Simulations in the epsilon-Regime of Chiral Perturbation Theory

TL;DR

This paper explores the use of Ginsparg-Wilson fermion simulations in the epsilon-regime of chiral perturbation theory to determine low energy constants, highlighting challenges in measurement and volume requirements.

Contribution

It analyzes the feasibility and limitations of lattice simulations in the epsilon-regime for extracting chiral low energy constants.

Findings

Measuring observables in the topologically trivial sector is very difficult.

Large statistics are required due to small eigenvalues.

Contact with chiral perturbation theory needs sufficiently large physical volume.

Abstract

We discuss the potential of Ginsparg-Wilson fermion simulations in the epsilon-regime of chiral perturbation theory, regarding the determination of the leading low energy constants of the effective chiral Lagrangian. It turns out to be very hard to measure observables in the topologically trivial sector. There a huge statistics would be required, due to the frequent occurrence of very small eigenvalues. Moreover, contact with chiral perturbation theory is only established if the physical volume of the system is sufficiently large.