Charmonium states in QCD-inspired quark potential model using Gaussian expansion method

TL;DR

This study models charmonium states using a QCD-inspired potential with Gaussian expansion, revealing the importance of scalar-vector mixing in confinement and predicting properties of newly observed states.

Contribution

It introduces a nonperturbative treatment of spin-dependent potentials with scalar-vector mixing, improving mass spectrum predictions and decay width calculations for charmonium.

Findings

Scalar-vector mixing confinement is crucial for accurate spectrum and decay widths.

The model predicts the masses of X(4160) and X(4350) as specific charmonium states.

Discrepancies in M1 transitions of J/ψ and ψ' are alleviated.

Abstract

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of $J/\psi$ and $\psi^{\prime}$ are alleviated spontaneously. This work also intends to provide an inspection and suggestion for the possible $c\bar{c}$ among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as $M(2^1D_2)= 4164.9$ MeV and $M(3^3P_2)= 4352.4$ MeV, which strongly favor the $J^{PC}=2^{-+}, 2^{++}$ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.