https://doi.org/10.1140/epjs/s11734-025-02025-9
Review
Gravitational form factors of pions, kaons and nucleons from dispersion relations
1
Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China
2
School of Physical Sciences, University of Chinese Academy of Sciences, 100190, Beijing, China
3
Institute for Particle and Nuclear Physics, College of Physics, Sichuan University, 610065, Chengdu, Sichuan, China
4
School of Physics and Electronics, Hunan University, 410082, Changsha, Hunan, China
5
Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, Hunan University, 410082, Changsha, Hunan, China
Received:
21
June
2025
Accepted:
11
October
2025
Published online:
29
October
2025
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 
and 
. These results offer a robust benchmark for future experimental and theoretical studies.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
