Mesons in nonlocal model with four-dimensional separable kernel

TL;DR

The paper develops a nonlocal quark model with a rank-1 separable Bethe–Salpeter kernel and a Gaussian vertex $\varphi(q^2)= e^{-q^2/\Lambda_H^2}$ to unify the description of light and heavy mesons. Meson–quark couplings are fixed via the compositeness condition, enabling UV-finite loop calculations across the spectrum, with parameters fitted to light observables and heavy-quark inputs constrained by masses and leptonic decays. It produces accurate predictions for $\pi^0\to\gamma\gamma$ and the transition form factor $F_{\pi\gamma}(Q^2)$, as well as heavy-quarkonia two-photon widths $\Gamma_{\eta_c\gamma\gamma}$ and $\Gamma_{\eta_b\gamma\gamma}$ and radiative decays $J/\psi\to \eta_c\gamma$ and $\Upsilon\to \eta_b\gamma$, in agreement with lattice QCD and experimental data. The framework offers a computationally efficient, unified approach suitable for extensions to open-flavor mesons and finite-temperature/density environments relevant to heavy-ion physics.

Abstract

In this work we study the meson properties in the framework of an effective quark model. We start from the Bethe-Salpeter equation choosing the interaction kernel in nonlocal form with the Gaussian meson vertex function, characterized by a meson size parameter $Λ_H$. We demonstrate the model's predictive power by applying it to both light and heavy systems. Key results include a calculation of the $π^0\toγγ$ decay width and the pion transition form factor $F_{πγ}(Q^2)$, which reproduces experimental data from low to high $Q^2$. We further predict the electromagnetic properties of heavy quarkonia, obtaining the two-photon decay widths of $η_c$ and $η_b$ and the radiative decay widths of $J/ψ$ and $Υ$, all of which show consistency with available data and other theoretical approaches. The model provides a computationally efficient and unified framework for describing mesons from the light to heavy quark sectors.

Figures (6)

• Figure 1: The meson polarization loop.
• Figure 2: The diagrams of $\rho\rightarrow\pi\pi$ decay.
• Figure 3: The diagram of electromagnetic $P\rightarrow\gamma\gamma$ decay.
• Figure 4: The transition form factor $F_{\pi\gamma}$ as function of the space-like photon momentum $Q^2$. Experimental data are taken from BaBar:2009rrjBelle:2012wwzCLEO:1997fhoCELLO:1991zPh.
• Figure 5: Form factor $F_{\eta_c\gamma}$ and $F_{\eta_b\gamma}$ as function of the space-like photon momentum $Q^2$. Data are taken from BaBar:2010siw for $\eta_c$ and from the light-front quark model for $\eta_b$Ryu:2018egt.