and of as

Their impact is larger for the sleptons than for the squarks by a factor of due to the different charges (). It is possible to vary the stau mass by  GeV with respect to the MSSM case while keeping the impact on the squarks under control. Having different sfermion masses in the BLSSM as compared to the MSSM has a net impact on the Higgs phenomenology, in particular in enhancing the coupling while keeping unaltered the SM-like Higgs coupling to gluons. As described at the end of this review, the new D-terms coming from the sector can further reduce the stau mass entering in the effective interaction (while ensuring a pole mass of GeV, compatible with exclusions) (with pole mass we denote the one-loop corrected mass at , while in the loop, leading to the effective coupling, the running tree-level mass at enters, being the SM-like Higgs boson; i.e., GeV) leading this mechanism to work also in the constrained version of the model. This mechanism has been recently reanalysed also in [47] in the very same model.

2.5. The Issue of R-Parity Conservation

We have encountered so far several neutral scalar fields which could develop , beside the Higgs bosons. If of fields charged under QCD and electromagnetism are forbidden because the latter are good symmetries, R-sneutrino , which are not by themselves problematic, would unavoidably break R-Parity. The issue of conserving R-Parity is of fundamental importance, since this is a built-in symmetry in our model where is gauged. We will therefore restrain ourselves to parameter configurations where the global minimum is R-Parity conserving.

When all neutral scalar fields are allowed to get , it is not trivial even at the tree level to find which is the deeper global minimum and whether it is of a “good” type, here defined as having the correct broken symmetries and being R-Parity conserving. One possible way to study this issue is to start from a simplified set of input parameters yielding a correct tree-level global minimum when only the Higgs fields get . and then look for the true global minimum when all other neutral fields (mainly R-sneutrinos) acquire , both at the tree level and at loop level. See [48] for further details.

At the tree level there seems to exist regions where the BLSSM has a stable, R-Parity-conserving global minimum with the correct broken and unbroken gauge groups. For this to happen one needs the R-sneutrino Yukawa coupling to be not so large and the trilinear parameter to be not large compared to the soft scalar mass , as, intuitively, large and can lead to large negative contributions to the potential energy for large values of , as well as reducing the effective R-sneutrino masses, as described above and clear from Figure 1.

It turns out that when loop corrections are taken into account, few points all over such regions of parameters exist where R-Parity is not preserved anymore, or where or is unbroken. This is apparently due to a very finely tuned breaking of and which often does not survive loop corrections. The reason for this is that, besides the known large contributions of third generation (s)fermions, the additional new particles of the sector also play an important role. As previously described for the charged sleptons sector, new SUSY breaking D-term contributions to the masses appear; see (18). Since, as shown in (16), the experimental bounds require to be in the multi-TeV range, these contributions can be much larger than in the MSSM sector, resulting in the observed importance of the corresponding loop contributions. Furthermore, these contributions are also responsible for the restoration of at the one-loop level.

Ultimately, overall safe regions of parameters cannot be found where the correct vacuum structure can be ensured. At the same time, if naive trends can be spotted for bad points to appear, these have nonetheless to be checked case by case due to the highly nontrivial scalar potential, and it might be possible that neighbour configurations still hold a valid global minimum. We will not check the validity of our scans from the vacuum point of view in the following, being confident that if any point is ruled out, a neighbour one yielding a very similar phenomenology can be found, which is allowed.

3. A Quick Look at Flavour Observables

Before moving to the Higgs phenomenology, we briefly show the impact on the BLSSM model when considering the constraints arising from low energy observables. For a review of the observables as well as for the impact on general SUSY models encompassing a seesaw mechanism, see [49, 50].

We consider here only the two most constraining ones, BR() and BR(). The present exclusions are BR() [18] and BR() [19]. In Figure 2 we plot these branching ratios as a function of the mass of the lightest (in black) and next-to-lightest (in red) SM-like neutrino, which display some pattern for evading the bounds. In particular, they are required to be rather light, below eV, while the model, due to the limited scans here performed, seems to prefer configurations with neutrinos heavier than 0.01 eV, hence the preferred region in between. Lighter mass values are nonetheless also allowed.

