QCD in the δ-regime

Abstract

The б-regime of QCD is characterised by light quarks in a small spatial box, but a large extent in(Euclidean)time. In this setting a specific variant of chiral perturbation theory — the б-expansion — applies, based on a quantum mechanical treatment of the quasi one dimensional system. In particular, for vanishing quark masses one obtains a residual pion mass MR, which has been computed to the third order in the б-expansion. A comparison with numerical measurements of this residual mass allows for a new determination of some Low Energy Constants, which appear in the chiral Lagrangian. We first review the attempts to simulate 2-flavour QCD directly in the б-regime. This is very tedious, but results compatible with the predictions for MR have been obtained. Then we show that an extrapolation of pion masses measured in a larger volume towards the б-regime leads to good agreement with the theoretical predictions. From those results, we also extract a value for the (controversial) sub-leading Low Energy Constant T3.