One flavor mass reweighting: foundations

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%.