Sgoldstino-Higgs mixing in models with low-scale supersymmetry breaking

We consider a supersymmetric extension of the Standard Model with low-scale supersymmetry breaking. Besides usual superpartners it contains additional chiral goldstino supermultiplet whose scalar components - sgoldstinos can mix with scalars from the Higgs sector of the model. We show that this mixing can have considerable impact on phenomenology of the lightest Higgs boson and scalar sgoldstino. In particular, the latter can be a good candidate for explanation of 2-sigma LEP excess with mass around 98 GeV.


Introduction
Discovery of a new scalar resonance at the ATLAS [1] and CMS [2] becomes one of the most pronounced events in the last few years. During the 1st run of the LHC experiments in 2011-2012 there was collected statistics about 5 fb at √ s = 7 TeV and up to 20.6 fb at √ s = 8 TeV. Obtained results indicate that properties of the new particle are very similar to those predicted for the Standard Model (SM) Higgs boson [3,4] which once again confirms the triumph of this Model. However, in spite of its beauty and capability of explaining vast amount of experimental results in particle physics SM has several drawbacks, e.g. zero neutrino masses, no dark matter candidate, hierarchy problem etc.. We are forced to believe that SM is a part of another theory which somehow cures its problems. Supersymmetry (SUSY) is among the most prominent and attractive ideas for SM extension [5,6]. It is interesting that the discovery of the light Higgs-like resonance being interpreted as the lightest Higgs boson h of the Minimal Supersymmetric Standard Model (MSSM) with mass of order 125 GeV is consistent with TeV scale supersymmetry. It is well known that the mass of h is bounded at tree level by Z-boson mass and to reconcile it with the observed value of the resonance mass requires sufficiently large quantum corrections [7,8] which implies (if other Higgs bosons are heavy) either heavy stop contribution or maximal mixing in stop sector. Unobservation of light squarks at the first run of LHC experiments indicates that this indeed may be the case. On the other hand it appears that the observed resonance is too heavy to be implemented "naturally" into supersymmetric extensions [9,10,11,12,13,14,15]. If supersymmetry is indeed inherent to our Nature it should be spontaneously broken. In a particular model this may happen in some hidden sector which does not have any renormalizable interactions with the visible one to avoid phenomenological problems with supertrace of squared mass matrix [16]. According to supersymmetric analog of the Goldstone theorem [17] there should exist a massless fermionic degree of freedom, goldstino. Being included into supergravity framework goldstino becomes longitudinal component of gravitino with mass related to the scale of supersymmetry breaking √ F as follows m 3/2 = F √ 3M P l where M P l is the Planck mass [18]. In the simplest case goldstino appears as a fermionic component of a chiral supermultiplet and interactions of this supermultiplet with other MSSM fields are suppressed by √ F . If the SUSY breaking scale √ F is considerably higher than the electroweak scale than the interactions of SM particles with the hidden sector are negligible. And this is the standard setup for phenomenological consideration of supersymmetric models. For instance, for gravity mediated SUSY breaking scenarios with soft parameters of order of TeV-scale this implies √ F > ∼ 10 11 GeV. In the case of gauge mediation the SUSY breaking scale can be considerably lower, but still its value is limited by √ F > ∼ 50 TeV [19]. However, it is phenomenologically possible (see, e.g. Refs. [20,21]) to have √ F not very far from the electroweak scale, somewhere around several TeVs. The main feature of these models is the presence of a sector responsible for SUSY breaking, i.e. goldstino and probably its scalar superpartners -sgoldstinos, in low energy spectrum. In this class of models if Rparity is conserved gravitino is the lightest supersymmetric particle (LSP) with the mass at sub-eV scale. Scalar and pseudoscalar sgoldstinos acquire nonzero masses after integrating out particles from hidden sector. It is phenomenologically possible to have them around electroweak scale. If these particles are light we have an opportunity to probe the scale of supersymmetry breaking already at present-day experiments, in particular, at the LHC.
