Abstract
The gradient-flow formulation of the energy–momentum tensor of QCD is extended to NNLO perturbation theory. This means that the Wilson coefficients which multiply the flowed operators in the corresponding expression for the regular energy–momentum tensor are calculated to this order. The result has been obtained by applying modern tools of regular perturbation theory, reducing the occurring two-loop integrals, which also include flow-time integrations, to a small set of master integrals which can be calculated analytically.
Highlights
The gradient-flow formalism as introduced by Lüscher [1] and further formalized by Lüscher and Weisz [2] has proven useful in lattice QCD in many respects
We have presented the universal Wilson coefficients for the gradient-flow definition of the energy–momentum tensor through NNLO QCD
The NNLO corrections modify the three numerically dominant coefficients c1, c2, c3 at the level of 10% (1-2%) for a central scale of μ0 = 3 GeV (μ0 = 130 GeV), where μ0 is related to the flow time t according to Eq (54)
Summary
The gradient-flow formalism as introduced by Lüscher [1] and further formalized by Lüscher and Weisz [2] has proven useful in lattice QCD in many respects. One of its main virtues is that composite operators at finite flow time t do not require ultra-violet (UV) renormalization beyond the one of the involved parameters and fields This means that the operators do not mix under renormalization-group running, which makes it simple to combine results from different regularization schemes. A powerful way to exhibit this possible interplay is obtained by considering the expansion of composite operators in the limit of small flow time, which expresses flowed operators in terms of QCD operators at t = 0, with t-dependent Wilson coefficients [2]. This method has been used by Makino and Suzuki [4,5] to derive a regularization-independent formula for the energy–
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