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 $γ$ 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 $γ$ 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 $γ$ in the $^{3}P_{0}$ model within the present framework.