Related papers: The two-loop energy-momentum tensor within the gra…
Recently, Harlander et al.\ [Eur.\ Phys.\ J.\ C {\bf 78}, 944 (2018)] have computed the two-loop order (i.e., NNLO) coefficients in the gradient-flow representation of the energy--momentum tensor (EMT) in vector-like gauge theories. In this…
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…
The non-perturbative computation of the energy-momentum tensor can be used to study the scaling behaviour of strongly coupled quantum field theories. The Wilson flow is an essential tool to find a meaningful formulation of the…
We analyze bulk thermodynamics and correlation functions of the energy-momentum tensor in pure Yang-Mills gauge theory using the energy-momentum tensor defined by the gradient flow and small flow time expansion. Our results on thermodynamic…
Various results for higher-order perturbative calculations in the gradient-flow formalism are reviewed, including the gradient-flow beta function and the small-flow-time expansion of the hadronic vacuum polarization and the energy-momentum…
The gradient flow in QCD is treated perturbatively through next-to-next-to-leading order in the strong coupling constant. The evaluation of the relevant momentum and flow-time integrals is described, including various means of validation.…
The chromo-magnetic dipole operator is expressed in terms of operators at finite flow time in the gradient-flow formalism. The matching coefficients are evaluated through next-to-next-to-leading order QCD.
The effective electroweak Hamiltonian in the gradient-flow formalism is constructed for the current-current operators through next-to-next-to-leading order QCD. The results are presented for two common choices of the operator basis. This…
The product of gauge fields generated by the Yang-Mills gradient flow for positive flow times does not exhibit the coincidence-point singularity and a local product is thus independent of the regularization. Such a local product can…
A non-perturbative renormalisation prescription for the energy-momentum tensor, based on space-time symmetries along the Wilson flow, has been proposed recently in the context of 4-dimensional gauge theories. We extend this construction to…
In this paper we focus on energy flows in simple quantum systems. This is achieved by concentrating on the quantum Hamilton-Jacobi equation. We show how this equation appears in the standard quantum formalism in essentially three different…
A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for…
The energy gradient theory was proposed in our previous studies. The mechanism of flow instability is very different in shear driven flows from pressure driven flows. In present paper, the relationship for the energy variation, work done,…
The gradient-flow formalism proves to be a useful tool in lattice calculations of quantum chromodynamics. For example, it can be used as a scheme to renormalize composite operators by inverting the short-flow-time expansion of the…
We propose a gravitational energy-momentum tensor of the general relativity obtained using Noethers theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the gravitational energy-momentum…
Local products of fields deformed by the so-called Yang--Mills gradient flow become renormalized composite operators. This fact has been utilized to construct a correctly normalized conserved energy--momentum tensor in the lattice…
The gradient-flow formalism provides a framework for the direct determination of moments of parton distribution functions (PDFs) from lattice QCD calculations. Their conversion from the gradient-flow scheme to $\overline{\text{MS}}$…
We propose and analyze numerical schemes for the gradient flow of $Q$-tensor with the quasi-entropy. The quasi-entropy is a strictly convex, rotationally invariant elementary function, giving a singular potential constraining the…
A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links…
We use gradient flow to compute the static force based on a Wilson loop with a chromoelectric field insertion. The result can be compared on one hand to the static force from the numerical derivative of the lattice static energy, and on the…