Scalar-glueball-mediated scale-anomaly dominance of the confining pressure of the pion in holographic QCD

TL;DR

The paper investigates how the QCD scale anomaly manifests in the internal mechanical structure of the pion by computing its gravitational form factors $A(t)$ and $D(t)$ within the Sakai–Sugimoto top-down holographic QCD framework and analyzing two-dimensional LF transverse densities $ ho_{2D}$ via trace–traceless EMT decomposition. It shows that $A(t)$ is entirely saturated by the tensor glueball ${ m T}_4(2^{++})$, while $D(t)$ receives contributions from ${ m T}_4(2^{++})$, ${ m T}_4(0^{++})$, and ${ m S}_4(0^{++})$, with the trace anomaly supplying a confining pressure $ abla p_{2D}$ in the central region. The confining pressure is mediated predominantly by scalar glueball exchanges in the large-$N_c$ limit, and the resulting 2D densities satisfy von Laue conditions, yielding a mass radius of about $0.23$ fm and a mechanical radius of about $0.50$ fm. These findings, echoing earlier nucleon results in a different dynamical form, support a universal role for the scale anomaly in hadron stability across forms and hadrons, with implications for the interpretation of internal hadron dynamics in holographic QCD.

Abstract

In this work, we analyze the energy density and the stress distribution inside the pion derived from gravitational form factors in top-down holographic QCD. In particular, we show that the dominance of the scale anomaly in the confining pressure, previously observed in the instant form for the nucleon, also holds for the pion in the light-front form. Furthermore, we find that in large-$N_c$ QCD described by this approach, the scalar glueball plays a mediating role in transmitting the confining pressure. These findings support the universal role of the scale anomaly in the stability of hadrons.

Figures (3)

• Figure 1: The pion GFFs $A(t)$ and $D(t)$, shown together with their multipole model fits and the lattice QCD results of Ref. Hackett:2023nkr.
• Figure 2: Energy density $\epsilon_{\rm 2D}(x_\perp)$, pressure $p_{\rm 2D}(x_\perp)$ and shear force distributions $s_{\rm 2D}(x_\perp)$.
• Figure 3: Pressure decomposition.