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

TL;DR

This paper demonstrates that the production amplitudes for certain heavy meson-antimeson pairs in electron-positron annihilation are approximately equal, reflecting heavy quark symmetry and near-threshold effects.

Contribution

It establishes the near-equality of production amplitudes for scalar-vector and pseudoscalar-axial heavy meson pairs up to higher-order heavy quark mass corrections.

Findings

Production amplitudes for $S V$ and $A P$ channels are approximately equal.

Cross sections for these channels are nearly identical near thresholds.

Results can be tested in charm and bottom meson production experiments.

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.