The twisted gradient flow running coupling in SU(3): a non-perturbative determination

Bribian, Eduardo I.; Pérez, Margarita Garcı́a; Ramos, Alberto

doi:10.48550/arxiv.2001.03735

Cited by 3 publications

(5 citation statements)

References 19 publications

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“…For instance, the GFcoupling with twisted boundary conditions explored in refs. [102,127,128,129] is promising. Differently from the SF case it enjoys full translational invariance and yet its perturbative expansion in finite volume appears feasible [130].…”

Section: Summary and Miscellaneous Remarksmentioning

confidence: 99%

Past, present, and future of precision determinations of the QCD coupling from lattice QCD

Brida

2021

Eur. Phys. J. A

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Non-perturbative scale-dependent renormalization problems are ubiquitous in lattice QCD as they enter many relevant phenomenological applications. They require solving non-perturbatively the renormalization group equations for the QCD parameters and matrix elements of interest in order to relate their non-perturbative determinations at low energy to their high-energy counterparts needed for phenomenology. Bridging the large energy separation between the hadronic and perturbative regimes of QCD, however, is a notoriously difficult task. In this contribution we focus on the case of the QCD coupling. We critically address the common challenges that state-of-the-art lattice determinations have to face in order to be significantly improved. In addition, we review a novel strategy that has been recently put forward in order to solve this non-perturbative renormalization problem and discuss its implications for future precision determinations. The new ideas exploit the decoupling of heavy quarks to match $${N_{\mathrm{f}}}$$ N f -flavor QCD and the pure Yang–Mills theory. Through this matching the computation of the non-perturbative running of the coupling in QCD can be shifted to the computationally much easier to solve pure-gauge theory. We shall present results for the determination of the $$\varLambda $$ Λ -parameter of $${N_{\mathrm{f}}}=3$$ N f = 3 -flavor QCD where this strategy has been applied and proven successful. The results demonstrate that these techniques have the potential to unlock unprecedented precision determinations of the QCD coupling from the lattice. The ideas are moreover quite general and can be considered to solve other non-perturbative renormalization problems.

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Section: Summary and Miscellaneous Remarksmentioning

confidence: 99%

Past, present, and future of precision determinations of the QCD coupling from lattice QCD

Brida

2021

Eur. Phys. J. A

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“…Finally, in blue, we have data with twisted boundary condition on an asymmetric lattice [30]. In this case the simulations are done on volumes L 2 × (L/3) 2 (see [22] for the theoretical motivation behind this particular geometry).…”

Section: Statistical Uncertaintiesmentioning

confidence: 99%

“…Here we see that Orange symbols are for the "magnetic" definition of the GF coupling; black symbols are for the average of "magnetic" and "electric" definitions of the GF coupling; the blue symbols are from the dataset of ref. [30].…”

Section: Scaling Violations Inmentioning

confidence: 99%

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An analysis of systematic effects in finite size scaling studies using the gradient flow

Nada,

Ramos

2020

Preprint

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We propose a new strategy for the determination of the step scaling function σ(u) in finite size scaling studies using the Gradient Flow. In this approach the determination of σ(u) is broken in two pieces: a change of the flow time at fixed physical size, and a change of the size of the system at fixed flow time. Using both perturbative arguments and a set of simulations in the pure gauge theory we show that this approach leads to a better control over the continuum extrapolations. Following this new proposal we determine the running coupling at high energies in the pure gauge theory and re-examine the determination of the Λ-parameter, with special care on the perturbative truncation uncertainties. Contents 3 Statistical uncertainties 114 The high energy regime of Yang-Mills revisited 13 4.1 The continuum limit of J 1 and J 2 13 4.1.

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“…In this work we will explore numerically a particular finite volume renormalization scheme, first introduced in [14,15,16] based on three ingredients. First, we choose a non-perturbative coupling based on the gradient flow [17,18,19,20] (see also [21] for a review).…”

Section: Introductionmentioning

confidence: 99%

Memory efficient finite volume schemes with twisted boundary conditions

et al. 2021

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In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N) gauge theories consists on a hypercubic box of size $$l^2 \times (Nl)^2$$ l 2 × ( N l ) 2 , a choice motivated by the study of volume independence in large N gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the $$\Lambda $$ Λ parameter in the SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value $$\Lambda _{\overline{\mathrm{MS}}}\sqrt{8 t_0} =0.603(17)$$ Λ MS ¯ 8 t 0 = 0.603 ( 17 ) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large N applications, is discussed in detail.

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The twisted gradient flow running coupling in SU(3): a non-perturbative determination

Cited by 3 publications

References 19 publications

Past, present, and future of precision determinations of the QCD coupling from lattice QCD

Past, present, and future of precision determinations of the QCD coupling from lattice QCD

An analysis of systematic effects in finite size scaling studies using the gradient flow

Memory efficient finite volume schemes with twisted boundary conditions

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