Sgoldstino signature in $hh$, $W^+W^-$ and $ZZ$ spectra at the LHC

In a supersymmetric extension of the Standard Model of particle physics (SM) with low scale of supersymmetry breaking, sgoldstino of (sub)TeV mass can be observed at the Large Hadron Collider (LHC) as a peak in diboson mass spectra. Moreover, as a singlet with respect to the SM gauge group, scalar sgoldstino can mix with the SM-like Higgs boson and interfere in all neutral channels providing with the promising signatures of new physics if superpartners are heavy. Sgoldstino couplings to the SM particles are determined by the pattern of soft supersymmetry breaking parameters. Here we concentrate on the cases with a noticeable sgoldstino contribution to di-Higgs channel. Having found a phenomenologically viable region in the model parameter space where scalar sgoldstino, produced at the LHC in gluon fusion, decays into a pair of the lightest Higgs boson we give predictions for corresponding cross section. Using the results of the LHC searches for scalar resonances we place bounds on the supersymmetry breaking scale $\sqrt{F}$ in this region of parameter space. Remarkably, in this region sgoldstino may also be observed in $W^+W^-$ and $ZZ$ channels, yielding independent signatures, since their signal strengths are related to that of di-Higgs channel.


Introduction
The first stages of LHC running culminated in 2012 with the discovery of the Higgs boson [1,2]. Further experimental program of the LHC experiments includes measurement and precise determination of the Higgs boson coupling constants using data on the Higgs boson production cross sections and decay widths. Numerous models of new physics predict deviations of these coupling constants from their SM values. In this respect, the Higgs boson self-coupling is of great interest as several classes of SM extensions imply some modification of the Higgs sector. Double Higgs boson production is one of the most sensitive observables to the Higgs boson selfinteraction and specific modifications of the Higgs sector. This process is expected to be seen with various signatures at LHC (see Ref. [3] for a review) operating in the high luminosity regime (HL-LHC). A deviation of the cross section from the SM prediction could indicate possible ways to extend the SM.
The cross section of the di-Higgs production in proton collisions in the SM was calculated in [4][5][6][7][8][9]. The double Higgs boson production can be resonantly enhanced if the Higgs sector contains new scalar(s) with the mass around TeV scale. Examples of such scenarios were discussed in Refs. [10][11][12][13][14][15][16]. In this paper we consider supersymmetric models with low scale supersymmetry breaking (see e.g. [17][18][19][20][21][22][23][24][25]). In this class of models the lightest supersymmetric particle is gravitino which acquires its mass via the super-Higgs mechanism [26][27][28]. The longitudinal component of gravitino appears after spontaneous supersymmetry breaking as a derivative of the Goldstone fermion -goldstino G. The latter can be the fermionic component of a chiral supermultiplet, where θ is the Grassmannian coordinate, φ is the complex scalar field called sgoldstino and F φ is the auxiliary field which acquires non-zero vev, i.e. F φ = F , triggering spontaneous SUSY breaking in the entire model. Here we consider scenarios in which the scale √ F of SUSY breaking is not very far from the electroweak scale while all the fields in the hidden sector except for those belonging to the goldstino multiplet are heavy. The purpose of our study is to investigate possibility of the resonant enhancement of di-Higgs production at the LHC due to contribution of relatively light scalar sgoldstino. To make the picture as clear as possible, yet realistic and phenomenologically viable, we restrict ourselves to the case in which all superpartners of the SM particles are also relatively heavy.
