Validity of chiral perturbation theory for isospin-2 pion–pion scattering in Sp(4) at large mπ/fπ

Determine whether leading-order chiral perturbation theory accurately describes the isospin-2 (Sp(4) 14-dimensional irrep) two-pion s-wave scattering in Sp(4) gauge theory with two degenerate fundamental fermions in the regime of large mπ^∞/fπ, specifically whether the predicted relation a0 mπ^∞ = (1/32)(mπ^∞/fπ)^2 holds for the lattice ensembles studied.

Background

The paper determines s-wave scattering parameters for two identical dark pions in Sp(4) gauge theory using lattice simulations and Lüscher’s finite-volume method. The authors extract the scattering length a0 and effective range r0 by fitting the effective range expansion to lattice-determined phase shifts, and compare the scattering length to the leading-order chiral perturbation theory (χPT) prediction a0 mπ^∞ = (1/32)(mπ^∞/fπ)^2.

Across ensembles at different β and fermion masses, the lattice results show consistently positive scattering lengths, with some ensembles agreeing within 1–2σ with the χPT prediction while others (notably at β=6.9) do not. Because the ratios mπ^∞/fπ are relatively large in these simulations (and thus outside the regime where χPT is naively expected to work), the authors explicitly state that they cannot confirm or rule out the applicability of χPT in this parameter regime based on their results.