Charmonia in a Contact Interaction

TL;DR

This paper calculates charmonium meson properties using a contact interaction model within Schwinger-Dyson equations, achieving results that align well with experimental data and advanced theoretical approaches.

Contribution

It introduces a symmetry-preserving contact interaction framework to compute charmonium masses and decay constants, providing a simpler yet accurate alternative to complex models.

Findings

Meson masses agree with experimental data

Decay constants are consistent with previous models

Charge radius matches lattice QCD results

Abstract

For the flavour-singlet heavy quark system of charmonia, we compute the masses of the ground state mesons in four different channels: pseudo-scalar ($\eta_c(1S)$), vector ($J/\Psi(1S)$), scalar ($\chi_{c_0}(1P)$) and axial vector ($\chi_{c_{1}}(1P)$), as well as the weak decay constants of the $\eta_c(1S)$ and $J/\Psi(1S)$ and the charge radius of $\eta_c(1S)$. The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation (SDEs) treatment of a vector$\times$vector contact interaction (CI). The results found for the meson masses and the weak decay constants, for the spin-spin combinations studied, are in fairly good agreement with experimental data and earlier model calculations based upon Schwinger-Dyson and Bethe-Salpeter equations (BSEs) involving sophisticated interaction kernels. The charge radius of $\eta_c(1S)$ is consistent with the results from refined SDE studies and lattice Quantum Chromodynamics (QCD).