$R$-parity Violating Decays of Wino Chargino and Wino Neutralino LSPs and NLSPs at the LHC

The $R$-parity violating decays of both Wino chargino and Wino neutralino LSPs are analyzed within the context of the $B-L$ MSSM heterotic standard model. These LSPs correspond to statistically determined initial soft supersymmetry breaking parameters which, when evolved using the renormalization group equations, lead to an effective theory satisfying all phenomenological requirements; including the observed electroweak vector boson and Higgs masses. The explicit decay channels of these LSPs into standard model particles, the analytic and numerical decay rates and the associated branching ratios are presented. The decay lengths of these RPV interactions are discussed. It is shown that the vast majority of these decays are prompt, although a small, but calculable, number correspond to displaced vertices of various lengths. It is demonstrated that for a Wino chargino LSP, the NLSP is the Wino neutralino with a mass only slightly higher than the LSP-- and vice-versa. As a consequence, we show that both the Wino chargino and Wino neutralino LSP/NLSP $R$-parity violating decays should be simultaneously observable at the CERN LHC.