Numerical Stochastic Perturbation Theory and the Gradient Flow

Brida, Mattia Dalla; Hesse, Dirk

doi:10.48550/arxiv.1311.3936

Cited by 5 publications

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“…to understand the structure of cutoff effects), but also perturbative computations of flow quantities are usually tedious. The application of numerical stochastic perturbation theory for flow quantities [41] is an interesting idea. The use of the gradient flow to extract matrix elements non-perturbatively with a simplified mixing pattern has also been considered recently [42], and shows a promising future.…”

Section: Discussionmentioning

confidence: 99%

Wilson flow and renormalization

Ramos¹

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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Section: Discussionmentioning

confidence: 99%

Wilson flow and renormalization

Ramos¹

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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“…On a finite volume the computation is even more involved (see [38]). The two-loop relation requires substantial effort [17,18], and for our particular choice of boundary conditions the result relies on novel methods [39,40,41,18] within the framework of Numerical Stochastic Perturbation Theory (NSPT). The results are [18]:…”

Section: Boundary Conditions and Coupling Definitionsmentioning

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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“…We have derived a convenient representation of the gauge field propagator using the set-up proposed in [8], which allows us to apply an orbifold reflection principle. We anticipate that the gauge propagator representation will be very useful in future perturbative computations which might be needed to complement a non-diagrammatic numerical approach [12,13].…”

Section: Discussionmentioning

confidence: 99%

Perturbative O$(a^2)$ effects in gradient flow couplings with SF and SF-open boundary conditions

Rubeo¹,

Sint²

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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The gradient flow provides a new class of renormalized observables which can be measured with high precision in lattice simulations. In principle this allows for many interesting applications to renormalization and improvement problems. In practice, however, such applications are made difficult by the rather large cutoff effects found in many gradient flow observables. At lowest order of perturbation theory we here study the leading cutoff effects in a finite volume gradient flow coupling with SF and SF-open boundary conditions. We confirm that O(a 2 ) Symanzik improvement is achieved at tree-level, provided the action, observable and the flow are O(a 2 ) improved. O(a 2 ) effects from the time boundaries are found to be absent at this order, both with SF and SF-open boundary conditions. For the calculation we have used a convenient representation of the free gauge field propagator at finite flow times which follows from a recently

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Numerical Stochastic Perturbation Theory and the Gradient Flow

Cited by 5 publications

References 0 publications

Wilson flow and renormalization

Wilson flow and renormalization

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

Perturbative O$(a^2)$ effects in gradient flow couplings with SF and SF-open boundary conditions

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