Investigation of new methods for numerical stochastic perturbation theory in 
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 theory

Brida, Mattia Dalla; Garofalo, Marco; Kennedy, A.D.

doi:10.1103/physrevd.96.054502

Cited by 10 publications

(7 citation statements)

References 41 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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“…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 idea of studying the convergence properties of a stochastic process order by order after an expansion in the coupling is actually quite general. In this spirit different NSPT schemes can be set up, also based on stochastic differential equations different from Langevin [22,23].…”

Section: Lattice Gauge Theories In Nsptmentioning

confidence: 99%

Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD

2018

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Numerical Stochastic Perturbation Theory (NSPT) allows for perturbative computations in quantum field theory. We present an implementation of NSPT that yields results for high orders in the perturbative expansion of lattice gauge theories coupled to fermions. The zero-momentum mode is removed by imposing twisted boundary conditions; in turn, twisted boundary conditions require us to introduce a smell degree of freedom in order to include fermions in the fundamental representation. As a first application, we compute the critical mass of two flavours of Wilson fermions up to order in a gauge theory. We also implement, for the first time, staggered fermions in NSPT. The residual chiral symmetry of staggered fermions protects the theory from an additive mass renormalisation. We compute the perturbative expansion of the plaquette with two flavours of massless staggered fermions up to order in a gauge theory, and investigate the renormalon behaviour of such series. We are able to subtract the power divergence in the Operator Product Expansion (OPE) for the plaquette and estimate the gluon condensate in massless QCD. Our results confirm that NSPT provides a viable way to probe systematically the asymptotic behaviour of perturbative series in QCD and, eventually, gauge theories with fermions in higher representations.

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Investigation of new methods for numerical stochastic perturbation theory in φ4 theory

Cited by 10 publications

References 41 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

Large-order NSPT for lattice gauge theories with fermions: the plaquette in massless QCD

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