Equality of $e^+e^-$ production amplitudes for scalar-vector and pseudoscalar-axial heavy meson-antimeson pairs

Abstract

The production of heavy meson-antimeson pairs of the type $S\,V$ and $P \, A$ in $e^+e^-$ annihilation is considered, with $P$ and $V$ being the ground-state $J^P=0^-$ and $J^P=1^-$ (anti)mesons from the $(1/2)^-$ doublet, and $S$ and $A$ standing for the excited $J^P=0^+$ and $J^P=1^+$ (anti)mesons from the $(1/2)^+$ doublet. It is argued that the production amplitudes in these two channels should be equal up to a higher (than one) order in the heavy quark mass ($\Lambda_{QCD}/M_Q$) expansion, $A(e^+e^- \to S \bar V) = A(e^+e^- \to A \bar P)$, including both the $S$-wave and the $D$-wave amplitudes. Given that the $S\,V$ and $P \, A$ thresholds are extremely close, the production cross section in both channels should be the same to a high degree of accuracy. In practice this behavior can be studied for the processes $e^+e^- \to D_{s0}(2317) \bar D_s^* +$ c.c. and $e^+e^- \to D_{s1}(2460) \bar D_s +$ c.c. in the charm sector and $e^+e^- \to B_{s0} \bar B_s^* +$ c.c. and $e^+e^- \to B_{s1} \bar B_s +$ c.c. in the $B$ sector.