The magnetic moment of $P_{c}(4312)$ as a $\bar{D}\Sigma_{c}$ molecular state

TL;DR

This paper investigates the magnetic moment of the $P_{c}(4312)$ pentaquark, modeling it as a $ar{D} ext{Sigma}_c$ molecular state and calculating its magnetic moment using QCD sum rules.

Contribution

It provides a novel calculation of the magnetic moment of $P_{c}(4312)$ as a molecular state using QCD sum rules in an external electromagnetic field.

Findings

Magnetic moment of $P_{c}(4312)$ is approximately 1.75 with uncertainties.

Supports the molecular state interpretation of $P_{c}(4312)$.

Demonstrates the application of QCD sum rules to pentaquark magnetic moments.

Abstract

In this paper, we tentatively assign the $P_{c}(4312)$ to be a $\bar{D}\Sigma_{c}$ molecular state with quantum number $J^{P}=\frac{1}{2}^{-}$, and calculate its magnetic moment using the QCD sum rule method in external weak electromagnetic field. Starting with the two-point correlation function in external electromagnetic field and expanding it in power of the electromagnetic interaction Hamiltonian, we extract the magnetic moment from the linear response to the external electromagnetic field. The numerical value of the magnetic moment of $P_{c}(4312)$ is $\mu_{P_{c}}=1.75^{+0.15}_{-0.11}$.