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 (34)

• Harmonic Polylogarithms
• The four-loop beta-function in Quantum Chromodynamics
• New features of FORM
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• The three-loop QCD $\beta$-function and anomalous dimensions
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• The renormalization of the axial anomaly in dimensional regularization
• The analytical value of the electron (g-2) at order alpha^3 in QED
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Quark Mass Anomalous Dimension to alpha_s**4
• Complete Corrections of O(αα_s) to the Decay of the Z Boson into Bottom Quarks
• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Massive Feynman diagrams and inverse binomial sums
• Renormalization and Running of Quark Mass and Field in the Regularization Invariant and MS-bar Schemes at Three and Four Loops
• Matching QCD and HQET heavy--light currents at two loops and beyond
• Renormalization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point
• New results for the epsilon-expansion of certain one-, two- and three-loop Feynman diagrams
• Extension of HPL to complex arguments
• - XSummer - Transcendental Functions and Symbolic Summation in Form
• Three loop anomalous dimension of non-singlet quark currents in the RI' scheme
• New results for two-loop off-shell three-point diagrams
• Three loop MSbar tensor current anomalous dimension in QCD
• 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
• Quark Mass Renormalization in the $\MSbar$ and RI schemes up to the NNLO order
• Single-scale diagrams and multiple binomial sums
• ep-Finite Basis of Master Integrals for the Integration-By-Parts Method
• Master Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs
• Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme
• Tuning FORM with large calculations
• Extension of the functionality of the symbolic program FORM by external software

Cited by in corpus (50)

• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Next-to-Next-to-Leading-Order Charm-Quark Contribution to the CP Violation Parameter epsilon_K and Delta M_K
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• Domain Wall QCD with Near-Physical Pions
• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
• Step Scaling with off-shell renormalisation
• Proton decay matrix elements on the lattice at physical pion mass
• Precise MS-bar light-quark masses from lattice QCD in the RI/SMOM scheme
• Determination of quark masses from ${\mathbf{n}}_{\mathbf{f}}=4$ lattice QCD and the RI-SMOM intermediate scheme
• Two loop QCD vertices at the symmetric point
• Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes
• Six dimensional QCD at two loops
• RI'/SMOM scheme amplitudes for quark currents at two loops
• Banks-Zaks fixed point analysis in momentum subtraction schemes
• Non-perturbative renormalization of overlap quark bilinears on 2+1-flavor domain wall fermion configurations
• Off-shell two loop QCD vertices
• Symmetric point quartic gluon vertex and momentum subtraction
• Three loop renormalization of 3-quark operators in QCD
• Opening the Rome-Southampton window for operator mixing matrices
• Bilinear quark operators in the RI/SMOM scheme at three loops
• Neutral kaon mixing beyond the Standard Model with nf=2+1 chiral fermions part II: Non Perturbative Renormalisation of the $\Delta F=2$ four-quark operators
• RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations
• Two loop renormalization of the n = 2 Wilson operator in the RI'/SMOM scheme
• Renormalisation of the tensor current in lattice QCD and the $J/\psi$ tensor decay constant
• Nucleon isovector couplings in Nf = 2 + 1 lattice QCD at the physical point
• Amplitudes for the n = 3 moment of the Wilson operator at two loops in the RI/'SMOM scheme
• Momentum subtraction and the R-ratio
• Quark masses: N3LO bridge from $RI/SMOM$ to $\overline{\mathrm{MS}}$ scheme
• Nucleon mass and isovector couplings in 2+1-flavor dynamical domain-wall lattice QCD near physical mass
• Three loop QCD MOM beta-functions
• Moments $n=2$ and $n=3$ of the Wilson twist-two operators at three loops in the RI${}^{\prime }$/SMOM scheme
• Four-loop QCD MOM beta functions from the three-loop vertices at the symmetric point
• Maximal abelian and Curci-Ferrari gauges in momentum subtraction at three loops
• RI'/SMOM scheme amplitudes for deep inelastic scattering operators at one loop in QCD
• RI/MOM and RI/SMOM renormalization of quark bilinear operators using overlap fermions
• Spontaneous mass generation and the small dimensions of the Standard Model gauge groups U(1), SU(2) and SU(3)
• Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics
• Non-perturbative renormalization of tensor currents: strategy and results for $N_f=0$ and $N_f=2$ QCD
• A note on Rome-Southampton Renormalization with Smeared Gauge Fields
• Three-loop vertex integrals at symmetric point
• Semileptonic weak Hamiltonian to $\mathcal{O}(\alpha {\alpha }_s({\mu }_{\mathrm{Lattice}}))$ in momentum-space subtraction schemes
• Bilinear quark operator renormalization at generalized symmetric point
• Renormalization of three-quark operators at two loops in the RI${}^{\prime }$/SMOM scheme
• Non-perturbative renormalization in lattice QCD
• Symmetric point flavour singlet axial vector current renormalization at two loops
• Phenomenology from the Lattice
• RI/(S)MOM renormalizations of overlap quark bilinears with different levels of hypercubic smearing
• Off-shell quark bilinear operator Green's functions at two loops
• Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit
• Non-perturbative renormalisation with interpolating momentum schemes