Spontaneous symmetry breaking and vector-meson dominance

Abstract

This article is a continuation of our previous work on the $\rho -\pi$ puzzle. It examines further consequences of the unification of partial conservation of axial-vector current (PCAC) and vector-meson dominance (VMD) in which the pion is a Goldstone state and the $\rho$ is "dormant" Goldstone state. Our new picture of the vector mesons does not require an $A_1$ meson although such a state is not ruled out. The Weinberg sum rules which provide the raison d'être for the $A_1$ are reexamined. The first Weinberg sum rule can be accommodated without a narrow $A_1$ state although some enhancement seems required. Examining the $J^{\mathrm{PC}}=1^{+-}$ nonet we conclude that a new state, the isoscalar octet partner of the $B\left(1235\right)\mathrm{}$ should exist around 1.7 GeV assuming ideal mixing. Without a detailed assumption on the mixing angle, its mass should be in the range 1.4 to 1.7 GeV. We also discuss the photon-$\rho$ interactions. In the standard VMD picture the predicted rate for $\rho \to \pi +\gamma$ fails by five standard deviations, while in our picture this undesired result is averted.