Though model-dependent, but typically the main sgoldstino production mechanism in pp collisions is through gluon-gluon fusion [29]. Being even with respect to R-parity, sgoldstino can decay into pairs of the SM particles. We single out the part of the parameter space where branching fraction of sgoldstino decay into pair of the Higgs bosons is close to the largest possible value which is 25%. This region of the model parameter space corresponds to sufficiently large mixing between sgoldstino and the lightest Higgs boson which can result in an amplification of the corresponding decay width and consequently di-Higgs production cross section. In this regime sgoldstino decays dominantly into hh, W + W − and ZZ with partial widths related as 1:2:1 respectively. We discuss the sgoldstino signature in spectra of these final states at the LHC and calculate cross sections of the corresponding processes. Using present experimental constraints on production of the scalar resonances decaying into the heavy bosons we obtain bounds on the SUSY breaking scale. This paper is organized as follows. In Section 2 we describe the model Lagrangian and derive the potential of scalar fields. We discuss interaction of sgoldstino and Higgs bosons and mixing in this sector. We obtain sgoldstino-Higgs bosons trilinear couplings. The scalar sgoldstino production channels and decay modes are discussed in Section 3. There we outline a region in the model parameter space where sgoldstino can decay into pair of the lightest Higgs bosons as well as into the pair of the massive vector bosons with a considerable probabilities. The resonant behavior of the di-Higgs, W + W − and ZZ cross sections and their dependence on model parameters are investigated in Section 4. There we also present bounds on the supersymmetry breaking scale extracted from results of ATLAS and CMS experiments in searches for di-boson resonances. Our findings are summarized in Section 5. Appendicies are reserved for explicit expressions for trilinear coupling constants of the neutral scalars.

The model
We consider a supersymmetric extension of the Standard Model with the chiral goldstino superfield (1). The model includes the Minimal Supersymmetric Standard Model (MSSM) in which soft supersymmetry breaking terms are generated through interactions with Φ, when the auxiliary component of F Φ gets replaced with its non-zero vacuum expectation value, i.e. F φ = F . The Lagrangian of the model can be written (see e.g. [30]) as the sum of the contributions from the Kähler potential L K , superpotential L W , vector fields L gauge and a part which describes dynamics of the goldstino supermultiplet L Φ . The first term in (2) has the form where the sum is taken over all matter superfields Φ k . The parts L W and L gauge read and where sum goes over a = 3, 2, 1, correspondingly to all the SM gauge groups where m 2 s and m 2 p are mass parameters for scalar and pseudoscalar sgoldstino fields. The model described above should be considered as an effective theory which contains higher order interaction terms suppressed by higher powers of F and for consistency we require smallness of the soft parameters, m sof t √ F . Using the Lagrangian (2) one can obtain the scalar potential of the Higgs and sgoldstino sector (see also [31]) Here T are the Higgs doublets and we consider pall the parameters entering the potential to be real. As √ F is the largest scale in the model, we are interested in the scalar potential to the leading order in 1/F . Moreover, since each sgoldstino field enters the interaction terms with factor 1/F , rates of multi-sgoldstino processes are naturally parametrically suppressed. Therefore, the most promising processes are those involving single sgoldstino production.
Now we expand the scalar fields around their vacuum expectation values. For the Higgs fields we have, as usual [32] where where s and p are its scalar and pseudoscalar components. In general, the sgoldstino field acquires a non-zero vev φ = v φ and one can show [33] that v φ scales as 1/F for scalar sgoldstino heavier than the lightest Higgs boson. Therefore, the terms with sgoldstino vev would contribute to the terms with smaller number of sgoldstino fields but suppressed by powers of 1/F 2 and hence are neglected in what follows. Naturally, for consistency reasons, we set v φ = 0. Likewise, is a true vacuum up to corrections suppressed by powers of 1/F 2 , which we ignore 1 .
One can substitute the expansions (12)- (14) into the potential (8)- (11) and find the sgoldstino-Higgs boson vertices to the leading order in 1/F . In order to simplify expressions for the interaction terms, let us introduce the notations 1 Let us note that for √ F ∼ few TeV the corrections of order 1/F 2 to the scalar potential can be valuable and contribute considerably to the mass of the lightest Higgs boson [34]. For the choice of parameters considered in the present study these corrections are negligible.
