Chiral Perturbation Theory and the $\bar B \bar B$ Strong Interaction

TL;DR

This paper calculates the potentials between heavy mesons using chiral perturbation theory, revealing attractive and repulsive interactions in different channels, which may aid in lattice QCD extrapolations.

Contribution

It provides a detailed calculation of heavy meson potentials up to second order in chiral perturbation theory, including various exchange diagrams and loop corrections, advancing understanding of heavy meson interactions.

Findings

Attractive potentials in certain isospin channels at low momentum.

Repulsive potential observed in the isospin-zero channel.

Potential analytical structures could assist lattice QCD extrapolations.

Abstract

We have calculated the potentials of the heavy (charmed or bottomed) pseudoscalar mesons up to $O(\epsilon^2)$ with the heavy meson chiral perturbation theory. We take into account the contributions from the football, triangle, box, and crossed diagrams with the 2$\phi$ exchange and one-loop corrections to the contact terms. We notice that the total 2$\phi$-exchange potential alone is attractive in the small momentum region in the channel ${\bar B \bar B}^{I=1}$, ${\bar B_s \bar B_s}^{I=0}$, or ${\bar B \bar B_s}^{I=1/2}$, while repulsive in the channel ${\bar B \bar B}^{I=0}$. Hopefully the analytical chiral structures of the potentials may be useful in the extrapolation of the heavy meson interaction from lattice QCD simulation.