Veneziano Ghost Versus Isospin Breaking

Abstract

It is argued that an account for the Veneziano ghost pole, appearing in resolving the U(1) problem, is necessary for understanding an isospin violation in the $ \pi - \eta - \eta' $ system. By virtue of a perturbative expansion around the $ SU(2)_{V} $ ( $ m_{u} = m_{d} $ ) symmetric Veneziano solution, we find that the ghost considerably suppresses isospin breaking gluon and s-quark matrix elements. We speculate further on a few cases where the proposed mechanism can play an essential role. We discuss the isospin violation in meson-nucleon couplings and its relevance to the problem of charge asymmetric nuclear forces and possible breaking of the Bjorken sum rule. It is shown that the ghost pole could yield the isospin violation of order 2 \% for the $ \pi N $ couplings and 20 \% for the Bjorken sum rule.