Running of the Schroedinger functional coupling with four massless flavours

Sommer, Rainer; Tekin, Fatih; Wolff, Ulli

doi:10.22323/1.105.0241

Cited by 3 publications

(3 citation statements)

References 35 publications

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“…The full evolution runs almost parallel to the two-loop evolution. Similar results have been obtained in full QCD with N f = 2, 3, 4 dynamical quarks [19,20,21]. Based on the results described above, one can state, though a mathematically rigorous proof is yet lacking, that QCD is in the confining phase over the entire range of coupling from zero to infinity.…”

Section: Continuum Limitsupporting

confidence: 72%

Kenneth Wilson and Lattice QCD

Ukawa

2015

J Stat Phys

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We discuss the physics and computation of lattice QCD, a spacetime lattice formulation of quantum chromodynamics, and Kenneth Wilson's seminal role in its development. We start with the fundamental issue of confinement of quarks in the theory of the strong interactions, and discuss how lattice QCD provides a framework for understanding this phenomenon. A conceptual issue with lattice QCD is a conflict of space-time lattice with chiral symmetry of quarks. We discuss how this problem is resolved. Since lattice QCD is a non-linear quantum dynamical system with infinite degrees of freedom, quantities which are analytically calculable are limited. On the other hand, it provides an ideal case of massively parallel numerical computations. We review the long and distinguished history of parallel-architecture supercomputers designed and built for lattice QCD. We discuss algorithmic developments, in particular the difficulties posed by the fermionic nature of quarks, and their resolution. The triad of efforts toward better understanding of physics, better algorithms, and more powerful supercomputers have produced major breakthroughs in our understanding of the strong interactions. We review the salient results of this effort in understanding the hadron spectrum, the Cabibbo-Kobayashi-Maskawa matrix elements and CP violation, and quark-gluon plasma at high temperatures. We conclude with a brief summary and a future perspective.

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Section: Continuum Limitsupporting

confidence: 72%

Kenneth Wilson and Lattice QCD

Ukawa

2015

J Stat Phys

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“…Over the years the SF couplings have been widely employed in step-scaling studies [42,9,34,56,8], and recently their perturbative behaviour has been carefully investigated in the context of determining the Λ-parameter of QCD to a few per-cent accuracy. From these studies, we expect the matching of the SF schemes with perturbation theory to be quantitatively much better than what we observed above for the GF schemes.…”

Section: Non-perturbative Matching To the Sf Schemementioning

confidence: 99%

The gradient flow coupling at high-energy and the scale of SU(3) Yang–Mills theory

Brida

Ramos

2019

Eur. Phys. J. C

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Using finite size scaling techniques and a renormalization scheme based on the Gradient Flow, we determine non-perturbatively the β-function of the SU (3) Yang-Mills theory for a range of renormalized couplingsḡ 2 ∼ 1 − 12. We perform a detailed study of the matching with the asymptotic NNLO perturbative behavior at high-energy, with our non-perturbative data showing a significant deviation from the perturbative prediction down toḡ 2 ∼ 1. We conclude that schemes based on the Gradient Flow are not competitive to match with the asymptotic perturbative behavior, even when the NNLO expansion of the β-function is known. On the other hand, we show that matching non-perturbatively the Gradient Flow to the Schrödinger Functional scheme allows us to make safe contact with perturbation theory with full control on truncation errors. This strategy allows us to obtain a precise determination of the Λ-parameter of the SU (3) Yang-Mills theory in units of a reference hadronic scale ( √ 8t 0 Λ MS = 0.6227 (98)), showing that a precision on the QCD coupling below 0.5% per-cent can be achieved using these techniques. References 512 / 55 1 We note while passing that, at present, the perturbative β-function is most accurately known in the MS scheme of dimensional regularization, where the b k -coefficients have been computed up to k = 4 [23,24,25,26,27]. Other specific cases will be presented in detail below.2 In the following we shall loosely refer to (RG invariant) low-energy scales of the SU (3) Yang-Mills theory as "hadronic" scales/quantities, although strictly speaking there are no hadrons in this theory. Popular examples of lowenergy scales are, for instance, the energies composing the spectrum of the theory, the distance r0 obtained from the potential between two static quarks [28], and the gradient flow time t0 [11]. We will come back to some of these in later sections.

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“…All these effects are currently analyzed and steps are taken to minimize their impact. Calculations that include both isospin breaking and EM are under way [32,33,34,35], as are calculations with dynamical charm quarks [35,36,37,38].…”

Section: Continuum Limit and Autocorrelationsmentioning

confidence: 99%

Uncertainty quantification in lattice QCD calculations for nuclear physics

Beane

Detmold

Orginos

et al. 2015

J. Phys. G: Nucl. Part. Phys.

103

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The numerical technique of Lattice QCD holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong interactions, quantum chromodynamics. A distinguishing, and thus far unique, feature of this formulation is that all of the associated uncertainties, both statistical and systematic can, in principle, be systematically reduced to any desired precision with sufficient computational and human resources. We review the sources of uncertainty inherent in Lattice QCD calculations for nuclear physics, and discuss how each is quantified in current efforts.

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Running of the Schroedinger functional coupling with four massless flavours

Cited by 3 publications

References 35 publications

Kenneth Wilson and Lattice QCD

Kenneth Wilson and Lattice QCD

The gradient flow coupling at high-energy and the scale of SU(3) Yang–Mills theory

Uncertainty quantification in lattice QCD calculations for nuclear physics

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