Low-Energy Limit in Hard-Pion Amplitudes and Magnetic Moment of ChargedρMesons

Abstract

A method previously used for deriving Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin (KSRF) -type relations is applied here to the radiative decay ${\ensuremath{\rho}}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}\ensuremath{\gamma}$. Comparing the amplitude calculated with the hard-pion technique to its exactly calculable (photon) low-energy limit, one obtains as consistency conditions the first Weinberg sum rule, the modified KSRF relation, and the magnetic moments of ${A}_{1}$ and ${\ensuremath{\rho}}^{+}$. The value for the last one is further investigated in a model devoid of the single-particle approximation, the result consisting of upper and lower bounds for it, namely, $\frac{16{\ensuremath{\pi}}^{2}{\ensuremath{\alpha}}^{2}{{g}_{\ensuremath{\rho}}}^{2}}{({{m}_{\ensuremath{\rho}}}^{4}\ensuremath{\int}{\ensuremath{\sigma}}_{{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}n}\mathrm{ds})}<{\ensuremath{\mu}}_{\ensuremath{\rho}}<2$.