Yi-Yi Rui | Searcharxiv

arXiv2026

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

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.

hep-ph↗

arXiv2026

Large Relativistic Corrections to Nonrelativistic $M1$ Transitions in Heavy Quarkonium

As double heavy quarkonia, charmonium and bottomonium are generally considered to have small relativistic corrections and can be treated using nonrelativistic models. However, this is not always the case. In this paper, we employ the relativistic Bethe-Salpeter (BS) equation method to calculate the electromagnetic (EM) radiative decays of heavy quarkonium where the $M1$ transition provides the leading-order contribution. Compared to nonrelativistic method which only computes $M1$ transition, our calculations include $M1+E2+M3+E4$ transitions, where the higher-order multipoles, $E2$, $M3$, and $E4$, account for relativistic corrections. The study finds that relativistic effects are large in such transitions even for bottomonium. For instance: the relativistic corrections in the decays $ψ(nS)\rightarrowγη_c(mS)$ ($n\geq m$) range from $68.1\%$ to $83.2\%$, while those for $Υ(nS)\rightarrowγη_b(mS)$ range between $65.9\%$ and $75.2\%$.

hep-ph↗