Nuclear Physics B232 (1984) 143-179 t~) North-Holland Publishing Company SIX-FERMION (B-L)-VIOLATING OPERATORS OF ARBITRARY GENERATIONAL STRUCTURE Sumathi RAO and Robert E. SHROCK Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, New York 11794, USA Received 3 February 1983 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)cXSU(2)LXU(1)y-invariant operators, violate (B-L) and, in the standard theory with no va's, do so by +2 units. The process for which the six-fermion SU(5)-invariant operators are most important is the n,--~fitransition. Accordingly, we enumerate and construct the complete set of multigenerational six-quark B - 13operators which are invariant under SU(3)c × SU(2) L× U(1) and SU(3)cxU(1)e.m. and determine which of these contribute to n~--~fi 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 coefficientfunctions. Finally, we comment on the absolute n ~ fi transition rate and derive a new lower bound on the masses of color sextet ( B - L)-violating Higgs bosons. 1. Introduction The violation of baryon and (total) lepton numbers, B and L, is a natural feature of grand unified theories. In addition to the prediction of proton and bound neutron decay, there is the intriguing and equally testable possibility of neutron-antineutron transitions [1, 2, 4, 5, 7, 8, 9]*. In an earlier work [10] we analyzed the single- generation operators which are responsible for such transitions at the SU(5), SU(3)color × SU(2) elect ..... k x U(1) y, and SU(3)c x U(1) .... levels, and computed the matrix elements of the resultant six-quark operators in the MIT bag model [11, 12]**. In this paper, we shall extend this work to enumerate and construct the full set of SU(5)-invariant six-fermion (B-L)-violating operators of arbitrary generational structure and, correspondingly, the full set of multigenerational SU(3)c×SU(2)L × U(1) y and SU(3)c x U(1) .... -invariant six-quark operators con- tributing to B,~,B transitions. The subset of these operators that contributes to n ~--~fi transitions is exhibited. We shall show that all six-fermion operators which * n-~ fi oscillations have also been considered in a partially unified theory by Mohapatra and Marshak (ref. [3]); also the phenomenological possibility of n~-+fioscillations was considered previously by Kuzmin (ref. [6]) (for recent reviews of n-~+fioscillations, see refs. [7-9]). ** For other work on bag models of hadron structure, see ref. [11]. 143