We consider a supersymmetric extension of the Standard Model with a broken supersymmetry. Our model contains the fields of the Minimal Supersymmetric Standard Model and goldstino multiplet, which is present due to the supersymmetric version of the Goldstone theorem. Scalar component of this multiplet is traditionally called sgoldstino. We consider the interval of sgoldstino masses from 260 GeV to 1 TeV.
We investigate the possibility of increase in resonant di-Higgs production cross section at the LHC energies due to processes with sgoldstino. Sgoldstino is an R-even particle and thus it can be produced by the gluon fusion and then decay into the pairs of the Standard Model particles, for instance, the pairs of light neutral Higgs bosons.
We show that there are two typical behaviors of sgoldstino branching ratio: gluon domination and the major decay to pairs of light neutral Higgses, W-bosons and Z-bosons. We estimate the borders of the corresponding regions in the parameter space. For particular values of sgoldstino-Higgs mixing angles we obtain an upper limit for the ratio $M_3/F$ from experimental searches for heavy scalar resonances made by the ATLAS and the CMS collaborations.