Analysis of $X$ Particle Spectra in Quarkonium Model

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.