Gravitational form factors of pseudoscalar mesons in a contact interaction

Abstract

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 π, ηc, ηb and the hypothetical strangeonium ηs(ss). 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 ð−1;−1=3Þ range; these bounds correspond to the massless (chiral limit) and infinitely massive cases, respectively. Considering the current interest in the GFFs, understanding the D term of pseudoscalar mesons and their GFFs can provide an important first step for future endeavors in the field.