Asymptotic Expansions in Momenta and Masses and Calculation of Feynman Diagrams

V.A. Smirnov

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Asymptotic Expansions in Momenta and Masses and Calculation of Feynman Diagrams

V.A. Smirnov

High Energy Physics - Theory · Submitted 7 Dec 1994

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is shown how they are applied for calculation of massive diagrams.

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General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

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s0	General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed.	background 0.72	0.10	0.16	asserted 0.82
s1	It is shown how they are applied for calculation of massive diagrams.	contribution 0.62	0.63	0.31	asserted 1.00

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Original abstract

General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

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References

Forward citations

Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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The first explicit 1/N corrections to <TJJ> and <TTT> in critical O(N) vector and Gross-Neveu-Yukawa models are computed, determining shape parameters that agree with bootstrap at small N.
On divergences in a four-derivative scalar field theory
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Four-loop top-quark QCD corrections to Delta r and Delta kappa are computed at subleading order in the large top-mass expansion, shifting the predicted W mass by about 0.2 to 0.8 MeV.
Hidden Region Finder: asymptotic expansions of Feynman integrals in Minkowski space
hep-ph 2026-09 conditional novelty 7.0 of 10

The Hidden Region Finder determines the hidden regions that Newton-polytope methods omit in Minkowski-space Feynman integral expansions, by linking them to Landau pinch singularities and the interplay of scaling with ...
The structure of quark mass corrections in the $gg \rightarrow HH$ amplitude at high-energy
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The leading-power mass logarithms in high-energy gg to HH are shown to originate solely from top-quark mass renormalization, enabling a resummation that sharply reduces the mass-scheme uncertainty of the virtual amplitude.

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Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
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All planar two-loop master integrals for Higgs to three partons with full heavy-quark mass dependence are computed analytically, including two elliptic sectors solved via a one-dimensional parametrization.
Calculation of Feynman loop integration and phase-space integration via auxiliary mass flow
hep-ph 2020-09 conditional novelty 6.0 of 10

The auxiliary-mass-flow method is extended to compute phase-space integrals, enabling high-precision calculations of collider observables at next-to-next-to-leading order.
Determine Arbitrary Feynman Integrals by Vacuum Integrals
hep-ph 2018-01 conditional novelty 6.0 of 10

A new representation expresses any Feynman loop integral as the analytic continuation of a series of vacuum integrals, yielding a step-by-step reduction method demonstrated on two-loop four- and five-point processes.
Associated production of a Higgs boson at NNLO
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A complete NNLO QCD calculation of W-H and Z-H production, combining Drell-Yan-like and top-Yukawa-loop contributions with full decays, implemented in the public MCFM 8.0 code.
$B_{s,d}^0 \to \ell^+\ell^-$ Decays in the Aligned Two-Higgs-Doublet Model
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A complete one-loop calculation of the Wilson coefficients for B_s,d to lepton pairs in the aligned two-Higgs-doublet model, with gauge-independence checks and bounds on the alignment parameters from current B_s to mu...
Gluon-induced Higgs-strahlung at next-to-leading order QCD
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Gluon-induced HZ production receives a next-to-leading-order QCD correction factor of about two, computed in the heavy-top effective theory and applied by rescaling the exact leading-order cross section.
Probing low energy scalar leptoquarks by the leptonic $W$ and $Z$ couplings
hep-ph 2019-01 conditional novelty 5.0 of 10

Including finite one-loop terms and external-momentum corrections, scalar leptoquarks shift the leptonic Z couplings by 14 to 22% at masses below 1.5 TeV, enough to change whether B-anomaly leptoquark models survive Z...
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How the literature uses it

37 arXiv papers cite this in 43 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 15 sentences without a confident label

Uses its method or tool 25 papers

We will now outline the procedure for expansion by subgraph as developed by Smirnov [ref] .

The asymptotic Hopf Algebra of Feynman Integrals · Expansion by subgraph · 0.98
The rules for a correct asymptotic expansion around a large mass limit have been elaborated in Refs. [ref] in the form of an expansion in sub-diagrams defined as F_G(q,M,m,ϵ) ∑_σ F_G/σ(q,M,m,ϵ) ·T_q^σ,m^σ F_σ(q^σ,M,m^σ,ϵ).

Simplified leptoquark models for precision $l_i \rightarrow l_f \gamma$ experiments: two-loop structure of $O(\alpha_S Y^2)$ corrections · Methodology · 0.97
The latter is obtained by straightforward application of the strategy of regions [ref] .

Leptonic CP violation in the charged sector and effective field theory approach · Anomalous dimensions and matching between LEFT and SMEFT · 0.97

Cites it as background 3 papers

The behaviour of a given Feynman integral in the large mass limit can be described [ref] (see also [ref] and Chapter 9 of [ref] ) by a simple formula with a summation over subgraphs which include all the large masses and whose connectivity components are one-particle-irreducible with respect to the lines with small masses.

Simplifying the large mass expansion · Introduction · 0.89
Although asymptotic expansion of Feynman integrals itself is not new [ref] , the novelty here is that our expansion is with respect to an auxiliary parameter introduced by hand and thus can be applied to any problem.

Determine Arbitrary Feynman Integrals by Vacuum Integrals · Introduction · 0.81
More than two decades ago, the integration-by-parts relations [ref] and asymptotic expansions [ref] became common in the Feynman diagram calculus.

Three-loop massive tadpoles and polylogarithms through weight six · Introduction · 0.99

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