(a)

(b)

Figure 2: (a) BR() and (b) BR() as a function of the light neutrino masses in GeV (black: , red: ). The blue horizontal lines represent the actual experimental limits, from [18] and [19], respectively. The parameters have been chosen as TeV, TeV, , TeV, , TeV, , and .

Figure 3: Branching ratios for with GeV. The -even sneutrino channel (brown) is superimposed.

Figure 4: Mixing between Higgs boson mass eigenstates (blue-orange: , cyan-red: ) and scalar doublet fields, as a function of . is the scalar mixing matrix. Orange/red points are the subset corresponding to BR.

For convenience, the impact of satisfying the earlier bounds will be shown only in the inverted hierarchy case, due to the smaller density of configurations therein. Instead, points not allowed in the normal hierarchy case are automatically dropped.

Regarding the long-lasting discrepancy, in the setup investigated here charginos and charged Higgses are too heavy, same for the boson, while the neutralino and sneutrino are too weakly coupled, to give a significant enhancement over the SM prediction.

4. Higgs Phenomenology

We review here the phenomenology of the Higgs sector, showing a first survey of its phenomenological features. First, results when normal hierarchy is imposed are presented. Then, we will show that the inverted hierarchy is also possible on a large portion of the parameter space. Without aim for completeness, the results are here presented as the starting point for a more thorough investigation. Finally, how model features pertaining to the extended gauge sector impinge on the Higgs phenomenology and in particular how the Higgs-to-diphoton branching ratio can be easily enhanced in this model, despite the experimental data now converging to a more SM-like behaviour than in the recent past, are described.

4.1. Normal Hierarchy

In this subsection we discuss the normal hierarchy case, with the lightest Higgs boson being the SM-like one (i.e., predominantly from the doublets), and a heavier Higgs boson predominantly from the bilepton fields (those carrying number and responsible for the spontaneous breaking). Their mixing is going to be small and solely due to the kinetic mixing.

In Figure 3 we first inspect the heavy Higgs boson branching ratios. Besides the standard decay modes, the decay into a pair of SM Higgs bosons exists, as well as two new characteristic channels of this model, comprising right-handed (s)neutrinos:

(1). Its BR can be up to before the top quark threshold and around afterwards.(2). A similar decay channel exists for the boson. The BRs are , up to depending on the heavy Higgs and neutrino masses.(3), where, is the -even sneutrino and the LSP, hence providing fully invisible decays of the heavy Higgs. If kinematically open, it saturates the Higgs BRs. Notice that only points with very light -even sneutrinos are shown, possible only for very large and negative (see Figure 1).

While the first two channels exist also in the non-SUSY version of the model (however, in the non-SUSY model, the Higgs mixing angle is a free parameter, directly impacting these branching ratios) (see, e.g., [51]), the last one, involving the -even sneutrino, is truly new and rather intriguing. This is because the sneutrino is light and it can be a viable LSP candidate if its mass is smaller than , as in this case [16]. It however implies that the heavy Higgs is predominantly bilepton-like, with a light Higgs very much SM-like. This can be seen in Figure 4, where the points with large BR() (in red) have the lowest mixing between and the SM scalar doublet fields, of the order of . It immediately follows that this channel will have very small cross section at the LHC, when considering SM-like Higgs production mechanisms. This is true for all heavy Higgs masses GeV. The GeV Higgs is well SM-like, with tiny reduction of its couplings to the SM particle content. On the other hand, the heavy Higgs is feebly mixed with the doublets, suppressing its interactions with the SM particles and hence its production cross section. This can be seen in Figure 5(a). Considering only the gluon-fusion production mechanism, and multiplying it by the relevant BR, we get the cross sections for the choice of channels displayed therein. The most constraining channels, and , are also compared to the exclusions at the LHC for TeV from [20] and [21], respectively. The channels are well below current exclusions, which are hence not shown.

