Gravitational form factors of pseudoscalar mesons in a contact interaction

Given the unique role played by the gravitational form factors (GFFs) in unraveling the internal mechanics of hadrons, we examine the GFFs of ground state pseudoscalar mesons $\pi$, $\eta_c$, $\eta_b$ and the hypothetical {\em strangeonium} $\eta_s(s\bar{s})$. We adopt the coupled framework of Dyson-Schwinger and Bethe-Salpeter equations within a contact interaction, and employ a novel approach to the dressed amputated meson-meson scattering amplitude which makes connection with the energy-momentum tensor and with the GFFs. The resulting GFFs fulfill the anticipated symmetry constraints. The corresponding charge and mass radii and the $D-$term are also computed. We show that the $D-$term for the pseudoscalar mesons is bounded within the $(-1, -1/3)$ range; these bounds correspond to the massless (chiral limit) and infinitely massive cases, respectively. Considering the current interest in the GFFs, understanding the \textit{D}-term of pseudoscalar mesons and their GFFs can provide an important first step for future endeavors in the field.