Zürich Gradient Flow Workshop 2025

12 Feb 2025, 08:30 → 14 Feb 2025, 17:50 Europe/Zurich

Y36-K08 (University of Zürich)

The Zürich Gradient Flow Workshop 2025 will take place from Feb. 12 - 14, 2025, at the University of Zürich, Switzerland, with the goal to bring together scientists working actively on non-perturbative and perturbative aspects of the gradient flow.

The gradient flow has been instrumental in a large variety of recent developments in non-perturbative QCD and it plays a crucial role in reaching a better understanding of strong dynamics and to provide input in precision phenomenology studies, searching for physics beyond the Standard Model.

A workshop with a similar theme was last held at the ECT* Center in Trento, Italy, in March 2023: https://indico.ectstar.eu/event/164/overview.

Confirmed speakers:

Alexei Bazavov (Michigan State University)
Martin Beneke (Technische Universität München)
Matthew Black (University of Edinburgh)
Stephan Dürr (University of Wuppertal)
Robert Harlander (RWTH Aachen University)
Anna Hasenfratz (University of Colorado Boulder)
Nikolai Husung (Universidad Autónoma de Madrid)
Viljami Leino (Helmholtz Institute Mainz and Johannes Gutenberg-Universität Mainz)
Julian Mayer-Steudte (Technische Universität München)
Christopher Monahan (Colorado College)
Kalman Szabo (Forschungszentrum Jülich)
Andrea Shindler (RWTH Aachen University, LBNL, UC Berkeley)
Hiromasa Takaura (Kyoto University)
Guilherme Telo Rodrigues Catumba (Università degli studi di Milano Bicocca)
Xiangpeng Wang (Technische Universität München)

Important deadlines:

Registration deadline (financial support): December 31, 2024
Hotel block reservations expire: January 10, 2025
Registration deadline (general): January 15, 2025
Abstract submission deadline for contributed talks: January 15, 2025

Organizing committee:

Òscar Lara Crosas (University of Zürich and Paul Scherrer Institut)
Tim Harris (ETH Zürich)
Fabian Lange (University of Zürich and Paul Scherrer Institut)
Peter Stoffer (University of Zürich and Paul Scherrer Institut)

 

This workshop is generously funded by the Pauli Center for Theoretical Studies (ETH and UZH) and the Graduate Campus of the University of Zürich.

zgf2025_poster_v3.pdf

Wednesday 12 February

1 Registration

2 Welcome

ZGFW2025_welcome.pdf

Session 1

3 Perturbative gradient flow at higher orders

Speaker: Robert Harlander (RWTH Aachen University)

Zuerich.pdf

10:00 Coffee Break

Session 2

4 The gradient flow extended to the Standard Model

The Gradient Flow (GF) has shown significant potential for determining operator renormalization matrices in effective field theories. Nevertheless, its application has predominantly focused on pure QCD, limiting its broader applicability, particularly in the context of the Standard Model Effective Field Theory (SMEFT). In this presentation, I will introduce a gradient flow framework for the flavor-preserving Standard Model in the unbroken phase, serving as an initial step toward systematic GF-based calculations of SMEFT operator renormalization. Key results, including flowed wave function renormalizations up to next-to-next-to-leading order, will be discussed.

Speaker: Janosch Borgulat (RWTH Aachen University)

GF-extended-to-the-SM.pdf

5 Two-loop perturbative calculations toward a new approach to quark mass determination using the gradient flow

We propose a new method for quark mass determination utilizing the gradient flow. The matching of a ratio of flowed bilinear operators between the perturbative and lattice results determines the MSbar mass, potentially contributing to a more precise determination. In this talk, we present perturbative results at two loops: semianalytic expressions in the small- and large-m^2 t limits and numerical results over a wide range of m^2 t. We develop a new method to expand loop integrals in m^2 t or 1/(m^2 t), based on the Laplace transform.

