Symmetries, angular distributions inψ′→γχ→γγψ, and the interpretation of theχ(3400−3550)levels

Abstract

Recently a family of particles (to be denoted $\chi$) has been discovered between 3400 and ∼ 3550 MeV. A formalism is presented for analysis of the decays ${\psi }^{\prime }\mathrm{}\left(3684\right)\mathrm{}\to \gamma \chi \to \gamma \gamma \psi or \gamma 0^{-}{0}^{-}$. This formalism is sufficiently general to allow for transitions of several multipolarities. Previous treatments have been restricted to the assumption that the above transitions are purely $E1\mathrm{}$ if $J^P\left(\chi \right)=0^{+}, 1^{+}, \mathrm{and} 2^{+}$. Here (with some modeldependent motivation) this restriction is removed. The predictions of specific heavy-quark models for the $\chi$ states are then discussed. On the basis of the single-quark-transition picture (the Melosh transformation), it is anticipated that the state $\chi \mathrm{}\left(3410\right)\mathrm{}$ will be identified as a ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ $q\overline{q}$ level, and will be found to have $J^{\mathrm{PC}}=0^{++}$. It is also anticipated that the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ level should be fairly prominent.