Gravitational form factors of the pion and meson dominance

We show that the recent MIT lattice QCD data for the pion’s gravitational form factors are, in the covered
\nmomentum transfer range, fully consistent with the meson dominance principle. In particular, the 2++ component
\ncan be accurately saturated with the f2(1270) meson, whereas the 0++ component with the σ meson. To
\nincorporate the large width of the σ, we use the dispersion relation with the spectral density obtained from
\nanalyses of the physical pion scattering data. Effects of the pion mass are estimated within Chiral Perturbation
\nTheory and are found to be small between the lattice and the physical point. We also discuss the implications
\nof the perturbative QCD constraints at high momentum transfers, leading to specific sum rules for the spectral
\ndensities of the gravitational form factors, and argue that these densities cannot be of definite sign.