Gauged B-x_i L origin of R parity and its implications

Gauged B-L is a popular candidate for the origin of the conservation of R parity, i.e. R = (-)^{3B+L+2j}, in supersymmetry, but it fails to forbid the effective dimension-five terms arising from the superfield combinations QQQL, uude, and uddN, which allow the proton to decay. Changing it to B-x_i L, where x_e+x_\mu+x_\tau=3 (with x_i not equal to 1) for the three families, would forbid these terms while still serving as a gauge origin of R parity. We show how this is achieved in two minimal models with realistic neutrino mass matrices, and discuss their phenomenological implications.