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
(\nu^c_1) is lighter than the LSP and its superpartner (\tilde{\nu}^c_1)
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 {\bf 16}_H is a few orders of magnitude lower than the VEV of {\bf 45}_H
(\approx 10^{16} GeV), and if a slepton (\tilde{e}^c_1) is relatively lighter
than squarks. The desired decay rate of the LSP, \Gamma_{\chi} \sim 10^{-26}
sec.^{-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 x SU(2)_L
x SU(2)_R x U(1)_{B-L} breaking scale (or the {\bf 16}_H 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.