One of the reasons is that these theories allow to go beyond the setup of MSSM which presently becomes strongly constrained by the LHC data. In this paper we consider possible consequences of sgoldstino mixing with particles in the Higgs sector of MSSM concentrating on the most intriguing case of mixing with the lightest Higgs boson. Interactions of sgoldstino with the Higgs boson and some aspects of the mixing between them have been discussed in Refs. [44,46,49,50,51]. In particular, it has been shown that nonrenormalizable interactions with goldstino supermultiplet result in additional contribution to the Higgs potential and as a result to change of the Higgs selfcouplings. These changes can raise the value of the lightest Higgs boson mass and on this way one try to cure naturalness problem [47]. In [49] the mixing of a heavy scalar sgoldstino with the lightest Higgs boson of MSSM has been discussed to explain the excess in h → γγ channel previously observed by ATLAS and CMS. In the present study we discuss the case when the mixing of scalar sgoldstino with the lightest Higgs boson gives an additional considerable positive contribution to the mass of the latter. This happens if sgoldstino mass is somewhat lower than the mass of h. The most interesting consequences of this mixing are modifications of the lightest Higgs boson production rates and decays as well as presence of an additional light scalar in the low energy spectrum. As by product we find that even small mixing can considerably change sgoldstino signatures at colliders 3 . We perform a scan over soft MSSM parameters in the decoupling regime, discuss constraints from LHC and other experiments, find out acceptable parameter space and calculate the signal strengths for the lightest Higgs boson and scalar sgoldstino. In particular, we find that the presence of lighter scalar sgoldstino can be consistent with small 2σ excess observed at LEP [53] in e + e − → Zh, where h → bb with mass around 98 GeV. The plan of the paper is the following. In Section 2 we introduce the model, describe interactions of goldstino supermultiplet with MSSM fields and in particular with the Higgs doublets. We calculate sgoldstino-Higgs mixing under assumption of CP-conservation in this sector and discuss the changes in coupling constants of new mass states. In Section 3 we describe the general strategy which we use to explore this scenario and discuss obtained results. In section 4 we present our conclusions. In Appendix A we present several auxiliary formulas.
2 The low-scale SUSY breaking model

The model description and sgoldstino-Higgs sector
In this section we describe a supersymmetric model within low-scale supersymmetry breaking framework. Let us introduce goldstino chiral superfield as Φ = φ + √ 2θG + F φ θ 2 , wherẽ G is goldstino, φ represents its scalar components, sgoldstinos, and F φ is auxiliary field. We suppose that due to some dynamics in the hidden sector the auxiliary field F φ acquires non-zero vacuum expectation value F φ and SUSY becomes spontaneously broken. Interactions of goldstino supermultiplet with MSSM are introduced in such a way that after the spontaneous supersymmetry breaking the standard set of soft terms appears (see [54,55,56] and references therein). Thus, we introduce the following lagrangian Here the contribution from Kähler potential has the form where k runs over all matter and Higgs supermultiplets, and the contributions from superpotential look as where α labels all the SM gauge fields, ǫ 12 = −1. The physics of goldstino supermultiplet can be described by the following effective lagrangian Here we single out the standard kinetic term Φ + Φ from total Kähler potential whileK(Φ + , Φ) represents higher dimension contributions. The above lagrangian should be considered as an effective field theory 4 which is valid at energies E < ∼ √ F and we consider higher order terms inK(Φ + , Φ) as suppressed by powers of F . The linear superpotential triggers spontaneous In what follows we take all soft parameters, µ and F to be real and thus neglect possible CP-violation.
Let us consider the scalar sector of the model in details. By integrating out auxiliary fields of two Higgs doublets, goldstino supermultiplet and D-terms of vector superfields we obtain the tree level scalar potential for the sector of the Higgs fields and sgoldstinos in the following form The lagrangian (2.1) does not contain full set of operators consistent with symmetries even to the leading order in 1/F because we limit ourselves only with the simplest set of terms which produce the MSSM soft parameters after SUSY breaking. Also here we face with an ambiguity: the soft term −Bǫ ij H i d H j u in MSSM lagrangian can be generated not only from the superpotential as in Eq. (2.3) but also from the in the Kähler potential. This is related to possibility of analytic superfield redefinitions, discussed in [55].
