Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes

Abstract

Light quark masses can be determined through lattice simulations in regularization invariant momentum-subtraction(RI/MOM) schemes. Subsequently, matching factors, computed in continuum perturbation theory, are used in order to convert these quark masses from a RI/MOM scheme to the MS-bar scheme. We calculate the two-loop corrections in quantum chromodynamics(QCD) to these matching factors as well as the three-loop mass anomalous dimensions for the RI/SMOM and RI/SMOM_gamma_mu schemes. These two schemes are characterized by a symmetric subtraction point. Providing the conversion factors in the two different schemes allows for a better understanding of the systematic uncertainties. The two-loop expansion coefficients of the matching factors for both schemes turn out to be small compared to the traditional RI/MOM schemes. For nf=3 quark flavors they are about 0.6-0.7% and 2%, respectively, of the leading order result at scales of about 2 GeV. Therefore, they will allow for a significant reduction of the systematic uncertainty of light quark mass determinations obtained through this approach. The determination of these matching factors requires the computation of amputated Green's functions with the insertions of quark bilinear operators. As a by-product of our calculation we also provide the corresponding results for the tensor operator.

24 pages, 2 figures; v2: version accepted for publication in the journal

References in corpus (5)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme
• Extension of the functionality of the symbolic program FORM by external software

Cited by in corpus (11)

• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
• Step Scaling with off-shell renormalisation
• Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme
• Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes
• RI'/SMOM scheme amplitudes for quark currents at two loops
• Two loop renormalization of the n = 2 Wilson operator in the RI'/SMOM scheme
• Amplitudes for the n = 3 moment of the Wilson operator at two loops in the RI/'SMOM scheme
• RI'/SMOM scheme amplitudes for deep inelastic scattering operators at one loop in QCD
• Phenomenology from the Lattice