(a)

(b)

Figure 5: Cross sections at TeV for (a) the SM-like channels and (b) the new channels, as a function of the heavy Higgs mass. The solid lines above are the exclusion curves from [20, 21].

We see that all (starting from GeV) the displayed configurations are allowed by the current searches (the exclusions shown by solid curves of the same color as the depicted channel). This is because of the suppression of the heavy Higgs boson cross sections due to the small scalar mixing.

In the lower plot the cross sections for the new channels are displayed. Those pertaining to model configurations for which the heavy Higgs boson decays to the -even sneutrino (LSP), yielding a fully invisible decay mode, are displayed in red. Contrary to all other cases, the production of the heavy Higgs for this channel is via vector boson fusion as searched for at the LHC [52]. Typical cross sections range between fb and fb. The channel is shown in blue and it can yield cross sections of fb for GeV. Last is the channel. It can be sizable only for very light masses, fb for GeV, although the further decay chain of the heavy neutrinos has to be accounted for. The latter can give spectacular multileptonic final states of the heavy Higgs boson ( and ) or high jet multiplicity ones (), via and in a 2 : 1 ratio (modulo threshold effects). Further, these decays are typically seesaw-suppressed and can therefore give rise to displaced vertices [53].

4.2. Inverted Hierarchy

In this subsection we discuss the inverted hierarchy case, where is the SM-like boson and a lighter Higgs boson exists.

We start once again by presenting the BRs for the next-to-lightest Higgs boson in Figure 6. This time, however, this is the SM-like boson, hence predominantly from the doublets. It has the same new channels as the heavy Higgs in the normal hierarchy, the only difference being the -odd R-sneutrino instead of the -even one. This is simply because the inverted hierarchy can happen only for large positive values, where only the -odd R-sneutrino can be light; see Figure 1. The configurations not allowed by the low energy observables or by HiggsBounds are displayed as gray points. We see that may have sizable decays into pairs of the lighter Higgs bosons, yielding -jets final states. This decay is still allowed with rates up to few percent. Further, rare decays into pairs of heavy neutrinos are also present, with BRs below the permil level. This channel can give rise to rare multilepton/jets decays for the SM-like Higgs boson, which are searched for at the LHC, even in combination with searches for displaced vertices [54]. The last available channel is the decay into pairs of -odd R-sneutrinos. Being the LSP, it will increase the invisible decay width and hence give larger-than-expected widths for the SM-like boson. Its rate is obviously constrained, and a precise evaluation of the allowed range is needed. It however goes beyond the scope of the present review and we postpone it to a future publication.

Figure 6: Branching ratios for the GeV Higgs boson (). The decay into heavy neutrinos is displayed with diamonds. All other decays are displayed with circles. Gray points are excluded by the low energy observables and by HiggsBounds. The decay into -odd sneutrinos is not shown.

Regarding the lightest Higgs boson (), this will obviously decay predominantly into pairs of -jets, see Figure 7. Notice that due to its large bilepton fraction it can also decay into pairs of very light RH neutrinos, at sizable rates depending on the neutrino masses. As in Figure 6, the nonallowed configurations are displayed as gray points. We see that the pattern of decays is not affected by the inclusion of the constraints, in the sense that this channel stays viable. Once again, the latter will yield multilepton/jet final state, which will be very soft and hence very challenging for the LHC. However, also in this case displaced vertices may appear.

Figure 7: Same as in Figure 6 for the lightest Higgs boson ().

As in the previous section, we show in Figure 8 the mixing between the Higgs mass eigenstates and the doublet fields as a function of the light Higgs mass, to show that is here rather SM-like. Once more, the gray points displayed here are excluded by the low energy observables and by HiggsBounds.

