One-loop matching of the LEFT to the QCD gradient flow

Abstract

We present the complete one-loop matching of the baryon- and lepton-number-conserving low-energy effective field theory (LEFT) to the QCD gradient flow. Using Euclidean conventions and the background-field formulation of the gradient flow, we derive the short-flow-time expansion for the full LEFT operator basis up to mass dimension six. The matching is performed in dimensional regularization in the algebraically consistent 't Hooft-Veltman scheme, including a systematic treatment of evanescent operators and the finite counterterms required to restore chiral symmetry in the spurion sense. Keeping fully generic flavor structures, we verify the cancellation of spurious chiral-symmetry-violating terms with the known finite symmetry-restoring counterterms. This demonstrates that the gradient flow as a gauge-invariant ultraviolet regulator enables an efficient extraction of both divergent and finite counterterms in addition to the matching contributions. We provide the matching coefficients both before and after field redefinitions that remove redundant operators, as well as power-divergent mixings into lower-dimensional operators. Our results establish a consistent perturbative link between continuum LEFT calculations and gradient-flow-based lattice-QCD matrix elements, enabling precision low-energy phenomenology beyond leading-logarithmic accuracy.

46 pages, 2 tables; version published in JHEP

References in corpus (53)

• Dimension-Six Terms in the Standard Model Lagrangian
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Properties and uses of the Wilson flow in lattice QCD
• Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• FLAG Review 2021
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching
• Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model
• Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions
• Chiral symmetry and the Yang--Mills gradient flow
• Low-energy effective field theory below the electroweak scale: matching at one loop
• A Proof of Concept for Matchete: An Automated Tool for Matching Effective Theories
• EFT approach to the electron Electric Dipole Moment at the two-loop level
• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields
• Confirming the Existence of the strong CP Problem in Lattice QCD with the Gradient Flow
• Indirect probes of the trilinear Higgs coupling: $gg\to h$ and $h\to \gamma \gamma$
• Holomorphy without Supersymmetry in the Standard Model Effective Field Theory
• The electric dipole moment of the neutron from 2+1 flavor lattice QCD
• Dimension-5 CP-odd operators: QCD mixing and renormalization
• Structure of two-loop SMEFT anomalous dimensions via on-shell methods
• Calculation of the neutron electric dipole moment with two dynamical flavors of domain wall fermions
• The two-loop energy-momentum tensor within the gradient-flow formalism
• Evanescent Operators in One-Loop Matching Computations
• The perturbative QCD gradient flow to three loops
• Neutron electric dipole moment using $N_f=2+1+1$ twisted mass fermions
• The nucleon electric dipole moment with the gradient flow: the $\theta$-term contribution
• Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator
• Contribution of the QCD $\Theta$-term to nucleon electric dipole moment
• Neutron and proton electric dipole moments from $N_f=2+1$ domain-wall fermion lattice QCD
• Small flow-time representation of fermion bilinear operators
• Functional Matching and Renormalization Group Equations at Two-Loop Order
• Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme
• Computing Tools for Effective Field Theories
• Non-perturbative renormalization scheme for the CP-odd three-gluon operator
• NLO QCD Renormalization Group Evolution for Non-Leptonic $\Delta F=2$ Transitions in the SMEFT
• Effective electroweak Hamiltonian in the gradient-flow formalism
• Background field method in the gradient flow
• Renormalization scheme factorization of one-loop Fierz identities
• Two-loop running effects in Higgs physics in Standard Model Effective Field Theory
• Hadronic vacuum polarization using gradient flow
• One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme
• Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators
• A Guide to Functional Methods Beyond One-Loop Order
• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• On the two-loop penguin contributions to the Anomalous Dimensions of four-quark operators
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• From the EFT to the UV: the complete SMEFT one-loop dictionary
• Two-loop anomalous dimensions for baryon-number-violating operators in SMEFT
• Two-Loop Anomalous Dimensions in the LEFT: Dimension-Six Four-Fermion Operators in NDR
• Two-loop gradient-flow renormalization of scalar QCD