Exploring the Aoki regime

Abstract

We compute next-to-leading order (NLO) corrections in the ε-regime of Wilson (WChPT) and Staggered Chiral Perturbation Theory (SChPT). A difference between the two is that in WChPT already at NLO, that is at O(ε^2), new low energy constants (LECs) contribute, whereas in SChPT they only enter at O(ε^4). We first determine the NLO corrections in WChPT for SU(2), and for U(N_f) at fixed index. This implies finite-volume corrections to the phase boundary between the Aoki phase and the Sharpe-Singleton scenario via corrections to the mean field potential. We also compute NLO corrections to the two-point function in the scalar and pseudo-scalar sector in WChPT. Turning to SChPT we determine the NLO corrections to the LECs and their effect on the taste splitting. Here the NLO partition function can be written as the leading order one with renormalized couplings, thus preserving the equivalence to staggered chiral random matrix theory at NLO for any number of flavors N_f. In WChPT this relation only appears to hold for SU(2).

32 pages, 6 figures, 4 tables, v2: Published version

References in corpus (10)

• The Chiral Condensate in a Finite Volume
• Eigenvalue Density of the non-Hermitian Wilson Dirac Operator
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• The epsilon regime with Wilson fermions
• Observations on the Wilson fermions in the epsilon regime
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime
• Finite size scaling of meson propagators with isospin chemical potential
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• Individual Eigenvalue Distributions for the Wilson Dirac Operator

Cited by in corpus (1)

• The $\epsilon$-regime of dilaton chiral perturbation theory