Speaker: Hiromasa Takaura (YITP, Kyoto University)

ZurichGF.pdf

6 Quark mass effects in the gradient flow at higher orders in perturbation theory

Calculations in the perturbative approach to the short-flow time expansion of the gradient flow have typically been completed for systems with massless quarks, simplifying computations and allowing for application of the method of projectors. However, processes such as vacuum expectation values can be considered without this method. For example, the condensate of the quark kinetic operator is known to the three loop level in the massless case. It has been suggested by Hiromasa et. al. that the gradient flow with massive quarks can be utilised in a precision determination of the values of the quark masses. Processes such as the flowed quark condensate have already been computed to the two loop level in the small- and large-mass limits. In this talk we discuss current progress in calculating the effect of the full mass dependence numerically up to the three loop level using ftint and to which processes these methods can be applied.

Speaker: Robert Mason (RWTH Aachen University)

Zurich_Talk (12).pdf

12:00 Lunch Break

Session 3

7 Gradient Flow Renormalisation for Meson Mixing and Lifetimes

Fermionic gradient flow in combination with the short flow time expansion provides a renormalisation scheme where hadronic matrix elements on the lattice are evolved along the flow time gradually removing UV divergences.
In this renormalisation scheme certain challenges such as mixing with operators of lower mass dimension are suppressed or shifted to the perturbative part of the procedure, matching e.g. to the $\overline{\rm MS}$ scheme.

We demonstrate our gradient flow renormalisation procedure determining matrix elements of four-quark operators describing neutral meson mixing or meson lifetimes.
While meson mixing calculations are well-established on the lattice and serve to validate our procedure, a lattice calculation of matrix elements for heavy meson lifetimes is still outstanding.
Preliminary results for mesons formed of a charm and strange quark are presented and prospects towards determinations for $B$ mesons are given.

Speaker: Matthew Black (University of Edinburgh)

FermionFlow_MB.pdf

8 Short-flow-time expansion of four-quark operators at NNLO QCD

Non-perturbative matrix elements of four-quark operators are essential ingredients for the determination of heavy meson lifetimes. The gradient flow formalism provides a way for their calculation in lattice gauge theory. This requires the knowledge of the coefficients of the short-flow-time expansion of the corresponding operators, which can be calculated in perturbation theory. In this talk, the relevant four-quark operators and the calculation of their short-flow-time expansions through NNLO QCD will be described.

Speaker: Jonas Kohnen (RWTH Aachen University)

SFTX_of_four_quark_operators.pdf

9 Discussion

discussion.pdf

15:30 Coffee Break

Session 4

10 Gradient flow for the strong CP problem and new sources of CP violation

Speaker: Andrea Shindler

Thursday 13 February

Session 5

11 The short-flow-time expansion and its applications

The short-flow-time expansion has proved to be a critical component of the gradient flow toolkit over the last decade. This expansion serves as an operator product expansion that links composite operators at finite flow time with their renormalised counterparts and provides an important bridge between nonperturbative calculations on the lattice and their phenomenological applications. In this talk, I will review the short-flow-time expansion, discuss some of its important applications, and highlight the need for quantitative investigations of the limits of its applicability.

Speaker: Chris Monahan (Colorado College)

monahan_gfzurich_2025.pdf

10:00 Coffee Break

Session 6

12 Scale setting on the (2+1+1)-flavor HISQ ensembles: current status

Speaker: Alexei Bazavov

slides.pdf

13 Gradient flow scales

Speaker: Kalman Szabo

14 Discussion

12:00 Lunch Break

Session 7

15 Universality and cutoff effects of pure gauge theories from gradient flow scales

The approach to the continuum stands as one of the main sources of uncertainty
in lattice studies. Recent investigations revealed complicated functional
forms for the lattice cutoff effects, making continuum extrapolations possibly
very difficult in practice. By using gradient flow scales we study the
continuum scaling of Yang-Mills theories using different lattice gauge actions
at the currently used lattice spacings. We first show how this can be done
using flow observables defined at different scales, and argue that to keep
systematic errors under control the comparison between several lattice actions
is required, together with the use of finer lattices. Moreover, by combining
flow scales with lattice perturbation theory we discuss the difficulty in
controlling the perturbative and scaling corrections in precise determinations
of the $\Lambda$ parameter

