Reweighting towards the chiral limit

Abstract

We propose to perform fully dynamical simulations at small quark masses by reweighting in the quark mass. This approach avoids some of the technical difficulties associated with direct simulations at very small quark masses. We calculate the weight factors stochastically, using determinant breakup and low mode projection to reduce the statistical fluctuations. We find that the weight factors fluctuate only moderately on nHYP smeared dynamical Wilson-clover ensembles, and we could successfully reweight ${16}^{4}$, $(1.85\text{ }\text{ }\mathrm{fm}{)}^{4}$ volume configurations from ${m}_{q}\ensuremath{\approx}20\text{ }\text{ }\mathrm{MeV}$ to ${m}_{q}\ensuremath{\approx}5\text{ }\text{ }\mathrm{MeV}$ quark masses, reaching the $ϵ$-regime. We illustrate the strength of the method by calculating the low energy constant $F$ from the $ϵ$-regime pseudoscalar correlator.