SMD-based numerical stochastic perturbation theory

Brida, Mattia Dalla; Lüscher, Martin

doi:10.1140/epjc/s10052-017-4839-0

Cited by 29 publications

(25 citation statements)

References 38 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%

“…There are also other challenges if one wants to use these couplings for a precise determination of the strong coupling. First, the known perturbative coefficients of the β-function show bad convergence [17,18]. This implies that even simple estimates of the theoretical perturbative uncertainties in the extraction of α s based on GF couplings, even at energies as high as the electroweak scale, are about half a percent.…”

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confidence: 99%

“…In fact it seems that the c-dependence of b GF,e 2 is quite mild, and its value is close to the corresponding infinite volume one also for values of c as large as 0.4 (cf. ref [18]…”

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confidence: 99%

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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%

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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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“…For completeness we mention a recently developed new formulations of NSPT, where the Langevin equation is replaced by an stochastic molecular dynamics (SMD) algorithm [34,35]. The SMD based NSPT has potential advantages over the Langevin formulation, like smaller autocorrelation times.…”

Section: Stochastic Quantization On the Latticementioning

confidence: 99%

Universal renormalons in principal chiral models

Bruckmann

Puhr

2020

Phys. Rev. D

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Perturbative expansions in many physical systems yield 'only' asymptotic series which are not even Borel resummable. Interestingly, the corresponding ambiguities point to nonperturbative physics. We numerically verify this renormalon mechanism for the first time in two-dimensional sigma models, that, like four-dimensional gauge theories, are asymptotically free and generate a strong scale through dimensional transmutation. We perturbatively expand the energy through a numerical version of stochastic quantization. In contrast to the first energy coefficients, the high order coefficients are independent on the rank of the model. Technically, they require a sophisticated analysis of finite volume effects and the continuum limit of the discretized model. Although the individual coefficients do not grow factorially (yet), but rather decrease strongly, the ratio of consecutive coefficients clearly obey the renormalon asymptotics.

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“…The openQ*D code uses the Fast Fourier Transform (FFT) algorithm to contruct π(p, µ) from π(x, µ) and vice versa. The FFT is implemented in the module dft which is an adaptation of the corresponding module in the NSPT-1.4 code written by Mattia Dalla Brida and Martin Lüscher [25]. 1.98000000 e -03 7.62000000 e +00 mu 0.00000000 e +00 delta 5 .…”

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openQ*D code: a versatile tool for QCD+QED simulations

et al. 2020

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We present the open-source package openQ*D-1.0 [1], which has been primarily, but not uniquely, designed to perform lattice simulations of QCD+QED and QCD, with and without C * boundary conditions, and O(a) improved Wilson fermions. The use of C * boundary conditions in the spatial direction allows for a local and gauge-invariant formulation of QCD+QED in finite volume, and provides a theoretically clean setup to calculate isospin-breaking and radiative corrections to hadronic observables from first principles. The openQ*D code is based on openQCD-1.6 [2] and NSPT-1.4 [3]. In particular it inherits from openQCD-1.6 several core features, e.g. the highly optimized Dirac operator, the locally deflated solver, the frequency splitting for the RHMC, or the 4th order OMF integrator.

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SMD-based numerical stochastic perturbation theory

Cited by 29 publications

References 38 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

Universal renormalons in principal chiral models

openQ*D code: a versatile tool for QCD+QED simulations

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