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

TL;DR

This paper analyzes gluon gravitational form factors of various particles using lattice QCD data, supporting the idea that the $\sigma$-meson acts as a dilaton and indicating possible infrared fixed point behavior in QCD.

Contribution

It introduces a dilaton effective theory fit to lattice data, providing new predictions for gravitational form factors and reinforcing the dilaton interpretation of the $\sigma$-meson.

Findings

Residues agree with dilaton effective theory predictions

Derived new dilaton-based predictions for $ ho$- and $\Delta$-form factors

Supports the hypothesis of an infrared fixed point in QCD

Abstract

We investigate the gluon gravitational form factors of the $\pi$, $N$, $\rho$, and $\Delta$ using lattice QCD data at $m_\pi \approx 450 \text{MeV}$ and $m_\pi \approx 170 \text{MeV}$. We base the analysis on fits to a simple $\sigma/f_0(500)$-meson pole, supplemented by a polynomial background term. The fitted residues agree with predictions from dilaton effective theory, in which the $\sigma$-meson acts as the dilaton, the pseudo Goldstone boson of spontaneously broken scale symmetry. We derive new dilaton-based predictions for the $\rho$- and $\Delta$-gravitational form factors, and comment on the $\eta_{c}$- and $\eta_b$-form factors in the context of the dilaton interpretation. These results reinforce our earlier findings, based on lattice total (quark and gluon) gravitational form factors, and provide further evidence that QCD dynamics may be governed by an infrared fixed point.