Two-pion exchange for coupled-channel scattering of two heavy mesons

TL;DR

This paper calculates the two-pion exchange potential for heavy meson scattering within chiral effective field theory, providing insights into multiquark states like Z_b and T_cc, and demonstrating the dominance of contact interactions at next-to-leading order.

Contribution

It introduces a detailed calculation of two-pion exchange contributions up to $O(Q^2)$ in chiral EFT for heavy meson scattering, supporting the convergence of the theory and explaining isovector and isoscalar potential differences.

Findings

TPE contributions are well-approximated by contact terms at $O(Q^2)$.

Chiral EFT converges for heavy meson scattering and multiquark states.

Differences in isovector and isoscalar potentials are explained by TPE.

Abstract

To improve the theoretical understanding of multiquark states like $Z_b(10610)$ and $Z_b(10650)$, we calculate the heavy-meson heavy-(anti)meson scattering potential up to next-to-leading order, $O(Q^2)$, within chiral effective field theory ($\chi$EFT) employing a power counting scheme that explicitly keeps track with the large momentum scale $Q \sim \sqrt{2\mu \delta}$ (where $\delta = m_V - m_P$ is the vector-pseudoscalar mass difference and $\mu$ their reduced mass) introduced by the coupled channel dynamics. We provide expressions for the two-pion exchange (TPE) terms up to $O(Q^2)$ and their partial-wave decomposition. We show that these potentials are well-approximated by contact terms at $O(Q^2)$, with minor residual non-analytic TPE contributions, supporting $\chi$EFT convergence in the theoretical predictions for $Z_b(10610)$ and $Z_b(10650)$, as well as their spin partners. These findings are also relevant for $D^{(*)}D^{(*)}$ scattering, especially for the $T_{cc}$ state, for both physical and lattice QCD data with moderately larger pion masses. We further demonstrate that the differences between isovector and isoscalar potentials for heavy mesons are naturally explained by the TPE contributions.