Distribution Amplitudes of Heavy Mesons and Quarkonia on the Light Front

TL;DR

This paper develops a unified framework to calculate the mass spectrum, decay constants, and distribution amplitudes of light and heavy mesons, including quarkonia, using an amended Bethe-Salpeter equation projected onto the light front.

Contribution

It introduces a flavor-dependent dressing function in the Bethe-Salpeter kernel, enabling simultaneous calculation of meson properties at physical pion mass within a consistent approach.

Findings

Calculated mass spectrum and decay constants for various mesons.

Reconstructed meson distribution amplitudes on the light front.

Compared distribution amplitudes with heavy quark effective theory results.

Abstract

The ladder kernel of the Bethe-Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the $D_u$, $D_s$, $B_u$, $B_s$ and $B_c$ mesons and the heavy quarkonia $\eta_c$ and $\eta_b$ within the same framework at a physical pion mass. The corresponding Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory. A comparison with the first inverse moment of the heavy meson distribution amplitude in heavy quark effective theory is made.