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Gravitational form factors of the pion and meson dominance
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Gravitational form factors of the pion and meson dominance
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We show that the recent MIT lattice QCD data for the pion's gravitational form factors are, in the covered momentum transfer range, fully consistent with the meson dominance principle. In particular, the $2^{++}$ component can be accurately saturated with the $f_2(1270)$ meson, whereas the $0^{++}$ component with the $\sigma$ meson. To incorporate the large width of the $\sigma$, we use the dispersion relation with the spectral density obtained from analyses of the physical pion scattering data. Effects of the pion mass are estimated within Chiral Perturbation Theory and are found to be small between the lattice and the physical point. We also discuss the implications of the perturbative QCD constraints at high momentum transfers, leading to specific sum rules for the spectral densities of the gravitational form factors, and argue that these densities cannot be of definite sign.
Forward citations
Cited by 5 Pith papers
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Gluon Gravitational $ D$-Form Factor: The $\sigma$-Meson as a Dilaton Confronted with Lattice Data II
Lattice fits to gluon gravitational form factors support the sigma meson as dilaton with new predictions for rho and delta, reinforcing evidence for scale symmetry in low-energy QCD.
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Hadronic form factors violate QCD dispersion relations due to incomplete time-like spectral data above the last known resonance, which radial Regge trajectories can fill as a minimal ansatz, shown for the pion form factor.
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A hadronic approach based on dispersion relations and meson dominance achieves a successful description of lattice QCD data for gravitational form factors of pions and nucleons.
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