The mixing angle α in Eqs. (12) and (13) is chosen in the standard way [32] tan 2α tan 2β Once again, any possible corrections suppressed by powers of 1/F 2 are small and neglected here. At the same time the loop corrections to the effective potential should be large enough to generate observed value of the Higgs boson mass. Their size is determined mainly by interactions with top-stop sector. In what follows we do not discuss squark sector of the model and just assume squarks to be sufficiently heavy. Therefore, we treat the quantum corrections which contribute to the Higgs boson masses as obligatory and of the size sufficient for saturating the lightest Higgs boson mass. Consequently, we neglect radiative corrections to the mixing term between h and H, that is justified by the decoupling regime we assume in this study. The mass terms in the Lagrangian for the scalar (H, h, s) and pseudoscalar (A, p) fields have the following matrix form where the mixing terms read According to the above discussion the diagonal values of the mass matrices, i.e. m 2 h , m 2 H and m 2 A already contain leading quantum corrections. Recall, that our primary goal is to consider the possible sgoldstino contribution to the pair productions of the lightest Higgs bosons h which are interpreted as the scalar Higgs-like particles discovered at the LHC. We present below expressions for the relevant trilinear coupling constants in the scalar sector. Corresponding part of the interaction Lagrangian is where are the MSSM Higgs trilinear couplings and are the trilinear coupling constants of the interaction between scalar sgoldstino and the Higgs bosons. Other trilinear couplings in the scalar sector are not relevant for the di-Higgs boson production in the model to the leading order in 1/F . However, in Appendix A we present expressions for those interaction terms containing single sgoldstino and two Higgs bosons for completeness. They agree with the similar expressions in Refs. [31,35]. At F → ∞ the decompositions (12), (13) and (14) make the mass matrices of the component fields (H, h, s) and (A, p) diagonal at tree level. At finite F and relatively light sgoldstino considered in this study the mixing between these fields can result in a considerable modification of the model phenomenology. Being interested primary in hh final state we concentrate below on the mixing in the scalar sector, i.e. between H, h and s, and denote the mass states asH, h ands. Similar transformation can be also performed for the mass matrix of pseudoscalars A, p by introducing fieldsÃ,p.
In order to make the 3×3 mass squared matrix in Eq. (19) diagonal, we consider the following rotation which is parameterized by the mixing angles φ, ψ, θ Hereinafter we work in the approximation of the small mixing angles. Given that the mixing terms are suppressed by 1/F we take the angles φ, ψ, θ to the leading non-zero order in 1/F . Then by writing the condition of zero off-diagonal elements in the first-order approximation in (30) one can obtain the expressions for the mixing angles while as 1-2 and 2-1 elements in the mass matrix (19) are equal to zero, the third mixing angle φ appears to be of the second order in 1/F : It can be easily seen from the equations (31), (32), (33)  Rotation to the mass eigenstates denoted asH,h,s is given by H h s = Hhs C, where in the approximation of small mixing the rotation matrix C can be written as Similar calculations can be performed for the mass matrix of the pseudoscalar fields. Corresponding mixing angle ξ reads In the basis of mass eigenstates the trilinear coupling constants which are relevant for resonant production of the pair of the lightest Higgs bosons can be written as follows where we omitted the terms of order 1/F 2 and higher.
In the next Sections these vertices are used in the calculation of sgoldstino decay rate into a pair of neutral Higgs bosons and of the resonant double-Higgs production cross section. Expressions for other vertices with one sgoldstino and two Higgs bosons (shH,sÃÃ,sH +H − ,pÃH, pÃh), irrelevant for the present study, can be found in Appendix B.
In the next sections we will discuss production and decay of scalar sgoldstino. The relevant part of the Lagrangian describing interactions of the scalar sgoldstino s with SM vector bosons has the form where W µν , Z µν , F µν and G a µν are the field strength tensors for the W ± -bosons, Z-boson, photon and gluons respectively; the mass parameters in front of the couplings read Interactions (37) along with (23) and sgoldstino-Higgs mixing given by (34) determine phenomenology of TeV scale scalar sgoldstino at hadron colliders. Results of our analysis depend upon the following parameters: tan β, µ, m A , m s , M 1 , M 2 , M 3 , F . Since formulas of Section 2 are obtained in the small mixing angles approximation, one should keep only those models in the parameter space that correspond to small mixing angles ψ, θ (for the numerical calculations we select the models with θ < 0.3, ψ < 0.3).

