The Gradient Flow in QCD and other Strongly Coupled Field Theories

Europe/Rome
Aula Renzo Leonardi (ECT*)

Aula Renzo Leonardi

ECT*

Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
Anna Hasenfratz (University of Colorado, Boulder, United States), Christopher Monahan (William & Mary), Oliver Witzel (Siegen University, Germany), Robert Harlander (Aachen University, Germany)
Description

Abstract

The gradient flow field transformation is a continuous smoothing transformation that removes ultraviolet fluctuations. It can serve as a tool to renormalize quantum field theories, allowing numerical studies of strongly coupled systems. The flow has been used extensively in lattice gauge theory calculations, both in QCD and in beyond  the  standard  model  settings  for  applications including scale setting, the determination of the running coupling constant and the corresponding renormalization group beta function, and the topological structure of the vacuum. Many of the newly emerging applications of the gradient flow depend on the perturbative connection of the gradient flow and continuum renormalization schemes,  requiring  difficult  perturbative  calculations  that match the non-perturbative lattice methods. This workshop will bring together experts in lattice and perturbative QCD to discuss recent progress in the application of the gradient flow, develop common ideas, identify needs and possibilities for the gradient flow and to spark collaborative efforts.

Main Topics

  • Perturbative approach
  • Non-perturbative renormalization
  • Electric dipole moments
  • Flavor physics
  • Conformal systems
  • BSM physics

Key speakers

* Nora Brambilla (Munich) - HQET/NRQCD, high temperature QCD * Luigi DelDebbio (Edinburgh) - Lattice QCD, QCD phenomenology * Partick Fritsch (Dublin) - Lattice QCD *  Pilar  Hernandez (Valencia) - BSM models, perturbative QCD * Fabian Lange (Karlsruhe) - High order perturbation theory [confirmed] * Maria-Paola Lombardo (INFN) - HQET/NRQCD, high temperature QCD * Julius Kuti (San Diego) - BSM theories on the lattice * Tobias Neumann (BNL) - High order perturbation theory * Daniel Nogradi (Budapest) - Lattice QCD, BSM models on the lattice * Antonio Rago (Plymouth, CERN) - Lattice QCD, BSM models on the lattice * Alberto Ramos (Valencia) - Lattice QCD * Kari Rummakainen (Helsinki) - BSM models on the lattice * Andrea Shindler (Michigan State University) - Lattice QCD, QCD phenomenology [confirmed] * Gerrit Schierholz (DESY) – Lattice QCD, QCD phenomenology [confirmed] * Stefan Sint (Trinity College Dublin) - Lattice QCD * Hiroshi Suzuki (Fukuoka) - Lattice QCD, BSM models on the lattice

Organizing Committee

Christopher Monahan (William & Mary, United States)
Robert Harlander (Aachen University, Germany)
Anna Hasenfratz (University of Colorado, Boulder, United States)
Oliver Witzel (Siegen University, Germany)

                       

Participants
  • Andrea Carosso
  • Andrea Shindler
  • Andrey Kotov
  • Anna Hasenfratz
  • Benjamin Svetitsky
  • Christopher Monahan
  • Curtis Peterson
  • Fabian Lange
  • Gerrit Schierholz
  • Ivan Soler
  • Janosch Borgulat
  • Jonas Kohnen
  • Julian Mayer-Steudte
  • Julius Kuti
  • Luigi Del Debbio
  • Martin Lüscher
  • Matthew Black
  • Michael Eichberg
  • Nora Brambilla
  • Oliver Witzel
  • Rainer Sommer
  • Robert Harlander
  • Simone Romiti
  • Stefan Sint
  • Viljami Leino
  • Xiangpeng Wang
  • Zeno Kordov
  • +2
Videoconference
The Gradient Flow in QCD ...
Zoom Meeting ID
81026694797
Host
Michela Chiste'
Zoom URL
    • 1
      Staff | Registration Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 09:30
      Welcome coffee/tea Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 2
      Selected results on renormalization and O(a) improvement Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Andrea Shindler (Michigan State University, East Lansing/US)
    • 3
      The gradient flow formulation of the electroweak Hamiltonian Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Fabian Lange (Karlsruhe Institute of Technology)
    • 12:00
      Lunch Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 4
      Welcome ECT* director Gert Aarts Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 5
      Using Gradient Flow to renormalise Matrix Elements for $B$ Meson Mixing and Lifetimes Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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.

