Six-fermion (B-L)-violating operators of arbitrary generational structure

We enumerate and construct the complete set of six-fermion SU(5)-invariant operators of arbitrary generational structure and prove that they, and, more generally, all six-fermion SU(3)_c×SU(2)_L×U(1)_Y-invariant operators, violate (B-L) and, in the standard theory with no ν_R's, do so by ±2 units. The process for which the six-fermion SU(5)-invariant operators are most important is the n↔n transition. Accordingly, we enumerate and construct the complete set of multigenerational six-quark B-B operators which are invariant under SU(3)_c×SU(2)_L×U(1) and SU(3)_c×U(1)_e.m. and determine which of these contribute to n↔n transitions. An interesting result of this analysis is that the contributions of certain six-fermion operators containing higher-generation fields can dominate over those of entirely first-generation operators, despite mixing-angle suppression, because of much larger coefficient functions. Finally, we comment on the absolute n↔n transition rate and derive a new lower bound on the masses of color sextet (B-L)-violating Higgs bosons.