Decay rates of charmonia within a quark-antiquark confining potentials

TL;DR

This paper investigates charmonia spectroscopy and decay rates using non-relativistic quantum mechanics with an approximate potential, incorporating relativistic corrections and binding energy effects to improve agreement with experimental data.

Contribution

It introduces a detailed calculation of charmonia decay rates using an approximate potential and NRQCD, highlighting the significance of binding energy effects for accurate predictions.

Findings

NRQCD with finite separation matrix elements aligns well with experimental decay widths.

Inclusion of binding energy effects improves di-gluon decay width predictions.

Predicted decay widths for higher excited states extend current understanding.

Abstract

In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of non-relativistic Schr\"{o}dinger equation by employing an approximate inter quark-antiquark potential. The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are employed to compute the spectroscopy of the excited S states and few low-lying P and D waves. The resultant wave functions at zero inter quark separation as well as some finite separation are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states by using the conventional Van Royen-Weisskopf formula. The di-gamma and di-leptonic decay widths are also computed by incorporating the relativistic corrections of order $v^4$ within the NRQCD formalism. We have observed that the NRQCD predictions with their matrix elements computed at finite radial separation yielded results which are found to be in better agreement with experimental value for both di-gamma and di-leptonic decays. The same scenario is seen in the case when di-gamma and di-leptonic decay widths are computed with Van Royen-Weisskopf formula. It is also observed that the di-gluon decay width with the inclusion of binding energy effects are in better agreement with the experimental data available for 1S-2S and 1P. The di-gluon decay width of 3S and 2P waves waves are also predicted. Thus, the present study of decay rates clearly indicates the importance of binding energy effects.