Two-Photon, Two-gluon and Radiative Decays of Heavy Flavoured Mesons

TL;DR

This paper calculates decay widths and radiative transition rates of heavy quarkonium states using a Coulomb plus power potential, finding optimal potential parameters for different systems to match observed spectra and decay behaviors.

Contribution

It introduces a unified potential model with variable exponent to accurately describe mass spectra and decay properties of heavy quarkonia.

Findings

Mass spectra and E1 transitions fit with potential exponent ν=1.0 for c-cbar and ν=0.7 for b-bbar.

M1 transitions and decay rates are better modeled with a shallower potential (ν<1.0).

The study provides specific potential parameters that best match experimental data.

Abstract

Here we present the two-photon and two-gluon decay widths of the S-wave ($\eta_{Q\in c,b}$) and P-wave ($\chi_{Q\in c,bJ}$) charmonium and bottonium states and the radiative transition decay widths of $c\bar c$, $b\bar b$ and $c\bar b$ systems based on Coulomb plus power form of the inter-quark potential ($CPP_\nu$) with exponent $\nu$. The Schr$\ddot{o}$dinger equation is solved numerically for different choices of the exponent $\nu$. We employ the masses of different states and their radial wave functions obtained from the study to compute the two-photon and two-gluon decay widths and the E1 and M1 radiative transitions. It is found that the quarkonia mass spectra and the E1 transition can be described by the same interquark model potential of the $CPP_\nu$ with $\nu=1.0$ for $c\bar c$ and $\nu=0.7$ for $b\bar b$ systems, while the M1 transition (at which the spin of the system changes) and the decay rates in the annihilation channel of quarkonia are better estimated by a shallow potential with $\nu<1.0$.