Results and techniques for higher order calculations within the gradient-flow formalism

Abstract

We describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of the five-dimensional field theory and the composite operators considered in this paper. Tools from standard perturbative calculations are used to obtain Green's functions at finite flow time $t$ at higher orders in perturbation theory. The three-loop results for the quark condensate at finite $t$ and the conversion factor for the "ringed" quark fields to the $\overline{\mbox{MS}}$ scheme are presented as applications. We also re-evaluate an earlier result for the three-loop gluon condensate, improving on its accuracy.

42 pages. v2: typo fixed in Eq.(64); matches published version, including (forthcoming) erratum

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Cited by in corpus (16)

• Integral Reduction with Kira 2.0 and Finite Field Methods
• Reconstructing Rational Functions with $\text{FireFly}$
• The two-loop energy-momentum tensor within the gradient-flow formalism
• Four quark operators for kaon bag parameter with gradient flow
• Short flow-time coefficients of CP-violating operators
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• Moments of parton distribution functions of any order from lattice QCD
• Past, present, and future of precision determinations of the QCD coupling from lattice QCD
• Effective electroweak Hamiltonian in the gradient-flow formalism
• Two-loop gradient-flow renormalization of scalar QCD
• Stout smearing and Wilson flow in lattice perturbation theory
• Latent heat and pressure gap at the first-order deconfining phase transition of SU(3) Yang-Mills theory using the small flow-time expansion method
• $t\to 0$ extrapolation function in SF$t$X method for the energy-momentum tensor
• The electroweak Hamiltonian in the gradient flow formalism
• Applications of the Perturbative Gradient Flow
• The gradient flow formulation of the electroweak Hamiltonian