Sgoldstino production and decay channels
To understand possible size of the resonant double Higgs boson production in the model we need to study sgoldstino production in proton collisions and its subsequent decay. Here we refer to Refs. [29,[35][36][37][38][39][40] for previous studies of sgoldstino collider phenomenology. To simplify notations, in what follows we use s and h for the mass eigenstates (which were denoted ass andh in the previous Section) and take into account contributions from the sgoldstino-Higgs mixing to the leading order in 1/F .

Production of scalar sgoldstino
For typical hierarchy between the soft SUSY breaking parameters the dominant sgoldstino production mechanism is gluon fusion [29]. This process, gg → s, occurs in this model already at the tree level due to sgoldstino interaction with gluons governed by the coupling M 3 /F , see Eq. (37). Mixing with the Higgs bosons yields additional contributions to the amplitude of this process, see Figs. 1a, 1b. The contribution from sgoldstino mixing with heavy neutral Higgs (similar to Fig. 1b) is suppressed by 1/ tan β from the Htt vertex and also by square of its mass m 2 H in the expression for the corresponding mixing angle, therefore we neglect it in the following calculation of sgoldstino production cross section. The leading order cross section of the sgoldstino production in gluon fusion can be calculated using the parton distribution function (PDF) g(x, m 2 s ) of gluons in proton as with Here √ S is the center-of-mass energy in pp collisions and A 4m 2 t m 2 s is the loop factor (see, e.g. [41]) Note that with the mixing angle θ given by (32) both amplitudes in (42) are of the same order in 1/F and in the loop part of the amplitude we leave only the dominant contribution with the heavy top quark loop. As we assume the superpartners (in particular, squarks) to be relatively heavy, their contribution to this process is negligible. The NLO corrections to the production cross section for a scalar which has both effective gluon interaction (38) and Yukawa interaction with top quark was calculated in [43]. According to these results, corresponding K-factor, i.e. K p = σ N LO /σ LO , is about 2 for chosen sgoldstino mass interval and √ S = 13, 14 TeV. Since dependence of the K-factor on the relevant parameters in the considered parameter space is weak, we use the value K p = 2 to correct the leading order sgoldstino production cross section calculated using CTEQ6 Parton Distribution Functions (the CTEQ6L1 PDF-set for computations in the leading order) [42].
The scalar sgoldstino production cross section is shown in Fig. 2    ). In the case of relatively small sgoldstino-Higgs mixing the cross section of sgoldstino production presented in Fig. 2a is dominated by the first term in (42), see Fig. 1a. In the opposite case of large mixing angle, the cross section in Fig. 2b reveals a non-trivial behavior related to the sgoldstino mass dependent contribution from the loop factor in the amplitude with sgoldstino-Higgs mixing, cf. Fig. 1b. For light sgoldstinos, the contribution from the mixing term dominates in the production cross section, see Fig. 1b. The effect is reduced with increasing sgoldstino mass and almost disappears as m s approaches 1 TeV, where the first term in (42) , Fig. 1a, fully dominates.
Other sgoldstino production channels [29] include vector boson fusion, sgoldstino associated production with a vector boson and tts production. They are suppressed as compared to gluon fusion for the parameter space discussed in this study (even the sgoldstino-Higgs mixing does not change the day). In the considered region of sgoldstino mass m s the gluon fusion gives the dominant contribution to production of virtual Higgs boson that mixes with sgoldstino. Since we consider regime of small values of mixing angle θ, the diagrams with sgoldstino-Higgs mixing are accordingly suppressed as compared to one in Fig. 1a. Therefore we consider for them only the gluon fusion channel of Higgs boson production.

