Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction

TL;DR

This paper critically examines a recent effective field theory study of the X(3872) particle, highlighting issues that challenge its conclusions about its molecular nature and pion mass dependence.

Contribution

It identifies and discusses technical and conceptual flaws in the previous EFT analysis of X(3872), questioning its claims about pion exchange dominance and lattice observability.

Findings

The previous EFT results are flawed due to technical issues.

Conceptual problems undermine the claim that X(3872) is solely pion-exchange bound.

The X(3872) may not disappear at higher pion masses as previously suggested.

Abstract

In a recent paper Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846), the charmonium state X(3872) is studied in the framework of an effective field theory. In that work it is claimed that (i) the one-pion exchange (OPE) alone provides sufficient binding to produce the X as a shallow bound state at the $D^0\bar{D}^{*0}$ threshold, (ii) short-range dynamics (described by a contact interaction) provides only moderate corrections to the OPE, and (iii) the X-pole disappears as the pion mass is increased slightly and therefore the X should not be seen on the lattice, away from the pion physical mass point, if it were a molecular state. In this paper we demonstrate that the results of Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846) suffer from technical as well as conceptual problems and therefore do not support the conclusions drawn by the authors.