One flavor mass reweighting: foundations

Understand

Reweighting is not a new method in lattice QCD, but a comprehensive analysis is missing in the literature.

• We close this gap by presenting: (i) a proof of an integral representation of the complex determinant of a complex matrix, (ii) a method to control the stochastic error of its Monte Carlo estimation, (iii) expansions of the stochastic error and the ensemble fluctuations of the one flavor reweighting factor.
• Based on (iii) we present a detailed scaling analysis and optimized reweighting strategies.
• As an application we analyze the ensemble fluctuations of the reweighting factor corresponding to the sea contribution to isospin splitting and predict at physical quark masses a standard deviation of +-20%.