We are going to investigate squared mass matrix of neutral scalars in electroweak symmetry breaking (ESB) minimum with leading order corrections in 1/F . In general electroweak symmetry breaking minimum of the scalar potential allows for non-zero value of sgoldstino field φ because it is a singlet with respect to the SM gauge group. In what follows we consider a case study and simplify matters by assuming that φ = 0 in ESB minimum of the potential 5 . This can be easily obtained by tuning third derivatives ofK(φ, φ * ) as follows up to higher order corrections in 1/F . After making this assumption we can expand scalar fields around electroweak breaking minima as follows [6] h 0 Here v ≡ v 2 u + v 2 d = 174 GeV and tan β = vu v d are introduced. The mixing angle α between h and H is defined by the following relations 5 We note that nonzero v.e.v. of φ in particular results in deviations of the Higgs couplings to SM fermions, see e.g. [46].
with standard tree level Higgs mass parameters In the chosen field basis (2.10)-(2.12) the squared mass matrices can be written in the following form for scalars and With the assumption about zero v.e.v. of φ one finds that the only new contributions from SUSY breaking sector to the tree level masses of the Higgs fields come from the term V Φ in the scalar potential. Another benefit of this assumption is that mixing terms between sgoldstino and Higgses appear from linear in φ part of the scalar potential. The diagonal mass squared elements for the Higgs fields read (c.f. [44]) As compared to the MSSM case the masses get additional contributions from new term [44,46,50] of the fourth order in Higgs doublets which comes from the part (2.8) of the scalar potential. The expressions for m 2 s and m 2 p can be easily obtained from Eq. (2.5) and are related to the fourth order derivatives of the To obtain the off-diagonal elements in the mass matrices we expand the scalar potential to the leading order in 1/F and keep only the terms which are linear in sgoldstino field φ.
For this part of the potential we find and for off-diagonal terms in (2.16) and (2.17) we obtain In what follows we concentrate on the decoupling limit, i.e. m A ≫ m h . Then all the Higgs bosons except for the lightest one become heavy. This limit corresponds to cos α = sin β, sin α = − cos β in Eqs. (2.10) and (2.11). Next, we consider the scalar sgoldstino squared mass parameter m 2 s to be somewhat less than m 2 h . In this case the mixing between the two states can give a positive contribution to the Higgs boson mass 6 . Corresponding mass states are given by the following linear combinations and the expressions for their masses squared look (in the case m h > m s ) as for new Higgs-like stateh and for new sgoldstino-like states. The mixing angle is given by following relation .

(2.29)
Expression for the mixing term X changes if we allow for nonzero v.e.v. of sgoldstino field. Also note that if other Higgs bosons are also light the mixing pattern becomes more complicated. We finish this subsection by reminding that interactions of the lightest Higgs boson with (s)quarks result in the large quantum correction δ to its mass squared. This can be taken into account in the expressions above by replacement m 2 h → m 2 h + δ.

