Gravitational form factors of the pion and meson dominance

TL;DR

This paper demonstrates that lattice QCD data for the pion's gravitational form factors align with meson dominance, with specific mesons saturating different components, and discusses implications of QCD constraints and spectral densities.

Contribution

It provides a detailed analysis showing meson dominance explains lattice data and explores spectral density properties under QCD constraints.

Findings

The $2^{++}$ component is saturated by the $f_2(1270)$ meson.

The $0^{++}$ component is saturated by the $\sigma$ meson.

Spectral densities of gravitational form factors cannot be of definite sign.

Abstract

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.