QCD in the delta-Regime

Abstract

The delta-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 delta-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 M_pi^R, which has been computed to the third order in the delta-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 delta-regime. This is very tedious, but results compatible with the predictions for M_pi^R have been obtained. Then we show that an extrapolation of pion masses measured in a larger volume towards the delta-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 \bar l_3.