Mesons in nonlocal model with four-dimensional separable kernel

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 \(π ^0→ γ γ \) decay width and the pion transition form factor \(Fπ γ(Q^2)\) , 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.