Proton stability and dark matter in a realistic string MSSM

Abstract

We demonstrate the existence of an extra nonanomalous $U(1)$ gauge symmetry in a three-generation Pati-Salam model constructed with intersecting D6-branes in Type-IIA string theory on a ${T}^{6}/({\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2})$ orientifold. This extra $U(1)$ forbids all dimension-4, 5, and 6 operators which mediate proton decay in the MSSM. Moreover, this results in the effective promotion of baryon and lepton number to local gauge symmetries, which can potentially result in leptophobic and leptophilic ${Z}^{\ensuremath{'}}$ bosons observable at the LHC. Furthermore, it is not necessary to invoke $R$-parity to forbid the dimension-4 operators which allow rapid proton decay. However, $R$-parity may arise naturally from a spontaneously broken $U(1{)}_{B\ensuremath{-}L}$. Assuming the presence of $R$-parity, we then study the direct-detection cross-sections for neutralino dark matter, including the latest constraints from the XENON100 experiment. We find that these limits are now within required range necessary to begin testing the model.