Analysis of $X$ Particle Spectra in Quarkonium Model

TL;DR

This paper investigates whether the newly established $X$ particles can be explained as charmonium states by calculating their mass spectra using a quarkonium model with spin-dependent forces and a linear confining potential.

Contribution

It provides a calculation of charmonium mass spectra considering spin-dependent interactions and fits parameters to observed data, testing the quarkonium model's applicability to $X$ particles.

Findings

Mass spectra calculated with spin-dependent forces match observed $X$ particle masses.

Linear confining potential used in the model fits experimental data.

Parameters determined via least squares method improve model accuracy.

Abstract

Three more $X$ particles are established in the 2014 Particle Data compared with the 2012 ones. There are now five established $X$ particles named as $X(3872)$, $X(3900)$, $X(4260)$, $X(4360)$, and $X(4660)$. Since the first $X$ particle $X(3872)$ was discovered during the search for the remaining P charmonium states, it is valuable to check whether the established $X$ particles can be explained by quarkonium model. In this paper, we try to calculate the mass spectra of charmonium system by considering spin-dependent forces deduced from one gluon exchange diagrams. The confining potential form is taken to be linear and the free parameters are determined by least squares method comparing the theoretical and the observed masses of charmonium states.