Sgoldstino decays
Let us discuss the main decay modes of (sub)TeV sgoldstinos. The Feynman diagrams for the dominant decay channels are shown in Fig. 3. Corresponding amplitudes are determined by the interactions (37) and sgoldstino-Higgs mixing. The latter is taken into account in the analysis to the leading order in 1/F . We start with the sgoldstino decay into a pair of gluons, s → gg. As in the case of sgoldstino production in gluon fusion there are two amplitudes in the leading order. Indeed, sgoldstino can decay directly into gluons or via mixing with the lightest Higgs boson, see Fig. 3a. Since in the leading order the decay to gluons is just the process cross symmetric to the gluon fusion, we find in the formula for sgoldstino rate to gluons the similar expression as in formula for production cross section (42), namely Γ (s → gg) = 1 4π In the absence of the mixing (i.e. when θ = 0) this expression can be found in Ref. [36]. We include NLO QCD corrections by introducing the factor K d = 1.6 for gluon decay channel of sgoldstino. In the considered regime of sgoldstino decaying dominantly into Higgs and massive vector bosons, its precise value is not very important and we conservatively choose it close to that of predicted for gluonic decay of the Higgs-like scalar (see Fig. 7 in [41]). In the sgoldstino decays to either pair of photons s → γγ (Fig. 3b), or photon and Z-boson s → γZ (Fig. 3c), we can neglect the mixing contribution, since the Higgs boson h decays into these particles through loops and the corresponding amplitudes are highly suppressed by gauge and loop factors. Therefore, the corresponding decay widths reads [36] Γ (s → γγ) = 1 32π Next we consider the scalar sgoldstino to be heavy enough for the decay into a pair of the lightest Higgs bosons (Fig. 3d). The decay width can be calculated with help of the trilinear coupling in Eq. (36) as The case of sgoldstino decays to massive vector bosons is more involved [36]. Let us consider the decay of sgoldstino into a pair of W-bosons (Fig. 3e). The sgoldstino Lagrangian contains two different terms responsible for the interaction between sgoldstino and W-bosons. The first one is the contribution of the first term in (37) which is determined by the coupling constant This term originates from the sgoldstino interaction Lagrangian (37) and is not affected by mixing with the neutral Higgs bosons (to the leading order in 1/F ). Another contribution is related to sgoldstino-Higgs mixing and the interactions of the Higgs bosons with W ± . The corresponding interaction Lagrangian has the form The width of s → W + W − decay from both contributions is given by the formula Similarly for Z-boson one obtains The respective trilinear coefficients for Z-bosons are The decay widths of sgoldstino to fermions s → ff are small as compared to the decay widths to bosons. Also note that sgoldstino can decay into pair of gravitinos, however the corresponding partial width is strongly suppressed in the interesting case of m s √ F . In summary, the total sgoldstino decay width can be found as the following sum over all the considered decay channels The total width scales as 1/F 2 and for m sof t , µ √ F sgoldstino width is typically considerably smaller than its mass.
Let us discuss how the hierarchy between different sgoldstino decay modes depends on its mixing with other part of the Higgs sector. It is known that at large √ F even small mixing with the Higgs bosons can change the patterns of dominant sgoldstino decay modes [38]. In our analysis we concentrate mostly on the decoupling regime, i.e. when m A , m H m h , which corresponds to sin α ≈ − cos β and cos α ≈ sin β. In this limit, along with m sof t , µ √ F which is required for small values of the mixing angles, the scalar sgoldstino of the mass at TeV scale mixes mainly with the lightest Higgs boson. The corresponding mixing angle determines the parameter X in (20) which becomes For the part of the model parameter space relevant for our study the last term in this expression dominates. To illustrate the hierarchy between the sgoldstino decay modes, we show in Fig respectively. This regime was discussed in Ref. [35] in the context of searches for sgoldstino at the LHC. Our present interest in this study is related to the possibility of resonant double Higgs production in this part of the model parameter space, as the branching ratio of two light neutral Higgs boson channel can reach 25%. Note that in this regime sgoldstino decays also into massive vector bosons which can help to test this scenario. In this calculation we use the approximate formulas for mixing angles for simplicity. We checked this approximation by computing mixing angles using (exact) numerical diagonalization of the mass matrix. The results from approximate formulas agree very well with branching ratios obtained numerically.
Let us study the dependence of the transition between gluon dominated and heavy boson dominated regimes of sgoldstino decays on the model parameters. As a conditional boundary between these two regimes we take Br(s → hh) = 0.125 and in Fig. 5 we show slices of this boundary on the planes (tan β, µ), (M 3 , µ), (m s , µ) and (m A , µ) assuming other parameters to be fixed. Regions between the lines on the plots correspond to smaller |µ| and therefore to the gluon dominated sgoldstino decay. Outside these regions sgoldstino decays mostly to hh, W + W − and ZZ and the ratio between their partial widths approaches 1:2:1 at larger |µ|. We see that larger values of tan β, M 3 , m s push the boundary of the region with gluon dominated sgoldstino decay to larger values of µ. A nontrivial dependence of the boundaries on m A is observed only for its small values, when the decoupling regime gets violated.
