BARYON NONCONSERVATION IN STANDARD MODEL AND YUKAWA INTERACTION

We consider the role of the Yukawa interactions in baryon nonconservation in the standard model which takes place due to the weak instantons. We have found a useful generalization of the usual gamma5 chirality for the case of massive fermions and proved that the selection rule DELTA(N(L) - N(R)BAR) = - Q(T) (Q(T) is the topological charge) remains valid for massive fermions if N(L)(N(R)BAR) is the number of the left- (right-) handed fermions (antifermions) in the sense of this generalized chirality. The result corresponds to a fact that a fermion zero-mode exists in the weak instanton field even in the case of massive fermions if the latter acquire their masses by spontaneous symmetry breaking. The zero-mode has a definite generalized chirality and the selection rule reflects a new index theorem for the massive Dirac operator. We consider also ''the weak theta problem'' and show that due to the existence of the zero-mode for massive fermions the effective action turns out to be independent of the value of the weak theta parameter and the weak theta term is unobservable.