Possible exotic mesons in the charmonium region

Abstract

We consider the possibility that a number of $PC=+ +$ mesons might appear in the charmonium region below ${\ensuremath{\psi}}^{\ensuremath{'}}(3.69 \mathrm{GeV})$. They are states made up of admixtures of $c\overline{c}g$ ($g=\mathrm{gluon}$), $c\overline{c}q\overline{q}$ ($q=u,d$), and the charmonium $^{3}P_{J}$ states. Masses, decay widths, and mixing matrix elements are studied with the help of the model of Horn and Mandula for $c\overline{c}g$ states and the results of Jaffe, and De R\'ujula and Jaffe, for $c\overline{c}q\overline{q}$ states. The presence of a $c\overline{c}$ pair suggests narrow hadronic widths if the mass is below the breakup thresholds of the $c\overline{c}q\overline{q}$ states. Their branching ratios for $\ensuremath{\gamma}$ transitions and $2\ensuremath{\gamma}$ anmihilations appear to be fairly small. They may have rather large spin-spin splittings. It is plausible that the lowest-mass states contain mostly $c\overline{c}g$ configurations. Although they share part of the charmonium $^{3}P_{J}$ $\ensuremath{\gamma}$-cascade strengths, it is likely that they are more readily produced in the hadronic decays of vector mesons in ${e}^{+}{e}^{\ensuremath{-}}$ annihilations. We also discuss the possible appearance of similar states in the $\ensuremath{\Upsilon}$ region and among light mesons. We suggest in particular that strange mesons in suitable decay modes might well provide the most ready experimental access to such gluon and four-quark states.