Sgoldstino and Higgs boson couplings
Here we write down the couplings of new mass statesh ands to the SM particles. Mainly we are interested in their couplings to the SM vector bosons and heavy fermions of the third generation. Corresponding effective lagrangian for h reads where we introduce the scaling factors C k for the couplings relative to their SM values. Similar interaction lagrangian for the scalar sgoldstino s can be obtained from the Eq. (2.1) as follows We see that the interaction of the lightest Higgs boson h and the scalar sgoldstino s with quarks and leptons have similar structure, so the coupling constants for the Higgs-like mass stateh read The scaling factors C t , C b and C τ are determined by the mixing of h and H and in the decoupling limit m H ≫ m h are close to unity, c.f. (2.10), (2.11) and (2.13). The effective couplings of the SM Higgs boson with gluons and photons result from loop contributions of quarks and W -bosons. The scaling factors C γγ and C gg in (2.30) take into account additional corrections from interactions with squarks, charginos etc. which are typically suppressed if these superpartners are heavy. For scalar sgoldstino the couplings to photons and gluons appear already at tree level, see (2.31), and putting them all together one obtains forh where dominant SM loop contributions look as follows [3] and loop formfactors read

40)
Interactions with W and Z bosons are described by different operators for the Higgs boson and scalar sgoldstino, see Eqs (2.30) and (2.31). Corresponding couplings for new Higgs-like mass state will have the following form in the momentum space The scaling factors C W and C Z are again close to unity in the decoupling regime. Effective coupling constants for sgoldstino-like states can be obtained from those above by the replacement cos θ → sin θ and sin θ → − cos θ.
3 Analysis of the model

Strategy for analysis
In this Section we discuss phenomenological implications of sgoldstino-Higgs mixing in context of the setup described above. For a given point in parameter space of the model which is characterized by MSSM parameters, scalar sgoldstino mass term m 2 s and the scale of supersymmetry breaking √ F one can ask whether this point is compatible with experimental data and in particular with results of LHC experiments. To explore this scenario we perform a scan over MSSM parameters space. In what follows we consider two parameter sets for comparison: • Set 2. This region has higher upper borders: 100 GeV < |µ| < 2000 GeV, 100 GeV All the MSSM parameters have been chosen at the electroweak scale. Other SUSY soft masses, which are not relevant for our analysis, are taken to be sufficiently large. In particular, given that we would like to consider decoupling regime, the Higgs pseudoscalar is also taken also to be heavy. The main difference between the two sets which will be important to us is that without additional contribution only very small fraction of models within Set 1 provides the lightest Higgs boson with the mass higher than about 123 GeV. On the contrary Set 2 includes rather large values of trilinear couplings A U 33 and stop mass parameters m Q 3 , m U 3 and larger values of m h (up to 128 GeV) can be obtained. For supersymmetry breaking scale we fix the value √ F = 10 TeV; later on we comment about this choice. For calculation of MSSM spectra and the lightest Higgs boson coupling constants without contribution of sgoldstino sector we use package NMSSMTools [57] in the MSSM regime. We remind reader that in the scenario of low-scale supersymmetry breaking gravitino is LSP. By default NMSSMTools package in the regime of general NMSSM excludes models where neutralino is not LSP, so we turn this option off in the program. We scan over the chosen parameter spaces and exclude unphysical models by checks for absence of unphysical global minimum of the scalar potential in Higgs sector. On this stage we use a set of experimental constraints implemented in NMSSMTools, including constraints from measurements of Br(b → sγ) and Br(B s → µ + µ − ) [58]. Note, that we do not impose the condition that the SUSY contribution to the anomalous magnetic moment of muon should explain the present 3σ difference between SM prediction and BNL result. The result of the scan is the spectrum of superpartners, the value m 2 h for the squared mass of the lightest Higgs boson including MSSM quantum corrections and coupling constants of h to photons, gluons, quarks and leptons which we use in the following analysis.
Then we turn on mixing with sgoldstino as follows. We randomly scan over sgoldstino mass parameter m s in the interval (m h − x, m h ) where x = 35 GeV. Such narrow interval was taken to enhance the mixing angle (2.29). We accept the model if resulting mass of the Higgs-like resonanceh falls in the range 123 GeV< mh <127 GeV. Now let us discuss collider constraints which are relevant for our study. We start with the LHC data. Detailed determination of the limits on the masses of superpartners for the lowscale supersymmetry breaking scenario lies beyond the scope of this study. Still we impose a set of constraints on masses of superpartners to omit obviously excluded points in parameter space. For chosen value √ F = 10 TeV all superpartners firstly decay into SM partners and next-to lightest supersymmetric particle (NLSP) which finally decays into gravitino. With gravitino LSP LHC signatures from the searches for superpartners will be the same as for general gauge mediation models [59,60]. Below we impose a set of constrains depending on the type of NLSP which can be in our case the lightest neutralino χ 0 1 or 3rd generation squark,t 1 andb 1 . We do not take into account an exotic case of χ ± 1 , which has been studied in [61]. Finally, only very small number of models in our scar have gluino NLSP and we neglect them completely for simplicity.
