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

TL;DR

This paper analyzes the reaction gamma pi to pi pi to determine the radiative couplings of rho resonances, providing a model-independent method for the rho(770) and estimates for the rho_3(1690).

Contribution

It introduces a formalism to extract the rho(770) radiative coupling directly from the amplitude without relying on vector-meson dominance, and estimates the rho_3(1690) radiative width.

Findings

Estimated radiative width of rho_3(1690): 48(18) keV.

Formalism for direct extraction of rho(770) coupling from amplitude.

Impact on the F-wave 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.