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 $\Lambda_H$. We demonstrate the model's predictive power by applying it to both light and heavy systems. Key results include a calculation of the $\pi^0\to\gamma\gamma$ decay width and the pion transition form factor $F_{\pi\gamma}(Q^2)$, 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 $\eta_c$ and $\eta_b$ and the radiative decay widths of $J/\psi$ and $\Upsilon$, 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.