Relativistic Bethe-Salpeter study of OZI-rule allowed strong decays: determination of total width of $h_{c}(2P)$ and $^{3}P_{0}$ model parameter

TL;DR

This work introduces a relativistic, parameter-free framework for OZI-rule-allowed strong decays via the Bethe-Salpeter equation with a screened Cornell kernel, avoiding the phenomenological light-quark-pair creation strength $\\gamma$ of the $^3P_0$ model. It applies the approach to the charmonium state $h_c(2P)$ decaying to $D\\bar{D}^*$ by solving the Salpeter equation for the relevant meson wave functions and evaluating the transition amplitude from the BS formalism. The authors predict a total width of $\\Gamma_{total}=69.6^{+40.4}_{-30.4}$ MeV for $h_c(2P)$ and extract a $^3P_0$ strength parameter of $\\gamma=0.411^{+0.109}_{-0.133}$ by matching to the BS result, illustrating a way to determine the $\\gamma$ parameter from first-principles-like calculations. The study demonstrates a consistent, relativistic alternative to the traditional $^3P_0$ approach and provides predictions that can inform future experimental searches for $h_c(2P)$ and its decay channels.

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 without additional parameters similar to $γ$. Using this method, we present the total width of $h_{c}(2P)$ and theoretically determine the value of the parameter $γ$ in the $^{3}P_{0}$ model.

Figures (2)

• Figure 1: Feynman diagrams of OZI rule-allowed strong decays within the BS approach (left) and the $^{3}P_{0}$ model (right).
• Figure 2: Width and $\gamma$-value as functions of $h_{c}(2P)$-mass.