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}.
Highlights
In Ref. [1], LHCb collaboration reported the discoveries of two pentaquark states Pc(4380) and Pc(4450) in the J/ψ p invariant mass spectrum of the process b → J/ψ pK
A static electromagnetic field a e-mail: xuyongjiang13@nudt.edu.cn b e-mail: mqhuang@nudt.edu.cn is introduced which couples to the quarks and polarizes the QCD vacuum, and the magnetic moments of hadrons can be extracted from the linear response to this field
In Refs. [63] and [64], the authors calculated the magnetic moment of Zc(3900) as an axialvector tetraquark state and an axialvector molecular state, respectively
Summary
In Ref. [1], LHCb collaboration reported the discoveries of two pentaquark states Pc(4380) and Pc(4450) in the J/ψ p invariant mass spectrum of the process b → J/ψ pK. In 2019, they confirmed the Pc(4450) state consisting of two narrow overlapping peaks Pc(4440) and Pc(4457), and observed a new narrow pentaquark state Pc(4312) [2]. Following these experimental discoveries, there have been many theoretical studies concerning these pentaquark states through various models/methods, such as the meson-baryon molecular scenario [3–30], the compact five quark states [31–. Analysis of the electromagnetic multipole moments of the exotic states can help us get valuable knowledge about the electromagnetic properties of these states, the charge distributions inside them, their charge radius and geometric shapes and their internal substructures. 2, the sum rule for the magnetic moment of the Pc(4312) state is given.
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