Gravitational form factors of pions, kaons and nucleons from dispersion relations

Abstract

The gravitational form factors of pions, kaons and the nucleons are investigated by employing modern dispersive techniques and chiral perturbation theory. We determine the gravitational form factors of pions and kaons, extending our analysis to explore the pion mass dependence of these form factors at several unphysical pion masses up to 391 MeV, for which lattice results exist for the meson-meson scattering phase shifts. We also review our analysis on the nucleon gravitational form factors at the physical pion mass, and then systematically calculate various three-dimensional spatial and two-dimensional transverse density distributions for the nucleons. These results provide new insights into the mass distribution inside nucleons. As a by-product, we match our dispersion relation results and those obtained from chiral perturbation theory with external gravitational source at the next-to-next-to-leading order, yielding values for the low-energy constants $c_8=-4.28_{-0.38}^{+0.37}{\mathrm{GeV}}^{-1}$ and $c_9=-0.68_{-0.05}^{+0.06}{\mathrm{GeV}}^{-1}$. These results offer a robust benchmark for future experimental and theoretical studies.

v2: 55 pages, 17 pages, 3 tables; references added, typos corrected, discussions of spectral functions and sum rules added; accepted for publication as a review in EPJST

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• Origin of the nucleon gravitational form factor $B_N(t)$: Exposition in light-front holographic QCD
• Renormalization of chiral perturbation theory with spinless matter field in curved spacetime