Spontaneous R-parity breaking, stop LSP decays and the neutrino mass hierarchy

The MSSM with right-handed neutrino supermultiplets, gauged B−LB−L symmetry and a non-vanishing sneutrino expectation value is the minimal theory that spontaneously breaks R  -parity and is consistent with the bounds on proton stability and lepton number violation. This minimal B−LB−L MSSM can have a colored/charged LSP, of which a stop LSP is the most amenable to observation at the LHC. We study the R-parity violating decays of a stop LSP into a bottom quark and charged leptons – the dominant modes for a generic “admixture” stop. A numerical analysis of the relative branching ratios of these decay channels is given using a wide scan over the parameter space. The fact that R  -parity is violated in this theory by a vacuum expectation value of a sneutrino links these branching ratios directly to the neutrino mass hierarchy. It is shown how a discovery of bottom-charged lepton events at the LHC can potentially determine whether the neutrino masses are in a normal or inverted hierarchy, as well as determining the θ23θ23 neutrino mixing angle. Finally, present LHC bounds on these leptoquark signatures are used to put lower bounds on the stop mass.