Spectroscopy and Decay Properties of Excited Charmonium States

TL;DR

This work develops a color-screened nonrelativistic potential model to compute the charmonium mass spectrum and analyzes a broad set of decays, including two-body strong decays, annihilation, leptonic and two-photon widths, and hadronic transitions. By solving $H=H_0+V$ with $V$ containing confining, contact, spin-orbit, and tensor interactions and expanding radial wavefunctions in a SHO basis with $n_{\max}=21$, the authors identify key high-lying states and map recently observed resonances to specific $c\bar{c}$ multiplets, notably assigning $X(4160)\equiv 3^3P_0$, $Y(4500)\equiv 3^3D_1$, and $Y(4710)\equiv 4^3D_1$, while predicting masses for higher excitations. Decay analyses rely on the $^3P_0$ model for strong decays, the Van Royen-Weisskopf formula with QCD corrections for leptonic and two-photon widths, and Kuang–Yan hadronic transitions, yielding results that largely agree with available data and offer testable predictions for future experiments. The work provides a cohesive framework linking mass spectra to decay behavior in the charmonium system and clarifies the nature of several newly observed resonances, with implications for understanding QCD in the heavy-quark regime.

Abstract

In this work, we investigate the mass spectra of excited charmonia employing a nonrelativistic potential model with screening effect, and analyze their two-body strong decay, two-photon decay, leptonic decay, and hadronic transitions. Especially, we find that the newly observed resonances $X(4160)$, $Y(4500)$, and $Y(4710)$ can be identified as $3^3P_0$, $3^3D_1$, and $4^3D_1$ states, respectively. We also predict the masses and the widths of higher excited states in the charmonia family.