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Selected results on renormalization and O(a) improvement

• Andrea Shindler (Michigan State University, East Lansing/US)

Room: Aula Renzo Leonardi

The gradient flow formulation of the electroweak Hamiltonian

• Fabian Lange (Karlsruhe Institute of Technology)

Room: Aula Renzo Leonardi

Welcome ECT* director Gert Aarts Room: Aula Renzo Leonardi

Using Gradient Flow to renormalise Matrix Elements for $B$ Meson Mixing and Lifetimes

• Matthew Black (University Siegen)

Room: Aula Renzo Leonardi Neutral $B$ meson mixing and $B$ meson lifetimes are theory-side parametrised in terms of $\Delta B=2$ and 0 four-quark operators which can be determined by calculating weak decay matrix elements using lattice QCD. While calculations of $\Delta B=2$ mixing matrix elements are standard, matrix elements with $\Delta B=0$ for extracting lifetimes suffer from complications in standard renormalisation procedures. Here dimension-6 four-quark operators mix with operators of lower mass dimension using standard renormalisation procedures and, moreover, quark-line disconnected diagrams contribute. We present work detailing the idea to use fermionic gradient flow to non-perturbatively renormalise $\Delta B=0,2$ matrix elements, later to be combined with perturbative input in order to develop renormalisation+matching-to-$\overline{\rm MS}$ procedures for these operators. The well-studied $\Delta B=2$ matrix elements governing $B$ mixing are first considered to test and validate the method before turning the focus to the quark-line connected $\Delta B=0$ matrix elements.

The Chromomagnetic Dipole Operator in the Gradient Flow

• Janosch Borgulat (RWTH Aachen)

Room: Aula Renzo Leonardi The baryon asymmetry of the universe requires sources of CP-violation beyond those predicted by the SM. At the same time, experimental constraints on the neutron electric dipole moment leave a large window for CP-violating contributions beyond the SM. Such contributions can be described by CP-violating effective interactions at hadronic energies in QCD. Because of confinement, these contributions cannot be computed perturbatively. However, they are accessible to lattice simulations. These, on the other hand, suffer from power divergences, leading to a mixing of operators with different mass dimension. This problem can be circumvented by using the gradient flow. The mixing matrix translating between regular and flowed effective operators in the small flow-time limit is accessible to perturbative calculations. In our work, we study the mixing of the flowed chromomagnetic operator with operators up to mass dimension five and compute their renormalized mixing matrix through next-to-next-to-leading order.

Gradient flow and topological properties of Quantum Chromodynamics

• Andrey Kotov

Room: Aula Renzo Leonardi

Gradient flow exact renormalization group

• Hiroshi Suzuki

Room: Aula Renzo Leonardi

Gradient Flow and Exact Renormalization Group

• Andrea Carosso (The George Washington University)

Room: Aula Renzo Leonardi

The strong CP problem revisited using the gradient flow

• Gerrit Schierholz (DESY)

Room: Aula Renzo Leonardi

From the chiral anomaly to the gradient-flow expression for the topological susceptibility

• Martin Lüscher (CERN)

Room: Aula Renzo Leonardi

Heavy quark diffusion with gradient flow

• Viljami Leino (Johannes Gutenberg Universität Mainz)

Room: Aula Renzo Leonardi

Gradient flow in nonrelativistic effective field theories

• Nora Brambilla (TU München, Germany)

Room: Aula Renzo Leonardi

QCD Static force from the lattice with gradient flow

• Julian Mayer-Steudte (Technical University Munich)

Room: Aula Renzo Leonardi Non-perturbative static force measurements on the lattice can be used to extract the QCD scale $\Lambda_\mathrm{QCD}$ by comparison to perturbative results. We measure the static force on the lattice directly. The corresponding observable consists of a Wilson loop with a discretized $E$-field insertion in one of the temporal Wilson lines. This causes discretization effects, which have to be considered in an additional $Z_E$ factor. We use gradient flow to improve the signal to noise ratio, to renormalize the $E$-field insertion, and to perform proper continuum limits. Our final numerical results can be compared to perturbative equations, and observations regarding the renormalization property of gradient flow for observables with field strength components insertions, which are needed for NREFTs, can be obtained.

Selected aspects of the gradient flow in perturbation theory

• Robert Harlander (Aachen University, Germany)

Room: Aula Renzo Leonardi

A novel nonperturbative renormalization scheme based on gradient flow

• Anna Hasenfratz (University of Colorado, Boulder, United States)

Room: Aula Renzo Leonardi

Fixed point and anomalous dimensions in a Composite Higgs theory

• Benjamin Svetitsky (Tel Aviv University)

Room: Aula Renzo Leonardi We have applied the gradient flow to an SU(4) gauge theory with two sets of fermions in separate gauge representations. We have a clean result for the beta function of the theory up to and beyond an infrared fixed point. Using the fermion GF we have obtained anomalous dimensions for mesonic operators and for the chimera operators that are needed for top quark mixing. We were able to reach strong couplings thanks to our use of Pauli-Villars fields to regulate short-distance fluctuations.

On the approach of smeared and gradient flow observables to the continuum llimit

• Rainer Sommer (DESY & Humboldt University)

Room: Aula Renzo Leonardi

QCD static force in gradient flow

• Xiangpeng Wang (Technical University of Munich)

Room: Aula Renzo Leonardi

Toward new gradient flow based lattice determination of the strong QCD coupling at the Z-pole

• Julius Kuti (U.C. San Diego)

Room: Aula Renzo Leonardi A lattice implementation is described for the beta-function defined over infinite Euclidean space-time in the continuum. It is based on scale changes of the renormalized gauge coupling generated by infinitesimal or finite steps on the gradient flow. Harlander and Neumann calculated in this scheme the three-loop approximation to the continuum beta-function. Our goal is the nonperturbative lattice implementation of the scheme with matching to the three-loop results at weak coupling as we work toward the determination of the strong QCD coupling at the Z-pole. First test results are discussed in the Yang-Mills gauge theory without dynamical fermions and in multi-flavor QCD with massless femions.

Lambda-parameter of the SU(3) Yang-Mills theory from the continuous beta-function

• Curtis Peterson (University of Colorado Boulder)

Room: Aula Renzo Leonardi

Use of the gradient flow in matching the QED 2+1 Hamiltonian and Lagrangian

• Simone Romiti (Uni-Bonn)

Room: Aula Renzo Leonardi

Studying the Vacuum structure of Yang-Mills using the gradient flow

• Ivan Soler (Friedrich-Schiller University of Jena)

Room: Aula Renzo Leonardi

Gradient Flow and Machine Learning

• Luigi Del Debbio (The University of Edinburgh)

Room: Aula Renzo Leonardi

Computation of relativistic corrections to the static potential from generalized Wilson loops at finite flow time

• Michael Eichberg

Room: Aula Renzo Leonardi