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

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.