The Gradient Flow in QCD and other Strongly Coupled Field Theories

20 Mar 2023, 08:10 → 24 Mar 2023, 18:00 Europe/Rome

Aula Renzo Leonardi (ECT*)

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

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)

                       

Poster Event

Monday 20 March

1 Staff | Registration

Coffee Time (Your Story) (4).pdf

09:30 Welcome coffee/tea

2 Selected results on renormalization and O(a) improvement

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

3 The gradient flow formulation of the electroweak Hamiltonian

Speaker: Fabian Lange (Karlsruhe Institute of Technology)

gf-workshop-lange.pdf

12:00 Lunch

4 Welcome ECT* director Gert Aarts

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

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)

TrentoFermionFlow.pdf

6 The Chromomagnetic Dipole Operator in the Gradient Flow

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)

GF_Workshop_MDM.pdf

Discussion

16:00 Afternoon break

7 Gradient flow and topological properties of Quantum Chromodynamics

Speaker: Andrey Kotov

GF_kotov_2023.pdf

19:30 Welcome Pizza Dinner

Tuesday 21 March

8 Gradient flow exact renormalization group

Speaker: Prof. Hiroshi Suzuki

ECTstar_suzuki.pdf

9 Gradient Flow and Exact Renormalization Group

Speaker: Andrea Carosso (The George Washington University)

Trento_GFRG_Talk_Mar2023 (2).pdf

10:30 Morning break

10 The strong CP problem revisited using the gradient flow

Speaker: Gerrit Schierholz (DESY)

Schierholz_ectGRAD.pdf

12:00 Lunch

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

Speaker: Martin Lüscher (CERN)

trento23.pdf

Discussion

16:00 Afternoon break

12 Heavy quark diffusion with gradient flow

Speaker: Viljami Leino (Johannes Gutenberg Universität Mainz)

Leino_trento23.pdf

Wednesday 22 March

13 Gradient flow in nonrelativistic effective field theories

Speaker: Nora Brambilla (TU München, Germany)

GradientflowECT2023Brambilla.pdf

14 QCD Static force from the lattice with gradient flow

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)

main.pdf

10:30 Morning break

15 Selected aspects of the gradient flow in perturbation theory

Speaker: Robert Harlander (Aachen University, Germany)

ECTstar_Trento.pdf

12:00 Lunch

16 A novel nonperturbative renormalization scheme based on gradient flow

Speaker: Anna Hasenfratz (University of Colorado, Boulder, United States)

Trento.pdf

Discussion

16:00 Afternoon break

17 Fixed point and anomalous dimensions in a Composite Higgs theory

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)

Svetitsky_Trento23_final.pdf

Thursday 23 March

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

Speaker: Rainer Sommer (DESY & Humboldt University)

Smearing-Trento.pdf

19 QCD static force in gradient flow

Speaker: Xiangpeng Wang (Technical University of Munich)

staticforce.pdf

10:30 Morning break

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

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)

jkTrento2023.pdf

12:00 Lunch

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

Speaker: Curtis Peterson (University of Colorado Boulder)

ct_peterson_nf0_btfntn_and_lmbda_param_gf_2023.pdf

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

Speaker: Simone Romiti (Uni-Bonn)

main.pdf

Discussion

16:00 Afternoon break

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

Speaker: Ivan Soler (Friedrich-Schiller University of Jena)

annihilation.gif

Instantons_gradient_flow.pdf

19:30 Social dinner

Friday 24 March

24 Gradient Flow and Machine Learning

Speaker: Luigi Del Debbio (The University of Edinburgh)

Del Debbio_trento23.pdf

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

Speaker: Michael Eichberg

Slides_Potential_Trento.pdf

10:30 Morning break

Discussion

12:00 Lunch