Decay rates of charmonia within a quark-antiquark confining potential

Abstract

In this work, we investigate the spectroscopy and decay rates of charmonia within the framework of the non-relativistic Schrödinger 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 a few low-lying P and D waves. The resultant wave functions at zero inter-quark separation as well as some finite separations are employed to predict the di-gamma, di-leptonic and di-gluon decay rates of charmonia states 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 yield results which are found to be in better agreement with experimental values 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 the 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.