Kaon gravitational form factors and mechanical structure in a three-flavor NJL model

Abstract

We investigate the gravitational form factors (GFFs) of the kaon in a proper-time-regularized three-flavor Nambu--Jona-Lasinio model. We treat the kaon as a light--strange pseudoscalar bound state and evaluate its energy--momentum-tensor matrix element using a dressed quark--graviton vertex. By retaining the interaction-induced contact contribution alongside the quark triangle diagrams, we preserve the gravitational Ward--Takahashi identity and ensure the conservation of the total energy--momentum tensor. We determine the light- and strange-quark contributions to the kaon GFFs, contrast them with the corresponding pion results, and extract the associated pressure and shear-force distributions, together with the Breit-frame and transverse light-front mass radii. Explicit flavor-symmetry breaking dictates that the strange sector carries a larger share of the kaon momentum and mechanical response. Consequently, compared to the pion, the kaon exhibits a less negative $D$-term and more compact mechanical distributions, featuring enhanced central pressure and shear. We further show that a Ward--Takahashi-identity-preserving reduction of the $C$-term projection is essential for maintaining the pion low-energy theorem in proper-time regularization.