Figure 8: Mixing between scalar mass eigenstates and Higgs doublets (black: , red: ) and scalar doublet fields, as a function of . is the scalar mixing matrix. Gray points are excluded by the low energy observables and by HiggsBounds.

Finally, the production cross sections for the lightest Higgs boson can be evaluated. In Figure 9 we compare the direct production (for the main SM production mechanisms, gluon fusion and vector boson fusion) with the pair production via decays only via gluon fusion, . When the latter channel is kinematically open, that is, GeV, the lightest Higgs boson pair production has cross sections up to pb at the LHC at TeV, and it can give rare , , or () decays of the SM-like Higgs boson. A thorough analysis of the phenomenology of the Higgs sector in the BLSSM for the upcoming LHC run 2, based on the first investigations shown here, will be performed soon.

Figure 9: Cross sections at TeV for different production mechanisms. Gluon-fusion (in red) and vector-boson-fusion (in green) mechanisms are displayed only for GeV for simplicity. Gray points are excluded by the low energy observables and by HiggsBounds.

4.3. Enhancement of the Diphoton Rate

A feature of gauge-extended models is that new SUSY-breaking D-terms arise, which give further contributions to the sparticle masses. In the case of the model under consideration, we showed discussing (18) that these terms can be large and that they bring larger corrections to sleptons than to squarks. We already discussed how the vacuum structure of the BLSSM is affected by this. Here, we discuss the impact of the new D-terms on the Higgs phenomenology, focusing on the Higgs-to-diphoton decay, despite being disfavoured by most recent data [17], as an illustrative case. See [46] for further details.

To start our discussion let us briefly review the partial decay width of the Higgs boson into two photons within the MSSM and its singlet extensions. This can be written as (see, e.g., [55])

corresponding to the contributions from charged SM fermions, bosons, charged Higgs, charginos, charged sleptons, and squarks, respectively. The amplitudes at the lowest order for the spin-1, spin-, and spin-0 particle contributions can be found, for instance, in [55]. denotes the coupling between the Higgs boson and the particle in the loop and is its electric charge. In the SM, the largest contribution is given by the -loop, while the top-loop leads to a small reduction of the decay rate. In the MSSM, it is possible to get large contributions due to sleptons and squarks, although it is difficult to realise such a scenario in a constrained model with universal sfermion masses [56–58]. In singlet or triplet extension of the MSSM also the chargino and charged Higgs can enhance the loop significantly [59, 60]. However, this is only possible for large singlet couplings which lead to a cut-off well below the GUT scale. In contrast, it is possible to enhance the diphoton ratio in the BLSSM due to light staus even in the case of universal boundary conditions at the GUT scale. We show this by calculating explicitly the contributions of the stau:

Here, and represent the D-term contributions of the left- and right-handed stau and we have neglected subleading contributions. Given that , for fixed values of the other parameters, and can be used to enhance the rate by suppressing the denominator.

We turn now to a fully numerical analysis to demonstrate the mechanism to enhance the Higgs-to-diphoton rate as a feature of the model with an extended gauge sector. This is a result of reducing the stau mass at the Higgs mass scale via extra D-terms as shown discussing (18). We recall here that this mechanism leaves the stop mass and hence, as we will show, the Higgs-to-gluons effective coupling nearly unchanged. In Table 2 we have collected two possible scenarios that provide SM-like Higgs particle in the mass range preferred by LHC results displaying an enhanced diphoton rate. In the first point, the lightest -even scalar eigenstate is the SM-like Higgs boson while the light bilepton is roughly twice as heavy. In Figure 10 we show that all the features arise from the extended gauge sector: it is sufficient to change only to obtain an enhanced diphoton signal and the correct dark matter relic density while keeping the mass of the SM-like Higgs nearly unchanged. The dark matter candidate in this scenario is the lightest neutralino that is mostly a bileptino (the superpartner of the bileptons). The correct abundance for is obtained due to a coannihilation with the light stau. In the second point, the SM-like Higgs is accompanied by a light scalar around GeV which couples weakly to the SM gauge bosons, compatibly with the LEP excess [61–63]. In this case, the LSP is a -odd sneutrino which annihilates very efficiently due to large . This usually results in a small relic density. To get an abundance which is large enough to explain the dark matter relic, the mass of the sneutrino has to be tuned below [16]. This can be achieved by slightly increasing and by tuning the Majorana Yukawa couplings , which tends to increase the SM-like Higgs mass for the given point. It is worth mentioning that a neutralino LSP with the correct relic density in the stau coannihilation region can also be found in this scenario. Notice that both points yield rates consistent with observations in the channels (measured at the LHC) (being ), as well as an effective Higgs-to-gluon coupling close to 1.

