Suppression of theS-wave production of(32)++(12)−heavy meson pairs ine+e−annihilation

Abstract

The heavy meson-antimeson pairs, where one is an excited $(\frac{3}{2}{)}^{+}$ meson and the other is a ground state $(\frac{1}{2}{)}^{\ensuremath{-}}$ meson, namely, the pairs (${D}_{1}(2420)\overline{D}+\mathrm{c}.\mathrm{c}.$), (${D}_{1}(2420){\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$), (${D}_{2}(2460){\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$) in the charm sector and (${B}_{1}(5721)\overline{B}+\mathrm{c}.\mathrm{c}.$), (${B}_{1}(5721){\overline{B}}^{*}+\mathrm{c}.\mathrm{c}.$), (${B}_{2}(5747){\overline{B}}^{*}+\mathrm{c}.\mathrm{c}.$) in the bottom sector, are allowed, by the quantum numbers, to be produced in the $S$ wave in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation. We show, however, that such $S$-wave production is forbidden by the heavy quark spin symmetry. Thus, the yield of the considered meson pairs in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation should be significantly suppressed near the respective thresholds. In our view, this substantially weakens the arguments for considering the $Y(4260)$ charmoniumlike resonance as a ${D}_{1}\overline{D}$ molecular state.