      Speaker: Matthew Black (University Siegen)
    • 6
      The Chromomagnetic Dipole Operator in the Gradient Flow Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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.

      Speaker: Janosch Borgulat (RWTH Aachen)
    • Discussion Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00
      Afternoon break Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 7
      Gradient flow and topological properties of Quantum Chromodynamics Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Andrey Kotov
    • 19:30
      Welcome Pizza Dinner ANTICO-POZZO RISTORANTE & PIZZA

      ANTICO-POZZO RISTORANTE & PIZZA

      Vicolo della S.A.T., 6 - 38122 - TRENTO
    • 8
      Gradient flow exact renormalization group Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Prof. Hiroshi Suzuki
    • 9
      Gradient Flow and Exact Renormalization Group Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Andrea Carosso (The George Washington University)
    • 10:30
      Morning break Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 10
      The strong CP problem revisited using the gradient flow Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Gerrit Schierholz (DESY)
    • 12:00
      Lunch Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 11
      From the chiral anomaly to the gradient-flow expression for the topological susceptibility Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Martin Lüscher (CERN)
    • Discussion Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00
      Afternoon break Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 12
      Heavy quark diffusion with gradient flow Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Viljami Leino (Johannes Gutenberg Universität Mainz)
    • 13
      Gradient flow in nonrelativistic effective field theories Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Nora Brambilla (TU München, Germany)
    • 14
      QCD Static force from the lattice with gradient flow Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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.

      Speaker: Julian Mayer-Steudte (Technical University Munich)
    • 10:30
      Morning break Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 15
      Selected aspects of the gradient flow in perturbation theory Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Robert Harlander (Aachen University, Germany)
    • 12:00
      Lunch Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16
      A novel nonperturbative renormalization scheme based on gradient flow Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Anna Hasenfratz (University of Colorado, Boulder, United States)
    • Discussion Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00
      Afternoon break Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 17
      Fixed point and anomalous dimensions in a Composite Higgs theory Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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.

      Speaker: Benjamin Svetitsky (Tel Aviv University)
    • 18
      On the approach of smeared and gradient flow observables to the continuum llimit Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Rainer Sommer (DESY & Humboldt University)
    • 19
      QCD static force in gradient flow Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Xiangpeng Wang (Technical University of Munich)
    • 10:30
      Morning break Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 20
      Toward new gradient flow based lattice determination of the strong QCD coupling at the Z-pole Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)

      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.

      Speaker: Julius Kuti (U.C. San Diego)
    • 12:00
      Lunch Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 21
      Lambda-parameter of the SU(3) Yang-Mills theory from the continuous beta-function Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Curtis Peterson (University of Colorado Boulder)
    • 22
      Use of the gradient flow in matching the QED 2+1 Hamiltonian and Lagrangian Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Simone Romiti (Uni-Bonn)
    • Discussion Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 16:00
      Afternoon break Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 23
      Studying the Vacuum structure of Yang-Mills using the gradient flow Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Ivan Soler (Friedrich-Schiller University of Jena)
    • 19:30
      Social dinner Ristorante Orso Grigio

      Ristorante Orso Grigio

    • 24
      Gradient Flow and Machine Learning Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Luigi Del Debbio (The University of Edinburgh)
    • 25
      Computation of relativistic corrections to the static potential from generalized Wilson loops at finite flow time Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
      Speaker: Michael Eichberg
    • 10:30
      Morning break Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • Discussion Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)
    • 12:00
      Lunch Aula Renzo Leonardi

      Aula Renzo Leonardi

      ECT*

      Strada delle Tabarelle 286, I-38123 Villazzano (Trento)