Fast summation of divergent series and resurgent transseries from Meijer-
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 approximants

Mera, H.; Pedersen, Thomas Garm; Nikolić, Branislav K.

doi:10.1103/physrevd.97.105027

Cited by 63 publications

(94 citation statements)

References 73 publications

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“…It is worth stressing that, as far as renormalons are concerned, there is no fundamental difference between this example and the real world QCD. The practical limitations of real QCD are that on one side, V (r, z) is computed up to a finite number of loops (three loops [43]), and on the other side, instanton's (19) via the Meijer G-function algorithm [35], as in Ref. [36].…”

Section: The Quark-antiquark Potential For An Infinite Number Of Fermmentioning

confidence: 99%

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Non-local Lagrangians from renormalons and analyzable functions

Maiezza

Vásquez

2019

Annals of Physics

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We embed in a generalized Borel procedure the notion of renormalization and renormalons. While there are several efforts in literature to have a semi-classical understanding of the renormalons, here we argue that this is not the fundamental issue and show how to deal with the problem. We find that the effective Lagrangians describing the effects of renormalons are non-local in space but local in time. The quark-antiquark potential in QCD with an infinite number of fermions is also analyzed. The connection between the analyzable functions, the Callan-Symanzyk equation and the renormalons, provides an insight of a non-perturbative renormalization from the standard perturbative renormalization approach.

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Section: The Quark-antiquark Potential For An Infinite Number Of Fermmentioning

confidence: 99%

“…Furthermore, within such regions the non-perturbative expressions can be resummed and obtained for example by means of the Meijer G-function algorithm recently proposed in Ref. [35] and applied to 4D QFT in Ref. [36].…”

Section: Renormalons and Scale Invariant Theoriesmentioning

confidence: 99%

Non-local Lagrangians from renormalons and analyzable functions

Maiezza

Vásquez

2019

Annals of Physics

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“…The Meijer G approximation The recently proposed Meijer G approximation scheme [64] relies on a similar idea that the Borel-Padé approximation makes use of. However instead of reconstructing the Borel transform BZ(g) by means of Padé approximants, it tries to "guess" its large order asymptotics by representing it by generalized hypergeometric functions,…”

Section: B Standard Approximation Schemesmentioning

confidence: 99%

“…The Laplace transform of BZ(g) can be carried out analytically and yields a Meijer G function. For details we refer the reader to [64].…”

Section: B Standard Approximation Schemesmentioning

confidence: 99%

Exploring high multiplicity amplitudes: The quantum mechanics analogue of the spontaneously broken case

Jaeckel

Schenk

2019

Phys. Rev. D

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Calculations of high multiplicity Higgs amplitudes exhibit a rapid growth that may signal an end of perturbative behavior or even the need for new physics phenomena. As a step towards this problem we consider the quantum mechanical equivalent of 1 → n scattering amplitudes in a spontaneously broken φ 4 -theory by extending our previous results on the quartic oscillator with a single minimum [1] to transitions n|x|0 in the symmetric double-well potential with quartic coupling λ. Using recursive techniques to high order in perturbation theory, we argue that these transitions are of exponential form n|x|0 ∼ exp (F (λn)/λ) in the limit of large n and λn fixed. We apply the methods of "exact perturbation theory" put forward by Serone et al. in [2,3] to obtain the exponent F and investigate its structure in the regime where tree-level perturbation theory violates unitarity constraints. We find that the resummed exponent is in agreement with unitarity and rigorous bounds derived by Bachas [4].

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“…For the surface density of the stellar disc of the Milky Way we have used R D = 3.2kpc, Σ 0 = 640.9M ⊙ pc −2 (Mera et al,1998). For σ R we consider R vel = 8.7kpc, σ 0 = 105.0km s −1 as observed by Lewis & Freeman (1989).…”

Section: Input Parameters and Numerical Solutionmentioning

confidence: 99%

General model of vertical distribution of stars in the Milky Way using complete Jeans equations

Sarkar

Jog

2019

Monthly Notices of the Royal Astronomical Society

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The self-consistent vertical density distribution in a thin, isothermal disc is typically given by a sech 2 law, as shown in the classic work by Spitzer (1942). This is obtained assuming that the radial and vertical motions are decoupled and only the vertical term is used in the Poisson equation. We argue that in the region of low density as in the outer disc this treatment is no longer valid. We develop a general, complete model that includes both radial and vertical terms in the Poisson equation and write these in terms of the full radial and vertical Jeans equations which take account of the non-flat observed rotation curve, the random motions, and the cross term that indicates the tilted stellar velocity ellipsoid. We apply it to the Milky Way and show that these additional effects change the resulting density distribution significantly, such that the mid-plane density is higher and the disc thickness (HWHM) is lower by 30-40% in the outer Galaxy. Further, the vertical distribution is no longer given as a sech 2 function even for an isothermal case. These predicted differences are now within the verification limit of new, high-resolution data for example from GAIA and hence could be confirmed.

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Fast summation of divergent series and resurgent transseries from Meijer- G approximants

Cited by 63 publications

References 73 publications

Non-local Lagrangians from renormalons and analyzable functions

Non-local Lagrangians from renormalons and analyzable functions

Exploring high multiplicity amplitudes: The quantum mechanics analogue of the spontaneously broken case

General model of vertical distribution of stars in the Milky Way using complete Jeans equations

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