Abstract
We study the magnetic moments and transition magnetic moments of $P_c$ and $P_{cs}$ states in the molecular picture. We first revisit the magnetic moments of $P_c$ states as the $S$ wave molecular states without coupled channel effects. The coupled channel effects and the $D$ wave contributions are then investigated carefully. The coupled channel effects contribute to the change of $0.1\sim 0.4$ nuclear magneton $\mu_N$ for most cases while the $D$ wave only induces the variation of less than $0.03 ~\mu_N$. In addition, we obtain the transition magnetic moments between different $P_c$ states and the related electromagnetic decay widths of $P_c'\to P_c\gamma$. The magnetic moments of $P_{cs}$ are much different for the assumption of spin being 1/2 and 3/2. The study of electromagnetic properties will help us disclose further the structure of these unconventional states.
Highlights
In 2015, LHCb collaboration announced their discovery of Pcð4380Þþ and Pcð4450Þþ in Λ0b → J=ψK−p decay with the significance of more than nine standard deviations [1]
Magnetic moments with coupled channel effects In Ref. [4], we studied these Pc states as hidden charmed molecular states within the one-boson exchange (OBE)
Inspired by the recently observed Pcð4312Þþ, Pcð4440Þþ, and Pcð4457Þþ as well as the Pcsð4459Þ0, we calculate the magnetic moments, the transition magnetic moments, and the electromagnetic transition decay widths of these particles. We consider these particles as pure molecular states without flavor mixing
Summary
In 2015, LHCb collaboration announced their discovery of Pcð4380Þþ and Pcð4450Þþ in Λ0b → J=ψK−p decay with the significance of more than nine standard deviations [1]. In 2020, LHCb collaboration performed an amplitude analysis of the Ξ−b → J=ψΛK− decay using the data of both Run 1 and Run 2 If Pc and Pcs are typical molecular states, their magnetic moments would be mainly related to those of conventional charmed mesons and baryons. Lattice QCD can extract the magnetic moments [85,86] We study both the magnetic moments and transition magnetic moments of Pc and Pcs states in the molecular picture in this work.
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