Three-loop QCD Mass Relation between the $\overline{\mathrm{MS}}$ and Symmetric-momentum Subtraction Scheme Away from the Chiral Limit

Abstract

The perturbative result for the quark-mass conversion factor between the $\overline{\mathrm{MS}}$ and regularization-independent symmetric-momentum subtraction scheme (RI/SMOM) away from the chiral limit, i.e. at non-zero quark masses (RI/mSMOM), is derived up to three loops in QCD, extending the existing result by two additional orders. We further explore an illuminating possibility that in Dimensional Regularization, the original RI/(m)SMOM renormalization conditions may be interpreted merely in a weaker sense, namely as equations holding just in the 4-dimensional limit rather than exactly in $d$ dimensions: they result in different, albeit simpler, renormalization constants but still the same finite conversion factor. This novel observation has the added benefit of reducing computational effort, particularly at high orders. Our high-order results for the conversion factor exhibit rich behaviors, and in particular a window is observed in the subtraction scale and mass where it receives less perturbative corrections than the RI/SMOM counterpart up to three loops; this finding may help to further improve the accuracy of $\overline{\mathrm{MS}}$ quark-mass determinations with Lattice QCD.

matched to the publication version in PLB

References in corpus (44)

• FLAG Review 2021
• FORM version 4.0
• Kira - A Feynman Integral Reduction Program
• Integral Reduction with Kira 2.0 and Finite Field Methods
• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• High-Precision c and b Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• AMFlow: a Mathematica package for Feynman integrals computation via Auxiliary Mass Flow
• A Systematic and Efficient Method to Compute Multi-loop Master Integrals
• Renormalization of quark bilinear operators in a momentum-subtraction scheme with a nonexceptional subtraction point
• Reconstructing Rational Functions with $\text{FireFly}$
• Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks
• High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Lattice Perturbation Theory
• Three loop anomalous dimension of non-singlet quark currents in the RI' scheme
• Interpolation of Dense and Sparse Rational Functions and other Improvements in $\text{FireFly}$
• First determination of the strange and light quark masses from full lattice QCD
• Precise charm to strange mass ratio and light quark masses from full lattice QCD
• Non-perturbative renormalization of quark bilinear operators and B_K using domain wall fermions
• Multiloop corrections for collider processes using auxiliary mass flow
• High-precision determination of the light-quark masses from realistic lattice QCD
• Determining Feynman integrals with only input from linear algebra
• Charmonium properties from lattice QCD + QED: hyperfine splitting, $J/\psi$ leptonic width, charm quark mass and $a_{\mu }^c$
• FeynGame
• Four-loop QCD propagators and vertices with one vanishing external momentum
• Charm and strange quark masses and $f_{D_s}$ from overlap fermions
• Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes
• Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice
• Massive vector form factors to three loops
• Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow
• 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
• Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
• Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
• An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting ${\gamma }_5$
• Bilinear quark operators in the RI/SMOM scheme at three loops
• RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations
• FeynGame 3.0
• Determination of ${\overline{m}}_b/{\overline{m}}_c$ and ${\overline{m}}_b$ from $n_f=4$ lattice QCD$+$QED
• Heavy-quark pair production at lepton colliders at NNNLO in QCD
• A discussion on leading renormalon in the pole mass
• A massive momentum-subtraction scheme
• Strong-Coupling Constant at Three Loops in Momentum Subtraction Scheme
• Quark masses: N3LO bridge from $RI/SMOM$ to $\overline{\mathrm{MS}}$ scheme
• RI/MOM and RI/SMOM renormalization of quark bilinear operators using overlap fermions