The gradient flow coupling from numerical stochastic perturbation theory

Brida, Mattia Dalla; Lüscher, Martin

doi:10.22323/1.256.0332

Cited by 6 publications

(5 citation statements)

References 12 publications

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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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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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“…(4.23) and (4.24) correspond to the gluon condensate F µν (x)F µν (x) 8. It might be possible to detect this leading renormalon on R × S 1 by using the stochastic perturbation theory[35][36][37][38][39].…”

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confidence: 99%

Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$

Ishikawa

Morikawa

Nakayama

et al. 2020

Progress of Theoretical and Experimental Physics

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Abstract In the leading order of the large-$N$ approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$ with the $\mathbb{Z}_N$ twisted boundary conditions. In our large-$N$ limit, the combination $\Lambda R$, where $\Lambda$ is the dynamical scale and $R$ is the $S^1$ radius, is kept fixed (we set $\Lambda R\ll1$ so that the perturbative expansion with respect to the coupling constant at the mass scale $1/R$ is meaningful). We extract the perturbative part from the large-$N$ expression of the gluon condensate and obtain the corresponding Borel transform $B(u)$. For $\mathbb{R}\times S^1$, we find that the Borel singularity at $u=2$, which exists in the system on the uncompactified $\mathbb{R}^2$ and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at $u=3/2$ for the compactified space $\mathbb{R}\times S^1$. The semi-classical interpretation of this peculiar singularity is not clear because $u=3/2$ is not dividable by the minimal bion action. It appears that our observation for the system on $\mathbb{R}\times S^1$ prompts reconsideration on the semi-classical bion picture of the infrared renormalon.

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“…Moreover the extrapolations in section 2.2.2 have completely ignored these effects, and our data in fact seem to scale like O(a 2 ) after dropping the coarser lattices. But due to the high precision of our data, these O(a) effects cannot be completely ignored, especially if we take into account the fact that our strategy uses data at large 4 In fact the first two coefficients c (i) 0,1 can be computed with the help of the ki coefficients calculated in [24]: c (1) 0 = 0.1426 (7) , c…”

Section: The Continuum Limit Of J 1 and Jmentioning

confidence: 99%

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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The gradient flow coupling from numerical stochastic perturbation theory

Cited by 6 publications

References 12 publications

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

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

Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$

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

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