Speaker: Guilherme Catumba (Università degli studi di Milano Bicocca)

main.pdf

16 Lattice artifacts of Gradient Flow quantities

The Yang Mills Gradient Flow is frequently used in lattice QCD and lattice pure gauge theory with particular focus on precision scale-setting. Other uses include, e.g., (non-perturbative) operator renormalisation and so called smearing.
Aiming at precision physics, all systematics must be kept under good control. I will focus here on the lattice artifacts relevant when attempting continuum extrapolations of Gradient Flowed quantities. Using the framework of Symanzik Effective Field Theory (SymEFT) we can learn about the asymptotically leading lattice-spacing dependence $a^n[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}$ for a chosen lattice setup, where $\bar{g}(1/a)$ is the running coupling and the $\hat{\Gamma}_i$ are accessible in SymEFT. These results may guide future ansätze for continuum extrapolations and allow to check for severe problems from $\hat{\Gamma}_i\ll 0$. Results for lattice pure gauge theory are discussed and some outlook on full QCD is given.

Speaker: Nikolai Husung

ZürichGF_Husung.pdf

15:00 Coffee Break

Session 8

17 Classically perfect gradient flows

Classically perfect fixed-point lattice actions preserve continuum classical properties while reducing lattice artifacts at the quantum level. They allow the extraction of continuum physics from coarser lattices and hence provide an effective way to overcome the challenges of critical slowing down and topological freezing as the continuum limit is approached. In this talk we show that fixed-point actions can be used to define classically perfect gradient-flow observables which are free of tree-level lattice artifacts to all orders. We demonstrate the effectiveness of this approach using a fixed-point action for four-dimensional SU(3) gauge theory obtained from a machine-learned gauge-covariant convolutional neural network.

Speaker: Urs Wenger

FPA_LGE-CNN_wenger_GFZurich.pdf

18 Stout smearing and Wilson flow in lattice perturbation theory (and beyond)

I present a sketch of the paper arXiv:2406.03493 (published in PRD) by Max Ammer and myself. It gives the expansion of stout smearing and the Wilson flow in lattice perturbation theory to order g_0^3, which is suitable for one-loop calculations. As the Wilson flow is generated by infinitesimal stout smearing steps, the results are related to each other by taking the appropriate limits. This yields a useful recipe for how to apply perturbative stout smearing or Wilson flow to the Feynman rules of a given lattice fermion action. This is illustrated through the self-energies of the clover-improved Wilson and Brillouin fermions. Also the upgrade of the 1-loop calculation of c_{SW} for Wilson and Brillouin fermions to stout smearing or Wilson flow will be briefly discussed. Time permitting, a few words on a non-perturbative calculation of the topological susceptibility with stout smearing and/or gradient flow, together with Gianluca Fuwa, may be added.

Speaker: Stephan Durr (University of Wuppertal)

gradflow_durr.pdf

19 Discussion

20 Dinner Information

ZGFW2025_dinner.pdf

18:30 Workshop Dinner

Friday 14 February

Session 9

21 Gradient-flow step scaling and the renormalization group

Speaker: Anna Hasenfratz

GF_workshop.pdf

10:00 Coffee Break

Session 10

22 Progress on the infinite volume based gradient flow for high precision determination of the $\Lambda_\overline{MS}$ scale of QCD.

We recently introduced and tested the application of the infinite volume based gradient flow for the scale dependent renormalization of the strong coupling. Recent developments of this alternative approach are reported for the high precision determination of the beta-function and the physical scale of the $\Lambda_\overline{MS}$ parameter in QCD with three massless flavors and its Yang-Mills limit.

