We calculate the decay width of the photon splitting into three photons in a model of quantum electrodynamics with broken Lorentz invariance. We show that this process can lead to a cut-off in the very-high-energy part of a photon spectra of astrophysical sources. We obtain the 95% CL bound on the Lorentz violating mass scale for photons from the analysis of the very-high-energy part of the Crab Nebula spectrum, obtained by HEGRA. This bound improves previous constraints by more than an order of magnitude.

We consider a supersymmetric extension of the Standard Model with lowscale 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 2σ LEP excess with mass around 98 GeV.

For supersymmetric extensions of the Standard Model with light sgoldstinos-scalar and pseudoscalar superpartners of goldstinos-we estimate the signal rate anticipated at the recently proposed fixed target experiment SHiP utilizing a CERN Super Proton Synchrotron beam of 400 GeV protons. We also place new limits on the model parameters from a similar analysis of the published results of the CHARM experiment.