If NLSP is bino-like neutralino it decays mainly asχ 0 1 → γG. Corresponding signal events have (multi)photon and missing E T signatures [62]. This type of searches at ATLAS and CMS results in rather stringent limits on masses of superpartners: for squarks and gluinos from 1.4 to 2 TeV [63,64,65]. However in their analysis it has been assumed that all squarks have the same mass and they decay directly to bino-like NLSP, so for our sets of parameters the constraints should be considerably weaker and we use here conservative bound 1.4 TeV on squarks masses. Limits on masses of the lightest wino-like chargino and χ 0 2 (if they are degenerate) are about 600 − 700 GeV [63] independently of χ 0 1 mass and we used in this case the strongest constraint. For the case of wino-like or higgsino NLSP neutralino it decays mainly into Z and/or h. Searches for a diphoton, Z + γ, W + γ and/or jets and E miss T signatures [64] result in the limits 900 − 2000 GeV for gluino and squark masses. Again here only a simplified case of degenerate squarks has been considered. The limit on mass of NLSP neutralino χ 0 1 in this case depends on branchings of χ 0 1 decay into ZG and hG and varies [66,67] from 380 GeV for Br(χ → ZG) = 1 to zero for Br(χ → hG) = 1.
Here we impose the strongest constraint by assuming that NLSP decays to Z boson pair with 100% branching ratio. When a squark is NNLSP and wino-like neutralino is NLSP we take into account constrains from cascade production of NLSP-lightest neutralino via stop mt 1 > 560 GeV [68] and sbottom mb 1 > 470 GeV [69] squarks. In the case of squark (t 1 orb 1 ) NLSP we impose the following bounds from searches for direct pair production of where σ(pp →h(s)) is the total production rate of the Higgs-like (sgoldstino-like) state given by sum of different production mechanisms, Br(h(s) → f ) is the branching ratio of the decay ofh (s) into final state f , while σ(pp →h SM ) and Br(h SM → f ) are similar quantities for the SM Higgs boson with the same mass. In what follows we consider the following final states γγ, ZZ, W W , bb and τ + τ − which are most relevant for current LHC searches. Further, we distinguish between several dominant production mechanisms, namely gluon-gluon fusion (ggF ) and vector boson fusion along with associated production with W and Z (V BF and V H) as they provide with different signatures. The signal strength (3.1) can be approximated by for the case of ggF and as for V BF or V H production mechanisms. Similar expressions are used for the case of sgoldstino-like states. Here we should note that interaction of sgoldstino with massive vector bosons are governed by operator which has different structure than that for the Higgs boson. But considering kinematics of the processes of Higgs production via VBF or VHstrahlung mechanisms it is easy to convince yourself that the momentum-dependent parts of (2.44) and (2.43) give negligible contribution for parameters in the Sets 1 and 2 in comparison with the SM parts of the couplings unless cos θ is not too small. The widths of the decays entering (3.2) and (3.3) are calculated using formulas in Ref. [3] and replacing corresponding coupling constants with those presented above. The only exception is decays into pair of massive vector bosons. In this case for the calculation of partial widths we use results of Ref. [72] and present corresponding formulas in Appendix A for completeness. Experimental constraints on signal strengths from ATLAS and CMS results will be discussed in the next Section.
