General non-perturbative mass gap to first order in 1V

The cluster expansion of the Lanczos matrix is studied in both vacuum and non-vacuum sectors of Hilbert space. The first order analytic diagonalization of the expanded Lanczos matrix is employed to obtain an expression for the lowest energy state in a given sector. Subtraction of the vacuum energy at the same order gives a non-perturbative expression for the lowest mass gap of that sector to order 1V. This general result is applied to the axial and tensor glueball sectors of SU(3) lattice gauge theory and the ratio R = MAMT is calculated analytically. We find that this approximate for R agrees with the higher order t expansion computations up to the transition from strong to weak coupling at 2g2 ∼ 1.5, thus explicitly demonstrating the non-perturbative nature of the mass-gap expression.