Study of $X_{c}(3250)$ as a $D_{0}^{*}(2400)N$ molecular state

TL;DR

This paper uses QCD sum rules to analyze whether the resonance $X_{c}(3250)$ can be described as a $D_{0}^{*}(2400)N$ molecular state, finding partial support but with some convergence issues.

Contribution

It provides a QCD sum rule analysis of $X_{c}(3250)$ as a $D_{0}^{*}(2400)N$ molecular state, including operators up to dimension 12 and addressing convergence challenges.

Findings

Mass of $D_{0}^{*}(2400)N$ state is $3.18 ext{ GeV}$, matching experimental data.

OPE convergence is difficult to achieve with standard criteria.

Predicted bottom counterpart $ar{B}_{0}^{*}N$ mass is $6.50 ext{ GeV}$.

Abstract

We present a QCD sum rule analysis for the newly observed resonance $X_{c}(3250)$ by assuming it as a $D_{0}^{*}(2400)N$ molecular state. Technically, contributions of operators up to dimension 12 are included in the operator product expansion (OPE). We find that it is difficult to find the conventional OPE convergence in this work. By trying releasing the rigid OPE convergence criterion, one could find that the OPE convergence is still under control in the present work and the numerical result for $D_{0}^{*}(2400)N$ state is $3.18\pm0.51 {GeV}$, which is in agreement with the experimental data of $X_{c}(3250)$. In view of that the conventional OPE convergence is not obtained here, thus only weak conclusions can be drawn regarding the explanation of $X_{c}(3250)$ in terms of a $D_{0}^{*}(2400)N$ molecular state. As a byproduct, the mass for the bottom counterpart $\bar{B}_{0}^{*}N$ state is predicted to be $6.50\pm0.49 {GeV}$.