The light quark mass ratio mᵤ/md and the pion mass have been derived from the Yukawa coupling structure of M-theory compactified on a seven-dimensional manifold of G2 holonomy. The first-generation Yukawa couplings, determined by the electromagnetic fine-structure constant and the geometric moduli of the Joyce orbifold, have yielded the scale-independent predictions mᵤ/md = 1/2 and (md - mᵤ) / (md + mᵤ) = 1/3, in agreement with the FLAG 2024 lattice averages at 0. 8 sigma and 1. 3 sigma, respectively. The pion mass has been obtained through the Gell-Mann-Oakes-Renner relation at next-to-leading order in chiral perturbation theory with lattice-determined non-perturbative parameters, giving mₚi = 140. 8 +/- 5. 3 MeV in 0. 9% agreement with the experimental value 139. 570 MeV. The geometric determination of the quark mass ratio has reduced the number of independent low-energy constants in the O (p⁴) SU (3) chiral Lagrangian from approximately twelve to approximately seven, representing a 40% parameter reduction. All predictions have employed the same three geometric constants (K₀, CLIG, CQG) previously used to derive twenty-two observables across the gauge, lepton, neutrino, cosmological, and nuclear sectors with a mean deviation of 2. 0%. The prediction mᵤ/md = 1/2 constitutes a sharp, falsifiable target for future sub-percent lattice QCD determinations.
Moustafa Radwan (Mon,) studied this question.