Mass spectra and decay constants of heavy-light axial quarkonia in the framework of Bethe-Salpeter equation

TL;DR

This paper calculates the mass spectra and decay constants of heavy-light P-wave mesons using a Bethe-Salpeter equation framework, incorporating spin structure and one-gluon exchange, providing new insights into meson properties.

Contribution

It introduces a novel Bethe-Salpeter equation approach with exact spin treatment and heavy-quark approximation for heavy-light mesons, improving spectral and decay constant calculations.

Findings

Mass spectra of heavy-light P-wave mesons are computed.

Decay constants of ground and excited states are evaluated.

Framework successfully incorporates confining and one-gluon exchange interactions.

Abstract

In this work we calculate the mass spectrum and decay constants of ground and excited states of heavy-light $P$-wave mesons such as $1^{++}$ and $1^{+-}$, with quark composition, $c\overline{u}, c\overline{s}, b\overline{u}, b\overline{s}$, and $b\overline{c}$ in the framework of a QCD motivated Bethe-Salpeter equation (BSE) by making use of the exact treatment of the spin structure $(\gamma_{\mu}\bigotimes\gamma_{\mu})$ in the interaction kernel, In this $4\times 4$ BSE framework, the coupled Salpeter equations for $Q\overline{q}$ are first solved for the confining part of interaction, and are shown to decouple under heavy-quark approximation. Then the one-gluon-exchange interaction is perturbatively incorporated, leading to their mass spectral equations. The analytic forms of wave functions obtained from these equations are then used for calculation of leptonic decay constants of ground and excited states of $1^{++}$, and $1^{+-}$ as a test of these wave functions and the over all framework.