We compute next-to-leading order (NLO) corrections in the \epsilon-regime ofWilson (WChPT) and Staggered Chiral Perturbation Theory (SChPT). A differencebetween the two is that in WChPT already at NLO, that is at O(\epsilon^2), newlow energy constants (LECs) contribute, whereas in SChPT they only enter atO(\epsilon^4). We first determine the NLO corrections in WChPT for SU(2), andfor U(N_f) at fixed index. This implies finite-volume corrections to the phaseboundary between the Aoki phase and the Sharpe-Singleton scenario viacorrections to the mean field potential. We also compute NLO corrections to thetwo-point function in the scalar and pseudo-scalar sector in WChPT. Turning toSChPT we determine the NLO corrections to the LECs and their effect on thetaste splitting. Here the NLO partition function can be written as the leadingorder one with renormalized couplings, thus preserving the equivalence tostaggered chiral random matrix theory at NLO for any number of flavors N_f. InWChPT this relation only appears to hold for SU(2).
Akemann G, Pucci F. Exploring the Aoki regime. JHEP. 2013;2013(6):59.
Akemann, G., & Pucci, F. (2013). Exploring the Aoki regime. JHEP, 2013(6), 59. doi:10.1007/JHEP06(2013)059
Akemann, G., and Pucci, F. (2013). Exploring the Aoki regime. JHEP 2013, 59.
Akemann, G., & Pucci, F., 2013. Exploring the Aoki regime. JHEP, 2013(6), p 59.
G. Akemann and F. Pucci, “Exploring the Aoki regime”, JHEP, vol. 2013, 2013, pp. 59.
Akemann, G., Pucci, F.: Exploring the Aoki regime. JHEP. 2013, 59 (2013).
Akemann, Gernot, and Pucci, Fabrizio. “Exploring the Aoki regime”. JHEP 2013.6 (2013): 59.
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