Let us present analytical estimates for the dependence of the boundaries between different regimes on the model parameters. At large mixing angle the leading contribution to the The vector bosons dominate in sgoldstino decays if Γ(s → gg) Γ(s → W W ) or where we denote A (4m 2 t /m 2 s ) = A t for brevity. For all values of sgoldstino mass in the range 200-1000 GeV we find |A t | ≤ 1.9 and α s A t /(3π) 1. Therefore, the condition of dominating decays of sgoldstino to vector bosons is |θ| θ cr , where 4 Phenomenology of the resonant sgoldstino signature In this Section we discuss sgoldstino production at the LHC yielding the resonant signatures in hh, W + W − and ZZ final states. Our primary interest here is in double-Higgs mode, which we start from; the other two we investigate similarly. Also recall, that sgoldstino partial decay widths for these double-boson final states are related as 1:2:1 for θ θ cr , and so the modes are compatible. To calculate the cross section of the resonant di-Higgs production in the process pp → s → hh, we work in the narrow width approximation for sgoldstino which means that the cross section for production of particles in a final state f in is found as a product of the sgoldstino production cross section (at the given energy of protons) and the corresponding branching ratio Br(s → f in).
The dependence of the resonant double Higgs boson production cross section on µ for chosen values of tan β and M 3 is shown in Figs. 6a and 6b. Other parameters are fixed as follows: m s = 1 TeV, m A = 5 TeV, M 1 = M 2 = 1 TeV, √ F = 20 TeV, K p = 2, K d = 1.6. We see that for small values of |µ| the cross section of this process is relatively small due to a suppression of the decay channel s → hh. At the same time, the cross section is increased for larger |µ|, i.e. for larger mixing between sgoldstino and the lightest Higgs boson (54) which corresponds to transition to the regime of sgoldstino decay to massive vector bosons. It is in this regime the resonant cross sections of pp → s → W + W − and pp → s → ZZ are directly related to that of di-Higgs production. As it can be seen from Fig. 6a, with the increase of tan β, the value of µ, at which the double Higgs production is enhanced, also increases. The sgoldstino production cross section grows with M 3 and therefore the double Higgs production cross section also increases.
At large values of M 3 the points with large absolute values of µ in Fig. 6b are excluded by existing experimental data obtained by ATLAS and CMS collaborations. The search for a scalar resonance that decays to two W -bosons was performed in [44,45]. Scalar resonance decaying into ZZ was studied in [46]; see also Refs. [47] for [48] the case of Z-boson and photon in the final state and Ref. [49] for a pair of photons. We also take into account current upper limits on the production cross section of a scalar which decays into two Higgs bosons which are presented in [50][51][52][53][54][55][56]. We use the whole set of the above experimental constraints to find the phenomenologically viable region in the model parameter space. In Fig. 6 we show the results for phenomenologically viable models only.
One can notice that the cross section in Fig. 6a is nearly constant at intermediate absolute values of µ but starts growing again at its larger absolute values. This behavior is due to the change in the dominant contribution to the sgoldstino effective coupling to gluons. Namely, according to (20) and (32) the larger values of |µ| correspond to larger |X| and |θ|. In this regime, the cross section of sgoldstino production (41) is determined mostly by the sgoldstino mixing with the Higgs boson. Parametrically this occurs when or |θ| θ cr with θ cr ≡ 6πvM 3 /(α s |A t |F ). Thus for θ larger than the critical value θ cr , the sgoldstino production cross section increases with the growth of |µ|. For θ cr θ cr , this cross section does not depend on the value of the mixing angle and it is determined fully by values of sgoldstino mass, M 3 and F .
