Scalar Bound States of $D^{\ast}\bar{D}^{\ast}$ and $B^{\ast}\bar{B}^{\ast}$ in the Bethe-Salpeter Formalism

TL;DR

This paper investigates scalar bound states of heavy meson pairs using the Bethe-Salpeter formalism, revealing isospin constraints and the conditions for their existence based on effective interactions.

Contribution

It applies the Bethe-Salpeter approach with chiral and heavy quark effective theories to analyze bound states of $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$, highlighting isospin restrictions.

Findings

Only $I=0$ scalar bound states exist within proper parameters.

$I=1$ bound states are not supported in the studied parameter range.

The results depend on the effective interaction parameters and wavefunction constraints.

Abstract

We study the scalar bound states of $D^{\ast}\bar{D}^{\ast}$ and $B^{\ast}\bar{B}^{\ast}$ in the Bethe-Salpeter formalism, with the effective interaction kernel extracted from the chiral perturbative theory and the heavy quark effective theory in the ladder approximation and the covariant instantaneous approximation. The results show that, in the scalar case ($J=0$), there can only exist $I = 0$ bound states for parameters in proper range, while there cannot exist the $I = 1$ bound states in the whole reasonable parameter range, due to more constraints arising from our definition of the Bethe-Salpeter wavefunction.