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]

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Summary

Introduction

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.

Evaluation
Results and discussion
Conclusion

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