Decaying LSP in SO(10) GUT and PAMELA's cosmic positron

We suppose that the lightest supersymmetric particle (LSP) in the minimal supersymmetric standard model (MSSM) is the dark matter. The bino-like LSP can decay through the SO(10) gauge interactions, if one right-handed (RH) neutrino (ν1c) is lighter than the LSP and its superpartner (ν˜1c) develops a vacuum expectation value (VEV), raising extremely small R-parity violation naturally. The leptonic decay modes can be dominant, if the VEV scale of 16H is a few orders of magnitude lower than the VEV of 45H (≈1016GeV), and if a slepton (e˜1c) is relatively lighter than squarks. The desired decay rate of the LSP, Γχ∼10−26s−1 to explain PAMELA data can be naturally achieved, because the gaugino mediating the LSP decay is superheavy. From PAMELA data, the SU(3)c×SU(2)L×SU(2)R×U(1)B−L breaking scale (or the 16H VEV scale) can be determined. A global symmetry is necessary to suppress the Yukawa couplings between one RH (s)neutrino and the MSSM fields. Even if one RH neutrino is quite light, the seesaw mechanism providing the extremely light three physical neutrinos and their oscillations is still at work.