Glueball mass from RGZ-inspired infrared gluodynamics: a Euclidean Bethe-Salpeter approach

TL;DR

This work addresses the nonperturbative infrared spectrum of pure Yang-Mills theory by formulating and solving a Euclidean Bethe-Salpeter equation for the lightest scalar glueball $0^{++}$ using the Refined Gribov-Zwanziger gluon propagator as input. With a minimal ladder truncation characterized by a constant kernel strength $g_C^2$ and the dominant $s$-wave, the authors extract $M_{0^{++}}$ in the range $M_{0^{++}} \in [1.7, 2.3]$ GeV, finding a preferred value near $M_{0^{++}} \approx 1.9$ GeV for $g_C^2 \approx 0.54$. The results align with RGZ correlator-based infrared moment analyses and lattice expectations, providing a cross-check of RGZ infrared gluodynamics from a bound-state perspective. This study demonstrates that Euclidean bound-state methods, fed by realistic IR input, can robustly capture glueball dynamics and sets the stage for more refined kernels and broader channel studies.

Abstract

We formulate and solve a Euclidean Bethe-Salpeter equation for the lightest scalar glueball (0++) in pure Yang-Mills theory, using the refined Gribov-Zwanziger gluon tree-level propagator as an infrared-complete input. In a minimal ladder truncation with an effective constant kernel strength g_C^2 and the dominant s-wave component, we extract scalar glueball masses in the range 1.7-2.3 GeV for representative values of g_C^2, with a preferred value around 1.9 GeV near g_C^2 = 0.54. The result is consistent with RGZ correlator-based infrared moment analyses and with lattice expectations, providing a cross-check of RGZ-inspired infrared gluodynamics from a bound-state viewpoint.

Figures (1)

• Figure 1: Largest eigenvalue $\lambda(P^2)$ of the Bethe--Salpeter kernel as a function of $P^2$ for an effective coupling $g_C^2 = 0.54$. The intersection with the horizontal line $\lambda=1$ fixes the scalar glueball mass.