Table 2: The input parameter used: Point I:  GeV,  GeV,  GeV, , ,  GeV, and (neutralino LSP); Point II:  GeV,  GeV,  GeV, , ,  GeV, and (CP-odd sneutrino LSP). denotes the coupling squared of the Higgs fields to vector bosons normalised to the SM values.

Point I
Point II

[GeV]
125.2
98.2

[GeV]
186.9
123.0

[GeV]
267.0
237.3

Doublet fr. [%]
99.5
8.7

Bilepton fr. [%]
0.5
91.3

0.992
0.087

1.001
0.085

0.005
0.911

0.005
0.921

[MeV]
4.13
0.22

1.57
0.085

1.03
0.089

0.98
0.05

[MeV]
4.8
3.58

0.005
1.79

0.006
0.95

0.01
0.88

LSP mass [GeV]

(a)

(b)

(c)

Figure 10: (a) The mass of the SM-like Higgs (bottom (blue line)), of the stau (middle (black) line, where the dashed line represents a reference unchanged value), and of the lightest neutralino (top (red) line); (b) the diphoton branching ratio; (c) the neutralino relic density as a function of . The other parameters have been chosen as GeV, GeV, , , GeV, and .

5. Conclusions

In this review I described the extension of the MSSM, focusing in particular on the scalar sector, described in detail. The fundamental role that the gauge kinetic mixing plays in this sector has been underlined.

The comparison to the most constraining low energy observables showed that a preferred region for the light neutrino masses exists to evade these bounds. Then, I presented a first systematic investigation of the phenomenology of the Higgs sector of this model, showing that both the normal hierarchy and the inverted hierarchy of the two lightest Higgs bosons are naturally possible in a large portion of the parameter space. Particular attention has been devoted to analysis of the new decay channels comprising both the -even and -odd R-sneutrinos, which are a peculiarity of the BLSSM. Based on these first findings, a thorough analysis of the Higgs sector in the BLSSM at the upcoming LHC run 2 will be soon prepared. The fit of the SM-like Higgs boson to the LHC data will also be performed with HiggsSignals [64].

Finally, I described how in the BLSSM model (and in general in gauge-extended MSSM models) the Higgs-to-diphoton decay can be easily enhanced. Despite being disfavoured by most recent data, this feature is a consequence of the potentially large new SUSY-breaking D-terms arising from the sector. At the same time these terms affect also the vacuum structure of the model, where naive R-Parity-conserving configurations at the tree level could develop deeper R-Parity-violating global minima, or partially restore the symmetry at one loop. It is however possible to still find R-Parity-conserving global minima on the whole parameter space, which can either accommodate an enhancement of the Higgs-to-diphoton decay or fit the most recent Higgs data.

Conflict of Interests

The author declares that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The author would like to thank S. Moretti and C. H. Shepherd-Themistocleous for helpful discussions in the early stages of this work. He is also really grateful to all his collaborators, and in particular to Florian Staub. He further acknowledges support from the Theorie-LHC France initiative of the CNRS/IN2P3 and from the French ANR 12 JS05 002 01 BATS@LHC.

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