Precise Relations between the Spectra of Vector and Axial-Vector Mesons

Abstract

Two sum rules are derived, relating moments of the spectral functions of the vector and axial-vector currents. If it is assumed that the $\rho$ and $A1\mathrm{}$ mesons dominate these moments, then their masses must be in the ratio $\frac{m_{A1\mathrm{}}}{m_{\rho }}=\sqrt{2}$, in very good agreement with experiment.