Analytic Prediction of the Glueball Mass Radius

Lattice QCD has numerically predicted the mass of the lightest scalar glueball (0⁺⁺) to be approximately 1.5–1.7 GeV for nearly four decades [1], but computation of its internal spatial structure — the mass radius — has only recently seen a breakthrough. In 2025, a lattice QCD collaboration reported the first calculation of the scalar glueball mass radius via gravitational form factors, obtaining R_g = 0.263(31) fm [2]. This paper provides a rigorous analytic formula for the glueball mass radius within the Gluon Elastic Lattice Theory (GELT): R_g = ℓ_c = d₀√ζ. With ζ = 0.02767 precisely determined by a first-principles direct triple summation using the Gaussian interaction function and d₀ ≈ 1.74 × 10⁻¹⁵ m calibrated from three independent experimental data, R_g ≈ 0.29 fm. The GELT prediction falls at the edge of the 1σ uncertainty interval [0.232, 0.294] fm of the lattice QCD result — within approximately 0.87 standard deviations of the central value. The glueball radius is uniquely determined by the medium correlation length — containing no free parameters. **References** [1] C. J. Morningstar and M. Peardon, The glueball spectrum from an anisotropic lattice study, Phys. Rev. D 60, 034509 (1999). [2] R. Abbott, D. C. Hackett, D. A. Pefkou, F. Romero-López, P. E. Shanahan, Lattice Evidence that Scalar Glueballs Are Small, Phys. Rev. Lett. 136, 041901 (2026), arXiv:2508.21821 [hep-lat].