$Q\bar Q$ ($Q\in \{b, c\}$) spectroscopy using Cornell potential

TL;DR

This paper models heavy quarkonium spectra and decays using a Cornell potential, employing numerical solutions to the Schrödinger equation, and achieves results consistent with experimental data and other theories.

Contribution

It introduces a parameter-efficient nonrelativistic model for quarkonium spectra and decays, including $B_c$ mesons, with comprehensive decay width calculations.

Findings

Spectra and decay properties align with experimental data.

Mass spectra and lifetimes of $B_c$ mesons are accurately predicted.

Electromagnetic transition widths agree with observations.

Abstract

The mass spectra and decay properties of heavy quarkonia are computed in nonrelativistic quark-antiquark Cornell potential model. We have employed the numerical solution of Schr\"odinger equation to obtain their mass spectra using only four parameters namely quark mass ($m_c$, $m_b$) and confinement strength ($A_{c\bar c}$, $A_{b\bar b}$). The spin hyperfine, spin-orbit and tensor components of the one gluon exchange interaction are computed perturbatively to determine the mass spectra of excited $S$, $P$, $D$ and $F$ states. Digamma, digluon and dilepton decays of these mesons are computed using the model parameters and numerical wave functions. The predicted spectroscopy and decay properties for quarkonia are found to be consistent with available experimental observations and results from other theoretical models. We also compute mass spectra and life time of the $B_c$ meson without additional parameters. The computed electromagnetic transition widths of heavy quarkonia and $B_c$ mesons are in tune with available experimental data and other theoretical approaches.