Error reduction technique using covariant approximation and application to nucleon form factor

Abstract: We demonstrate the new class of variance reduction techniques for hadron propagator and nucleon isovector form factor in the realistic lattice of $N_f=2+1$ domain-wall fermion. All-mode averaging (AMA) is one of the powerful tools to reduce the statistical noise effectively for wider varieties of observables compared to existing techniques such as low-mode averaging (LMA). We adopt this technique to hadron two-point functions and three-point functions, and compare with LMA and traditional source-shift method in the same ensembles. We observe AMA is much more cost effective in reducing statistical error for these observables.