Lattice Subtraction Methods at Low Quark Mass*

In Lattice QCD, the evaluation of quark loop effects is an essential, but computationally expensive, part of the evaluation of quark operators. Because of this, approximation techniques must be employed, which introduce statistical uncertainty in the extraction of signals. In this study, we present new noise subtraction techniques for the evaluation of disconnected quark loop diagrams using a finite number of noises to help reduce the error in the calculation of quark operators. This study uses a 24³ x 32 Wilson lattice in the quenched approximation for testing. Results for deflation, polynomial subtraction, and combination methods are presented, along with a new method termed “Hermitian Forced Eigenvalue and Polynomial Subtraction (HFPOLY)”. We are able to improve signals down to zero quark mass using a combination of linear solvers called GMRES-DR and MINRES-DR, for the nonHermitian and Hermitian Wilson matrices, respectively.