Simple discrete symmetries in phenomenologically viableE6superstring models

We analyze the simplest discrete symmetries of the superpotential of superstring-inspired $E_6$ models necessary to simultaneously suppress (i) proton decay, (ii) neutrino masses, and (iii) tree-level flavor-changing neutral currents in $E_6$ superstring models without any intermediate scale. We show that there are two and only two different $Z_2$ symmetries that incorporate (i)–(iii). These symmetries put restrictions on the decays of exotic particles; in particular, the exotic quarks always decay semileptonically. A $Z_3$-symmetric model satisfying (i)–(iii) and with μ→eγ forbidden is also constructed.