Scalar Exchange Forces and Generalized Most Attractive Channel Rule

Abstract

We discuss the possibility that fermionic condensates arise from the dominance of scalar exchange forces over vector gluon exchange. When a scalar in the adjoint representation is exchanged in the reaction $A+A \to A+A$, the usual most attractive channel (MAC) rule is reversed in sign, with the consequence that the formation of a condensate with the largest possible Casimir is favored. More generally, when a scalar in a general representation is exchanged in the reaction $A+B \to B+A$, the group theoretic sum giving the force sign and strength can be expressed in terms of a Racah coefficient for the group in question. We illustrate the formalism in the case of the group SU(2), and give possible applications to SO(10) and $E_6$ grand unification.