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arXiv · 1103.3311

QCD in the delta-Regime

W. Bietenholz·N. Cundy·M. Gockeler·R. Horsley·Y. Nakamura·D. Pleiter·P. E. L. Rakow·G. Schierholz·J. M. Zanotti
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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.

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W. Bietenholz, N. Cundy, M. Gockeler, R. Horsley, Y. Nakamura, D. Pleiter, P. E. L. Rakow, G. Schierholz, J. M. Zanotti. 2011-03-16. QCD in the delta-Regime. https://doi.org/10.1088/1742-6596%2F287%2F1%2F012016

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