The two-loop energy-momentum tensor within the gradient-flow formalism

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.

24 pages, 2 figures, 5 ancillary files. v2: References added; sign fixed in Eq.(63); minor typos fixed; main results unchanged; results in ancillary files now distinguish different quark flavors. v3: typo fixed in Eq.(43). v4: Figs. 1 and 2 replaced; analytical results unchanged

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• Results and techniques for higher order calculations within the gradient-flow formalism
• Four quark operators for kaon bag parameter with gradient flow
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• Viscosity of pure-glue QCD from the lattice
• 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
• Effective electroweak Hamiltonian in the gradient-flow formalism
• Distribution of Energy-Momentum Tensor around a Static Quark in the Deconfined Phase of SU(3) Yang-Mills Theory
• QCD Static Force in Gradient Flow
• Hadronic vacuum polarization using gradient flow
• Supersymmetric gradient flow in the Wess-Zumino model
• Off-lightcone Wilson-line operators in gradient flow
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
• ftint: Calculating gradient-flow integrals with pySecDec
• Gradient Flow: Perturbative and Non-Perturbative Renormalization
• Two-loop gradient-flow renormalization of scalar QCD
• Energy-momentum tensor in QCD: nucleon mass decomposition and mechanical equilibrium
• 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
• Stout smearing and Wilson flow in lattice perturbation theory
• Perturbative analysis of the Wess-Zumino flow
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• QCD static force in gradient flow
• The electroweak Hamiltonian in the gradient flow formalism
• Applications of the Perturbative Gradient Flow
• $t\to 0$ extrapolation function in SF$t$X method for the energy-momentum tensor
• Stress distribution in quark--anti-quark and single quark systems at nonzero temperature
• The gradient flow formulation of the electroweak Hamiltonian
• Renormalon effect of quasi-PDF in gradient flow formalism
• One-loop matching of the LEFT to the QCD gradient flow
• Accessing the Gluon Momentum Fraction of Nucleons through the Gradient Flow
• Single static-quark system above $T_c$ investigated by energy-momentum tensor in SU(3) Yang-Mills theory