Power Counting and Perturbative One Pion Exchange in Heavy Meson Molecules

TL;DR

This paper analyzes power counting schemes in effective field theories for heavy meson molecules, showing that one pion exchange can be treated perturbatively and coupled channels are suppressed at lowest order.

Contribution

It introduces a framework for applying power counting to heavy meson molecules, demonstrating the perturbative nature of one pion exchange and the insignificance of coupled channels at leading order.

Findings

Coupled channels are suppressed by at least two orders in EFT expansion.

One pion exchange tensor force is perturbative within certain momentum ranges.

At lowest order, the EFT simplifies to contact interactions only.

Abstract

We discuss the possible power counting schemes that can be applied in the effective field theory description of heavy meson molecules, such as the X(3872) or the recently discovered Zb(10610) and Zb(10650) states. We argue that the effect of coupled channels is suppressed by at least two orders in the effective field theory expansion, meaning that they can be safely ignored at lowest order. The role of the one pion exchange potential between the heavy mesons, and in particular the tensor force, is also analyzed. By using techniques developed in atomic physics for handling power-law singular potentials, which have been also successfully employed in nuclear physics, we determine the range of center-of-mass momenta for which the tensor piece of the one pion exchange potential is perturbative. In this momentum range, the one pion exchange potential can be considered a subleading order correction, leaving at lowest order a very simple effective field theory consisting only on contact-range interactions.