Gravitational $ D$-Form Factor: The $\sigma$-Meson as a Dilaton confronted with Lattice Data

TL;DR

This paper models the nucleon and pion gravitational D-form factors using a sigma meson pole within a dilaton effective theory, aligning lattice data with the concept of spontaneously broken scale symmetry in QCD.

Contribution

It provides a novel interpretation of the sigma meson as a dilaton and connects lattice data with dilaton effective theory predictions.

Findings

Residues are compatible with dilaton effective theory predictions.

Supports the idea of an infrared fixed point in QCD.

Offers a physical interpretation of the D-term in the soft limit.

Abstract

We investigate the nucleon and pion gravitational $D$-form factors, by fitting a $\sigma/f_0(500)$-meson pole, together with a background term, to lattice data at $m_\pi \approx 170\text{MeV}$. We find that the fitted residues are compatible with predictions from dilaton effective theory. In this framework, the $\sigma$-meson takes on the role of the dilaton, the Goldstone boson of spontaneously broken scale symmetry. These results support the idea that QCD may be governed by an infrared fixed point and offer a physical interpretation of the $D$-form factor (or $D$-term) in the soft limit.