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 $$^{3}P_{0}$$ 3 P 0 model is non-relativistic and contains unknown adjustable parameter $$\gamma $$ 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 $$^{3}P_{0}$$ 3 P 0 parameter $$\gamma $$ 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 $$h_{c}(2P)$$ h c ( 2 P ) and allows a theoretical determination of the parameter $$\gamma $$ γ in the $$^{3}P_{0}$$ 3 P 0 model within the present framework.