Superstring standard model from Z_{12-I} orbifold compactification with and without exotics, and effective R-parity

Abstract

We construct a supersymmetric standard model in the context of the $Z_{12-I}$ orbifold compactification of the heterotic string theory. The gauge group is $SU(3)_c\times SU(2)_L\times U(1)_Y\times U(1)^4\times[SO(10)\times U(1)^3]'$. We obtain three chiral families, $3\times\{Q,d^c,u^c,L,e^c,\nu^c\}$, and Higgs doublets. There are numerous neutral singlets many of which can have VEVs so that low energy phenomenology on Yukawa couplings can be satisfied. In one assignment (Model E) of the electroweak hypercharge, we obtain the string scale value of $sin^2\theta_W^0={3/8}$ and another exactly massless {\it exphoton} (in addition to the photon) coupling to exotic particles only. There are color triplet and anti-triplet exotics, $\alpha$ and $\bar{\alpha}$, $SU(2)_L$ doublet exotics, $\delta$ and $\bar{\delta}$, and $SU(3)_c\times SU(2)_L$ singlet but $Y={2/3},-{1/3},-{2/3},{1/3}$ exotics, $\xi,\eta,\bar{\xi}, \bar{\eta}$. We show that all these vector-like exotics achieve heavy masses by appropriate VEVs of neutral singlets. One can find an effective R-parity between light (electroweak scale) particles so that proton and the LSP can live sufficiently long. In another assignment (Model S) of the electroweak hypercharge, there does not appear any exotic particle but $sin^2\theta_W^0={3/14}$.