Resonances decaying to a photon and aJ(ψ)particle

Abstract

If $L=1\mathrm{}$ orbital excitations ${}_{}{}^3{}_{}{}^{}P_{2,1,0}^{}{}_{}{}^{}$ of the $J\left(\psi \right)$ particle exist (assuming it to be a ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ quark-antiquark state), the decays ${}_{}{}^3{}_{}{}^{}P_{2,1}^{}{}_{}{}^{}\to J\left(\psi \right)+\gamma$, $J\left(\psi \right)\to {\left(\mathrm{lepton}\right)}^{+}+{\left(\mathrm{lepton}\right)}^{-}$ are predicted to yield $W({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{},\theta ) \alpha 1+(0.4 \mathrm{to} 6){cos}^2\theta$ and $W({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{},\theta ) \alpha {sin}^2\theta$. Here $W\left(\theta \right)$ is the distribution in angle $\theta$ between the photon and either lepton in the $J\left(\psi \right)$ rest frame. The decay ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\to J\left(\psi \right)+\gamma$ [which must have $W({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{},\theta )\sim 1+{cos}^2\theta$] is predicted to be suppressed.