Speaker: Chik Him Wong

presentation.pdf

23 Off-lightcone Wilson-line operators in gradient flow

Off-lightcone Wilson-line operators are constructed using local operators cononumberected by time-like or space-like Wilson lines, which ensure gauge invariance. Off-lightcone Wilson-line operators have broad applications in various contexts. For instance, space-like Wilson-line operators play a crucial role in determining quasi-distribution functions (quasi-PDFs), while time-like Wilson-line operators are essential for understanding quarkonium decay and production within the potential non-relativistic QCD (pNRQCD) framework.
In this work, we establish a systematic approach for calculating the matching from the gradient-flow scheme to the $\overline{\rm MS}$ scheme in the limit of small flow time for off-lightcone Wilson-line operators. By employing the one-dimensional auxiliary-field formalism, we simplify the matching procedure, reducing it to the matching of local current operators. We provide one-loop level matching coefficients for these local current operators.
For the case of hadronic matrix element related to the quark quasi-PDFs, we show at one-loop level that the finite flow time effect is very small as long as the flow radius is smaller than the physical distance $z$, which is usually satisfied in lattice gradient flow computations.
Applications include lattice gradient flow computations of quark/gluon quasi-PDFs, gluonic correlators related to quarkonium decay and production in pNRQCD, and spin-dependent potentials in terms of chromoelectric and chromomagnetic field insertions into a Wilson loop.

Speaker: Xiangpeng Wang

talk.pdf

24 Discussion

12:00 Lunch Break

Session 11

25 Gradient-flow renormalon subtraction and the hadronic tau decay series

The inconsistency between the fixed-order (FO) and contour-improved (CI) representation of the QCD corrections to the inclusive hadronic tau decay width limits the precision to which the strong coupling can be determined from this process. It has been shown that subtracting the infrared renormalon divergence related to the gluon condensate resolves the discrepancy. We employ the gradient flow to define gauge-invariant regularized operators and to use the corresponding condensates in the operator product expansion. The associated rearrangement of the perturbative series results in automatic renormalon subtraction without the need to determine explicitly the Stokes constants that normalize the divergent asymptotic series. Applying this method to the gluon condensate, we find that the CI series is modified and now agrees with the (unmodified) FO series.

Speaker: M Beneke

zurich.pdf

26 Heavy Quark(onium) transport with GF on the lattice

The dynamics of heavy particles in a strongly coupled plasma is determined by transport coefficients. Especially for heavy quarkonia, the real-time evolution is described by transport coefficients $\kappa$ and $\gamma$.
On the lattice, these transport coefficients can be measured from correlators of chromoelectric fields connected by a Wilson line. Gradient flow is a beneficial tool to measure these correlators, as it both suppresses the uv noise and renormalizes the field strength tensor components. Extra care has to be taken with the remaining divergences.

Speaker: Viljami Leino (Helmholtz Institute Mainz)

esitys.pdf

27 The Static force with gradient flow from the lattice

We measured the static force directly in the continuum limit on the lattice in quenched theory for the first time. A generalized Wilson loop with a chromoelectric field insertion in one of the temporal Wilson lines is the operator that measures the static force directly. However, chromoelectric field insertions converge slowly to the continuum and require an improvement. We use gradient flow to improve the field insertion, to perform the continuum limit at finite flow time followed by a zero-flow-time limit, and to extract $\sqrt{t_0}/r_0$ and $\Lambda_0$. This study serves as a preparation for similar objects with chromo field insertions needed in NREFTs at zero and finite temperatures.

Speaker: Julian Mayer-Steudte (Technical University of Munich)

JulianMayer-Steudte_GFZurich.pdf

15:00 Coffee Break

Session 12

28 Final Discussion

final_discussion.pdf