A well-posed gap in the two-color lattice literature: T_c/√σ for SU(2) with N_f=3 light fundamental flavours

Abstract

Two-color QCD has a substantial finite-temperature literature at N_f = 2. To our knowledge, following a literature sweep dated 2026-07, no published determination of the transition temperature in string-tension units, T_c/√σ, is available for N_f = 3 light fundamental Dirac flavours. We state the computation cleanly: separate chiral and deconfinement crossovers, a chiral extrapolation, a continuum statement at least two temporal extents, and an explicit confrontation of the staggered-rooting versus Wilson trade-off in a pseudo-real theory. The gap is scientifically interesting independent of any particular dark-sector model: flavour dependence of T_c/√σ is well mapped in SU(3), while SU(2)'s enlarged chiral pattern and different Goldstone count leave the saturation of that flavour dependence open. This note reports no lattice measurement and no new numerical result; its content is the gap statement and the requirements of a serious determination. An optional transparency remark on a pre-registered external stake is deferred to a short final paragraph and is not the purpose of the note.