In Fig. 7 we show the similar dependencies of the cross section pp → s → hh as in Fig. 6 but calculated for √ S = 14 TeV. The cross section is depicted for five different combinations of tan β and M 3 and for the same set of other parameters. Similarly, in Fig. 8 the cross sections of the processes pp → s → W W and pp → s → ZZ are calculated for √ S = 14 TeV. Let us note again that at θ > θ cr the following relations between the resonant sgoldstino production cross sections are valid.
In the rest of this Section we assume the regime of sgoldstino decaying dominantly into hh, W + W − and ZZ with the relation 1:2:1 between their partial widths. In this regime, the results of searches for neutral scalar resonances by the ATLAS and the CMS collaborations at √ S = 13 TeV discussed above can be used to constrain sgoldstino production cross section and corresponding parameters of the model. Assuming θ θ cr (which corresponds to the regime 1:2:1 for sgoldstino decays) as well as θ θ cr (meaning that the first term in the expression (42) for the sgoldstino production cross section dominates) one obtains that the cross section depends on the combination M 3 /F only. Hence the experimental data can be used     Figure 9: Upper limits at 95% CL on ratio M 3 /F obtained from the experimental data [44][45][46], [50][51][52][53][54][55][56] for √ S = 13 TeV. Constraints obtained from the searches for a heavy scalar resonance decaying into a pair of Z-bosons, W -bosons and Higgs bosons are shown in green, blue and red, respectively. The yellow line connects points of joint constraint on M 3 /F (minimum upper limit).
to constrain this quantity.
here σ prod is the sgoldstino production cross section for M 3 = 3 TeV, √ F = 20 TeV, and X runs through {h, W, Z}. The obtained constraints are presented in Fig. 9. In the case of not very heavy sgoldstinos (m s < ∼ 600 GeV) the most rigorous constraints are given by the decay mode s → hh.
Using lower limits on M 3 from the searches for gluino in models with gauge-mediated supersymmetry breaking along with the upper bound on M 3 /F presented above one can obtain constraints on the supersymmetry breaking scale √ F . In most of the experimental studies [57][58][59][60][61][62][63] lower limits on gluino mass were obtained for several simplified models and the presented experimental bound varies in the range 1.8-2 TeV. Adopting for the estimate the conservative lower bound (M 3 ) LL > 2 TeV and using the constraints on M 3 /F from √ S = 13 TeV data shown in Fig. 9, we apply to find lower bounds on √ F depending on the mass of the scalar sgoldstino, which are shown in Fig. 10. We find that in the considered part of the model parameter space the bounds on m s , GeV Figure 10: Lower limit on √ F obtained using the upper limit on M 3 /F (Fig. 9) and a conservative lower bound M 3 > ∼ 2 TeV from experimental data [57][58][59][60][61][62][63] at √ S = 13 TeV.

Conclusions
To summarize, in this work we have investigated the impact of sgoldstino-Higgs mixing on sgoldstino decays and production in proton-proton collisions. We have observed two different regimes in sgoldstino decays. At the small mixing sgoldstino decays dominantly into gluons while at the large one it decays into the lightest Higgs bosons and vector bosons, W + W − and ZZ, with the relation between the corresponding branching ratios as 1:2:1. In this region of the model parameter space there can be enhanced resonant di-Higgs production. Using current experimental data from the LHC experiments we obtained constraint on the ratio M 3 /F . With the current conservative constraint M 3 > ∼ 2 TeV we placed the bounds on the supersymmetry breaking scale √ F varying in 8 − 12 TeV range for sgoldstino of masses 200-1000 GeV and in the regime of massive boson dominance in its decays. Since √ F can be treated as a scale of SUSY breaking, the estimate of its lower limit may be useful for a theoretical consideration of similar low-scale supersymmetry breaking models with sgoldstino. A characteristic signature of the considered scenario is the appearance of sgoldstino resonance in di-Higgs, W + W − and ZZ spectra with the relation between corresponding cross section close to 1:2:1. Searches for the resonant production of massive boson resonances at HL-LHC are expected to either reveal the sgoldstino signature or put further constraints on the models with sgoldstino using updated results of experimental searches for this process.

Acknowledgements
The work of EK was supported by the grant of "BASIS" Foundation no. 19-2-6-16-1.