Short-distance RG-analysis of $X(3872)$ radiative decays

TL;DR

This paper uses renormalization-group analysis within effective field theory to study the radiative decays of the $X(3872)$, highlighting the importance of both short- and long-distance physics and providing decay width estimates.

Contribution

It introduces a novel RG-analysis approach to $X(3872)$ decays, emphasizing the role of contact interactions and setting decay width lower limits.

Findings

Short- and long-distance physics are equally important in $X(3872)$ decays.

Provides lower bounds for decay widths that can be tested experimentally.

Guides model building for the $X(3872)$ short-distance structure.

Abstract

We present a renormalization-group analysis of the $X(3872)$ radiative decays into $J/ \psi \gamma$ and $\psi(2S) \gamma$. We assume a $D\bar{D}^{*}$ molecule for the $X$ long-distance structure and parametrize its short-distance physics as contact interactions. Using effective field theory techniques and power-divergence subtraction scheme, we find that short- and long-distance physics are equally important in these decays. Our calculations set a lower limit to the corresponding decay widths, which can in principle be tested experimentally. Our results may be used as guide to build models for the $X$ short-distance.