Measurement of radiative widths of $a_2(1320)$ and $\pi_2(1670)$

Abstract

The COMPASS Collaboration at CERN has investigated the reaction $\pi^- \gamma \rightarrow \pi^-\pi^-\pi^+$ embedded in the Primakoff reaction of $190~\textrm{GeV}$ pions scattering in the Coulomb field of a lead target, $\pi^- \text{Pb} \rightarrow \pi^-\pi^-\pi^+ \text{Pb}$. Exchange of quasi-real photons is selected by isolating the sharp Coulomb peak observed at momentum transfer below $0.001~(\text{GeV}/c)^2$. Using a partial-wave analysis the amplitudes and relative phases of the $a_2(1320)$ and $\pi_2(1670)$ mesons have been extracted, and the Coulomb and the diffractive contributions have been disentangled. Measuring absolute production cross sections we have determined the radiative width of the $a_2(1320)$ to be $\Gamma_0(a_2(1320) \rightarrow \pi\gamma) = (358 \pm 6_{\textrm{stat}} \pm 42_{\textrm{syst}})~\textrm{keV}$. As the first measurement, $\Gamma_0(\pi_2(1670) \rightarrow \pi\gamma) = (181 \pm 11_{\textrm{stat}} \pm 27_{\textrm{syst}})~\textrm{keV} \cdot (\textrm{BR}^{\textrm{PDG}}_{f_2 \pi}/\textrm{BR}_{f_2 \pi})$ is obtained for the radiative width of the $\pi_2(1670)$, where in this analysis the branching ratio $\textrm{BR}^{\textrm{PDG}}_{f_2 \pi}=0.56$ has been used. We compare these values to previous measurements and theoretical predictions.