# Charm-beauty meson bound states from $B(B^*)D(D^*)$ and $B(B^*)\bar D(\bar D^*)$ interaction

## TL;DR

This paper investigates the potential existence of charm-beauty meson molecules by analyzing s-wave interactions of various B and D meson combinations, predicting bound states using unitarized potentials respecting heavy quark symmetry.

## Contribution

It introduces a novel unitarized approach to predict charm-beauty meson bound states from vector and pseudoscalar meson interactions, extending hidden gauge symmetry to heavy flavors.

## Key findings

- Bound states predicted above 7 GeV in specific meson combinations.
- Exotic meson states with $ar b$ and $ar c$ quarks suggested.
- Scattering lengths calculated for lattice QCD tests.

## Abstract

We evaluate the s-wave interaction of pseudoscalar and vector mesons with both charm and beauty to investigate the possible existence of molecular $BD$, $B^*D$, $BD^*$, $B^*D^*$, $B\bar D$, $B^*\bar D$, $B\bar D^*$ or $B^* \bar D^*$ meson states. The scattering amplitude is obtained implementing unitarity starting from a tree level potential accounting for the dominant vector meson exchange. The diagrams are evaluated using suitable extensions to the heavy flavor sector of the hidden gauge symmetry Lagrangians involving vector and pseudoscalar mesons{, respecting heavy quark spin symmetry}. We obtain bound states at energies above 7 GeV for $BD$ ($J^P=0^+$), $B^*D$ ($1^+$), $BD^*$ ($1^+$) and $B^*D^*$ ($0^+$, $1^+$, $2^+$), all in isospin 0. For $B\bar D$ ($0^+$), $B^*\bar D$ ($1^+$), $B\bar D^*$ ($1^+$) and $B^*\bar D^*$ ($0^+$, $1^+$, $2^+$) we also find similar bound states in $I=0$, but much less bound, which would correspond to exotic meson states with $\bar b$ and $\bar c$ quarks, and for the $I=1$ we find a repulsive interaction. We also evaluate the scattering lengths in all cases, which can be tested in current investigations of lattice QCD.