As it has been already noted gluon-gluon fusion is the most important production mechanism for γγ, ZZ and W W channels. At the same time as we observed above the coupling of the Higgs bosonh to the gluons receives tree level contribution (2.37) due to the mixing with sgoldstino. Let us require that this contribution should not dominate over the SM part. It can be suppressed either by small mixing angle or by sufficiently large √ F . Considering the case of non-negligible mixing the sgoldstino coupling is smaller than 1-loop SM contribution . Given chosen limit M 3 > ∼ 1.5 TeV from the direct searches for gluinos at the LHC one finds √ F > ∼ 7 TeV. This explains our choice of sufficiently large value of supersymmetry breaking scale √ F = 10 TeV. We note in passing that the real constraint on M 3 in a given model can be considerably lower with current ATLAS and CMS data. Thus, smaller values of √ F are possible along with large sgoldstino-Higgs mixing. Now let us turn to the discussion of sgoldstino-like state which is somewhat lighter than the Higgs-like resonance. Here we impose additional constraints from LEP [73] and TeVatron [74]. Particularly strong limits come from LEP results on Higgs boson searches [53,73,75] in e + e − → Zh with h → bb, τ + τ − and γγ. We remind reader that a small, about 2σ, excess has been observed at LEP in this channel around invariant mass 98 GeV of bb pair. In what follows we would like to explore interesting possibility that this sgoldstino-like state with mass around 98 GeV could be source of this excess. For such models we additionally require that the mass ofs should be in the range 95 − 101 GeV and additionally 0.1 < R V BF/V H bb (s) < 0.25, see Ref. [53]. Alternative explanations of this excess have been proposed within Non-minimal Supersymmetric Standard Model (NMSSM) in papers [76,77].

Results and discussions
Here we present results of the scan over MSSM parameter space with two sets of parameters introduced in Section 3.1. In the figures below we show the different physical quantities for phenomenologically acceptable models. Red points mark models which do not satisfy chosen bounds on masses of superpartners. By orange points we show models which are excluded by LEP constraints on sgoldstino-like state production in e + e − → Zs discussed above. Models which pass all these constraints are shown in green.
We start with Set 1 of parameters. In Fig. 1 (left panel) we show distributions of models over the mass of the Higgs resonance before and after mixing. We see that without the mixing mass m h is always below 123 GeV except for very limited number of models. The mixing with sgoldstino can increase the mass of Higgs-like stateh till observed value. However, the number of acceptable models considerably decreases with increase of mh. In Fig. 1 (right panel) we show mixing angle versus mass mh. We see that for the parameter space given by Set 1, the Higgs-like resonance should have considerable admixture of sgoldstino with | sin θ| ∼ 0.4 − 0.6 to get observable value for its mass. Thus, in the most of the acceptable models the Higgs mass reaches its observed value without large masses of stops and mixing in their sector. The models with negligible mixing with sgoldstino on the right plot corresponds to those models on the left plot in which mass m h exceeds 123 GeV. These models appear to be closed by searches for superpartners. In Fig. 2 we show the masses The masses of the lightest neutralino and chargino are shown in the lower left panel in Fig. 3.
In the lower right panel we show the masses of lightest stop and sbottom squarks. We see that there are plenty of models in which these masses can be as light as 500 − 700 GeV what can be explored in the future LHC runs. Scatter plots similar to those in Figs. 1-3 can be obtained for the Set 2 of parameters which is considerably wider. But in this case they are not so informative as corresponding models admit arbitrary mixing between the lightest

Higgs boson and scalar sgoldstino.
Now we turn to the discussion of LHC signal strengths for the Higgs-like resonanceh.
On the plots below we drop all the models excluded by the LEP constraints or LHC bounds on masses of superpartners and for remaining models we introduce constraints for signal strengths obtained by ATLAS and CMS experiments in their searches for the Higgs boson [80,81]. Although for γγ and ZZ (W W ) channels the dominating production mechanism is ggF while for τ τ and bb channels this is V BF/V H still we conservatively impose the following constraints (obtained by unification of ATLAS and CMS results) independently of the Higgs production mechanism In the figures below we show in magenta the models which satisfy the bounds (3.5). Also we mark in blue color the models in which additionally sgoldstino-like resonance can explain 98 GeV LEP excess.
