QCD in the delta-Regime

TL;DR

This paper investigates the delta-regime of QCD using chiral perturbation theory, computing the residual pion mass to third order, and compares theoretical predictions with numerical simulations to determine Low Energy Constants.

Contribution

It applies the delta-expansion of chiral perturbation theory to compute the residual pion mass and uses numerical data to extract Low Energy Constants in the delta-regime of QCD.

Findings

Computed residual pion mass to third order in delta-expansion.

Numerical simulations agree with theoretical predictions for residual pion mass.

Extracted value for the Low Energy Constant  l_3 from extrapolated data.

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.