Magnetic dipole moments of the hidden-charm pentaquark states: P_c(4440), P_c(4457) and P_{cs}(4459)

Ulaş Özdem

doi:10.1140/epjc/s10052-021-09070-3

Abstract

In this work, we employ the light-cone QCD sum rule to calculate the magnetic dipole moments of the P_c(4440), P_c(4457) and P_{cs}(4459) pentaquark states by considering them as the diquark–diquark–antiquark and molecular pictures with quantum numbers J^P = frac{3}{2}^-, J^P = frac{1}{2}^- and J^P = frac{1}{2}^-, respectively. In the analyses, we use the diquark–diquark–antiquark and molecular form of interpolating currents, and photon distribution amplitudes to obtain the magnetic dipole moment of pentaquark states. Theoretical examinations on magnetic dipole moments of the hidden-charm pentaquark states, are essential as their results can help us better figure out their substructure and the dynamics of the QCD as the theory of the strong interaction. As a by product, we extract the electric quadrupole and magnetic octupole moments of the P_c(4440) pentaquark. These values show a non-spherical charge distribution.

Highlights

The magnetic dipole moments of the pentaquark states Pc(4440), Pc(4457) and Pcs(4459) are obtained by employing the diquark–diquark–antiquark and molecular interpolating currents within the light-cone QCD sum rule (LCSR)
In order to obtain the magnetic dipole moment of the corresponding states with the QCD sum rule method, we begin by writing the correlation function suitable for the calculations
The QCD representation of the correlation function can be obtained with the help of photon distribution amplitudes (DAs) according to quark-gluon properties and after performing the Fourier transform to transfer the calculations to the momentum space

Summary

Motivation

With the experimental discovery of the exotic X(3872) state, i.e., state that cannot be interpreted by the conventional meson or baryon picture, a new era began in high energy physics. In order to understand the internal structure and nature of these particles, different properties should be studied besides their decay channels and spectroscopic properties Investigating their electromagnetic form factors may provide important insights on this point. [60], they achieved the magnetic dipole moment of the Pc(4312) pentaquark state in the c Dmolecular picture by means of the QCD sum rule (QCDSR) in the external weak electromagnetic field. The magnetic dipole moments of the pentaquark states Pc(4440), Pc(4457) and Pcs(4459) (hereafter we will show these states as Pc1, Pc2 and Pcs, respectively) are obtained by employing the diquark–diquark–antiquark and molecular interpolating currents within the LCSR. The LCSR is a powerful tool to obtain qualitative and quantitative information about hadron properties In this method, hadrons are analytically studied by matching their behaviors at high and low energies. The explicit expressions of the magnetic moment of the Pc1 pentaquark in the diquark–diquark–antiquark picture is presented in Appendix A

Magnetic dipole moments of the pentaquark states via LCSR

Formalism of the Pc2 and Pcs states

Formalism of the Pc1 state

Numerical analysis and discussions