We show signal strengths for the Higgs-like resonance in gluon-gluon fusion production 0  channel in different combinations in Fig. 4 for the Set 1 and in Fig. 5 for Set 2. From the plots in Figs. 4 and 5 we see that all the signal strengths except for R ggF γγ are somewhat larger than unity for phenomenologically acceptable models, while for γγ channel there are two regions with higher and lower values of the signal strengths. Since sgoldstino s has tree level couplings to photons and gluons while for the Higgs boson h these couplings appear only at loop level, in general one expects large sensitivity of the couplings of Higgs-like stateh to sgoldstino The color notations are the same as in Fig. 4. admixture and to corresponding parameters which govern these couplings, namely M 3 and M γγ . Depending on relative signs between the mixing angle (which is determined by the sign of µ) and soft gaugino mass parameters M 1,2,3 the couplings to gluons and photons can either increase or decrease with respect to their values without the mixing. We have found that M 3 and µ should have opposite signs for the coupling gh gg be close to experimentally observed value. With another choice of the signs the coupling ofh to gluons become unacceptably small; we do not show corresponding models in all the Figures below. The signs of M 1 and M 2 can be arbitrary (we choose them of the same sign) and they correspond to two different domains for R ggF γγ in Figs. 4 and 5. The increase in the signal strengths for fermionic and massive vector boson channels is related to the fact that with our choice of parameters and of the signs of µ and M 3 the coupling ofh to gluons appears to be somewhat larger than its value in SM. Hence, the production cross section in ggF increases.
Similar plots for the case of V BF and V H production mechanisms are presented in Fig. 6 for Set 1 and in Fig. 7 for Set 2. In this case the production cross section is typically  suppressed by the mixing as compared to the case of the SM Higgs boson because the contribution to the coupling with massive vector bosons from sgoldstino is small as we discuss in Section 3.1. Almost the same can be said about the couplings to heavy fermions: tree level Higgs part of the couplings in Eqs. (2.33)-(2.35) are typically larger than sgoldstino contribution for the chosen values of parameters, in particular for √ F = 10 TeV. Note that due to this reason we expect that the total width of the Higgs-like resonance is suppressed by factor cos 2 θ with respect the SM Higgs boson decay width. Summarizing, in Fig. 6 and Fig. 7 the Higgs signal strengths for fermion and massive vector boson channels in V BF/V H for most of the models become suppressed due to the mixing with sgoldstino, in particular, for models in which sgoldstino explains 98 GeV LEP excess. Also we show correlations between different production mechanisms, ggF and V BF/V H, for γγ and ZZ channels in Figure 7: Scatter plots in R   It has been previously studied in Refs. [31,40,41,42,43] but without including effects of its possible mixing with the Higgs boson. As we find this mixing can be extremely important. Firstly, let us discuss the main decay channels and the hierarchy between their branchings for sgoldstinos with masses at electroweak scale. In general the interactions of scalar sgoldstino with SM particles are similar to those of the lightest Higgs boson but the hierarchy between the coupling constants is quite different. The main distinction is the fact that sgoldstino couplings to gluons and photons appear already at tree level as it have been discussed in Section 2. photons which is governed by parameters M 3 and M γγ , respectively. Then it can decay into pairs of quarks and leptons and corresponding decay rates are governed by corresponding trilinear soft terms which enter interactions for superpartners of these quarks and leptons in (2.31). Also sgoldstinos can decay into pair of gauge bosons and these decay widths are governed by corresponding soft gaugino masses. And finally sgoldstinos can decay into pair of gravitinos, which looks as invisible decay. The hierarchy of the branching ratios depends on hierarchy of the soft terms in MSSM lagrangian. In Fig. 10 we show how the hierarchy of branching ratios for scalar sgoldstino decays changes depending on mixing angle. Again we set √ F = 10 TeV and for the time being we consider here very wide interval of