The Scalar Glueball of Pure G2 Yang–Mills Theory: a Continuum Estimate of m0++/√σ

We compute the mass of the lightest scalar glueball of pure G2 Yang–Mills theory in 3+1 dimensions on the lattice, in units of the square root of the string tension. Three ensembles with the Wilson action at β = 9.6, 9.7 and 10.0 (16³×32, 16³×32 and 20³×40; 2000 configurations each) were analysed once, with code fixed before any correlation function of these ensembles was built. Masses are obtained from a variational basis of 25 smeared operators, and the string tension from Wilson loops. A continuum extrapolation linear in a²σ gives m0++/√σ = 3.87 ± 0.09 (stat) ± 0.85 (syst) for pure G2. The systematic error is dominated by a 20% uncertainty assigned to the mass estimator, which was selected after inspecting SU(2) and SU(3) control ensembles and then tested out of sample on two coarser SU(2) ensembles. At this precision the value is compatible with the continuum SU(N) values, 3.07–3.78, and with the value 3.28 that the conjectured Casimir scaling of m0++²/σ implies for G2; it cannot discriminate between them. We have found no previous lattice determination of this quantity for pure G2. The limitations are stated explicitly:- the estimator was chosen post hoc;- three spacings do not test the functional form of the continuum extrapolation;- finite-volume effects specific to a group without centre symmetry were not studied;- no value of m0++/Λ(MS-bar) is given, because two-loop asymptotic scaling fails its own SU(3) calibration at these couplings. The data of this note (glueball operator time series, Wilson loops and gradient-flow data of the three G2 ensembles and of the four SU(2)/SU(3) control ensembles), the simulation and analysis code, and a script that reproduces its numbers will be added in a later version of this record. Until then they are available from the author on request. The code, the analysis and the manuscript were prepared with the assistance of an AI system (Anthropic's Claude) under the author's direction. The author takes full responsibility for the content.