Relativistic Bethe-Salpeter study of OZI-rule allowed strong decays: determination of total width of $h_c(2P)$ and ${}^3{P}_0$ model parameter

Abstract

Strong decays allowed by the Okubo-Zweig-Iizuka rule play a decisive role in determining the properties of particles. The widely used ${}^3{P}_0$ model is non-relativistic and contains unknown adjustable parameter $\gamma$ that need to be determined experimentally. Based on the Bethe-Salpeter equation, we have derived a relativistic calculation formula in which the effective strength related to the ${}^3{P}_0$ parameter $\gamma$ is not introduced as an independent fitting parameter, but is consistently determined by the interaction kernel of the Bethe-Salpeter equation. Using this method, we present the total width of $h_c(2P)$ and allows a theoretical determination of the parameter $\gamma$ in the ${}^3{P}_0$ model within the present framework.

Comments: 13 pages, 2 figures