sgoldstino masses. We see that even small value of mixing angle drastically changes the hierarchy between possible decay channels and already at mixing angle of 0.4 the hierarchy becomes very similar to the case of the Higgs, except for the partial widths are now suppressed by square of sine of mixing angle. This fact can considerably change the strategy of sgoldstino searches at colliders [31,40,41,42,78]. Now we return to the light sgoldstino-like state in our scenario and we show the signal strengths ofs for bb, ττ , γγ and ZZ channels in gluon-gluon fusion production process in Fig. 11 for Set 1 and in Fig. 12 for Set 2. We see that for ggF production the sgoldstino   [82] searches for Higgs boson in γγ channel and put additional constraints on R ggF f (s). They are shown in lower right panel in Fig. 12 where all the models above red and orange curves are excluded. Other searches for the Higgs boson made by LHC and TeVatron [74] experiments put limits which do not introduce additional constraints. Similar scatter plots for V BF/V H production process are shown in Fig. 13 for the case of Set 1 and in Fig. 14 for the case of Set 2. We see that the signatures of V BF/V H sgoldstino production look quite promising: corresponding signal strengths can reach values up to 1.2 − 1.3 for γγ and for other channels they can be as large as 0.3. This indicates that the discussed scenario is out of reach of TeVatron experiments but hopefully can be probed in the future LHC runs.

Concluding remarks
To summarize, in this paper we discussed implications of the possible mixing between the supersymmetric Higgs sector and hidden sector in models with low-scale supersymmetry breaking. We have found that the mixing of scalar sgoldstinos to the lightest Higgs boson  h can result in an additional increase of mass of the latter. As an attractive feature of this scenario, we have found that new sgoldstino-like scalar states which is somewhat lighter than the Higgs-like boson is present in low energy spectrum. In particular, there is a region in the parameter space of the model where this state can explain 2σ LEP excess in e + e − → Zs withs → bb having mass around 98 GeV.
Performing a scan over parameters for √ F = 10 TeV and selecting phenomenologically acceptable models we have found that the mixing with sgoldstino results in a distinctive features in signal strengths for the Higgs-like resonance in this scenario. In gluon-gluon fusion the signal strengths for fermion and massive vector boson channels are somewhat larger than unity with values about 1.0 − 1.5. On the contrary, for vector boson fusion or associative production with massive vector boson the signal strengths are predicted to be within the range about 0.7 − 1.0. If sgoldstino is required to be 98 GeV LEP resonance then even more strict bounds on the signal strength are predicted, which hopefully can be probed in the next runs of the LHC experiments.
Note that here we have performed a simplified analysis by limiting ourselves to the case of MSSM decoupling limit, zero vacuum expectation value for sgoldstino field and fixed value for supersymmetry breaking scale √ F = 10 TeV. By going beyond these assumptions one could obtain that the life with sgoldstino-Higgs mixing can become even more complicated. In particular, we expect different mixing patterns due to presence of heavier Higgs boson in spectrum (see e.g. [83]) and shifts in the Yukawa couplings of the lightest Higgs boson to fermions [46]. Among the other possible phenomenological issues which are not covered in the present study we mention possibility of new decays of the lightest Higgs boson in which sgoldstino can be involved including those with flavour violation (see also Ref. [29]). For sufficiently light sgoldstinos decaysh →sh * with subsequents → γγ andh → bb orh →ss * withs → γγ become possible resulting in new signatures in the Higgs boson decays. Another interesting area to explore is models of low-scale supersymmetry breaking in which gauginos have Dirac masses (see, e.g. [84] and references therein). In this case sgoldstino interactions with the SM fields can be different as compared to the case discussed in our paper resulting in different mixing properties and the couplings of mass states. We leave investigations of these interesting possibilities for future work.
In this Appendix we present formulas for partial widths of the decay of the Higgs-like res-