Renormalization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point

TLDR: In this paper, the authors extended the RI/SMOM scheme for bilinear operators to one with a nonexceptional, symmetric subtraction point and derived conversion factors to convert results obtained in lattice calculations into the MS? scheme.

Abstract: We extend the Rome-Southampton regularization independent momentum-subtraction renormalization scheme (RI/MOM) for bilinear operators to one with a nonexceptional, symmetric subtraction point. Two-point Green’s functions with the insertion of quark bilinear operators are computed with scalar, pseudoscalar, vector, axial-vector and tensor operators at one-loop order in perturbative QCD. We call this new scheme RI/SMOM, where the S stands for “symmetric.” Conversion factors are derived, which connect the RI/SMOM scheme and the MS? scheme and can be used to convert results obtained in lattice calculations into the MS? scheme. Such a symmetric subtraction point involves nonexceptional momenta implying a lattice calculation with substantially suppressed contamination from infrared effects. Further, we find that the size of the one-loop corrections for these infrared improved kinematics is substantially decreased in the case of the pseudoscalar and scalar operator, suggesting a much better behaved perturbative series. Therefore it should allow us to reduce the error in the determination of the quark mass appreciably.