Abstract
We consider the renormalization of the matrix elements of the bilinear quark operators ψ¯ψ, ψ¯γμψ, and ψ¯σμνψ at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the MS‾ scheme and the regularization invariant symmetric momentum subtraction (RI/SMOM) scheme. The obtained results can be used to reduce the errors in determinations of quark masses from lattice QCD simulations. The results are given in Landau gauge.
Highlights
The lattice formulation of quantum chromodynamics (QCD) provides a possibility to estimate long-distance operator matrix elements from first principles using Monte Carlo methods
One of the popular schemes is the regularization independent momentum subtraction (RI/MOM) scheme or its variant, the RI /MOM scheme [1], where the subtraction is done at the momentum configuration p2 = q2 = −μ2, (p + q)2 = 0
The regularization independent symmetric MOM (RI/SMOM) scheme has been suggested in Ref. [2]
Summary
The lattice formulation of quantum chromodynamics (QCD) provides a possibility to estimate long-distance operator matrix elements from first principles using Monte Carlo methods. The pseudoscalar current receives contributions from the pseoduscalar-meson pole at (p + q)2 = 0 and is sensitive to condensate effects of order O(Λ2QCD/μ2). To avoid such problems, the regularization independent symmetric MOM (RI/SMOM) scheme has been suggested in Ref. The regularization independent symmetric MOM (RI/SMOM) scheme has been suggested in Ref. The n = 2 and n = 3 twist-two operators have been considered at the two-loop level in Refs. The goal of the present work is to evaluate the matching factors between the MS and RI/SMOM schemes for the bilinear quark operators in the three-loop approximation.
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