Radiative resonance couplings in $\gamma \pi \to \pi \pi$

Abstract

Studies of the reaction $\gamma \pi \to \pi \pi$, in the context of the ongoing Primakoff program of the COMPASS experiment at CERN, give access to the radiative couplings of the $\rho (770)$ and ${\rho }_3(1690)$ resonances. We provide a vector-meson-dominance estimate of the respective radiative width of the ${\rho }_3$, ${\Gamma }_{{\rho }_3\to \pi \gamma }=48(18)$ keV, as well as its impact on the $F$-wave in $\gamma \pi \to \pi \pi$. For the $\rho (770)$, we establish the formalism necessary to extract its radiative coupling directly from the residue of the resonance pole by analytic continuation of the $\gamma \pi \to \pi \pi$ amplitude to the second Riemann sheet, without any reference to the vector-meson-dominance hypothesis.

Comments: 7 pages, 3 figures; journal version