Asymptotic Expansion of Laplace Transforms Near the Origin

Handelsman, Richard A.; Lew, John S.

doi:10.1137/0501012

Cited by 34 publications

(17 citation statements)

References 4 publications

(1 reference statement)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although this is not necessary for one-loop calculations, we note that in general extraction of the Λ → ∞ asymptotics can be efficiently done by exploiting a theorem by Handelsman and Lew [19] which relates the requisite coefficients in the asymptotics of the Laplace transform of the general form…”

Section: Jhep11(2016)105mentioning

confidence: 99%

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

Chankowski

Lewandowski

Meissner

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff Λ (implemented through an exponential damping factor). We construct the necessary finite counterterms restoring the BRST invariance of the effective action by analyzing the relevant Slavnov-Taylor identities. We find the relation between the renormalized parameters in our scheme and in the conventional MS scheme which allow us to obtain the explicit two-loop renormalization group equations in our scheme from the known two-loop ones in the MS scheme. We calculate in our scheme the divergences of two-loop vacuum graphs in the presence of a constant scalar background field which allow us to rederive the two-loop beta functions for parameters of the scalar potential. We also prove that consistent application of the proposed regularization leads to counterterms which, together with the original action, combine to a bare action expressed in terms of bare parameters. This, together with treating Λ as an intrinsic scale of a hypothetical underlying finite theory of all interactions, offers a possibility of an unconventional solution to the hierarchy problem if no intermediate scales between the electroweak scale and the Planck scale exist.

show abstract

Section: Jhep11(2016)105mentioning

confidence: 99%

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

Chankowski

Lewandowski

Meissner

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…That is, (1.1) ±{f}=$~ f(t)e-stdt, whenever the integral on the right converges. In a recent paper, Handelsman and Lew [2] have studied the asymptotic behavior of L{/} as s -► 0, when/(0 satisfies…”

mentioning

confidence: 99%

On Laplace Transforms Near the Origin

Wong¹

1975

Mathematics of Computation

View full text Add to dashboard Cite

“…Their method, which is based on the Laplace transform, gives explicit asymptotic expansions for a limited class of exponentially small Hankel integrals. A powerful method of obtaining explicit asymptotic expansion of a Hankel integral is the Mellin-Barnes method [7], which is a modification of the classical Mellin transform method [6,17,18] based on the asymptotic expansion of the ratio of products of gamma functions [19][20][21][22][23]. This method is capable of obtaining explicit expansions where the method of Franzen and Wong can give only order estimates.…”

Section: Introductionmentioning

confidence: 99%

Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales

Galapon

Martinez

2014

Proc. R. Soc. A.

View full text Add to dashboard Cite

We obtain an exactification of the Poincaré asymptotic expansion (PAE) of the Hankel integral,We find that, for halfinteger orders of the Bessel function, the exactified asymptotic series terminates, so that it gives an exact finite sum representation of the Hankel integral. For other orders, the asymptotic series does not terminate and is generally divergent, but is amenable to superasymptotic summation, i.e. by optimal truncation. For specific examples, we compare the accuracy of the optimally truncated asymptotic series owing to the McClure-Wong distributional method with owing to the Mellin-Barnes integral method. We find that the former is spectacularly more accurate than the latter, by, in some cases, more than 70 orders of magnitude for the same moderate value of b. Moreover, the exactification can lead to a resummation of the PAE when it is exact, with the resummed Poincaré series exhibiting again the same spectacular accuracy. More importantly, the distributional method may yield meaningful resummations that involve scales that are not asymptotic sequences.

show abstract

Asymptotic Expansion of Laplace Transforms Near the Origin

Cited by 34 publications

References 4 publications

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

On Laplace Transforms Near the Origin

Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales

Contact Info

Product

Resources

About