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The inverse Mellin transform via analytic continuation


Behring, A; Blümlein, J; Schönwald, K (2023). The inverse Mellin transform via analytic continuation. Journal of High Energy Physics, 2023(6):62.

Abstract

We present a method to calculate thex-space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin indexN, directly, without computing the Mellin-space expressions in explicit form analytically. HereNbelongs either to the even or odd positive integers. The method is based on the resummation of the operators into effective propagators and relies on an analytic continuation between two continuous variables. We apply it to iterated integrals as well as to the more general case of iterated non-iterative integrals, generalizing the former ones. Thex-space expressions are needed to derive the small-xbehaviour of the respective quantities, which usually cannot be accessed inN-space. We illustrate the method for different (iterated) alphabets, including non-iterative$_{2}$F$_{1}$and elliptic structures, as examples. These structures occur in different massless and massive three-loop calculations. Likewise the method applies even to the analytic closed form solutions of more general cases of differential equations which do not factorize into first-order factors.

Abstract

We present a method to calculate thex-space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin indexN, directly, without computing the Mellin-space expressions in explicit form analytically. HereNbelongs either to the even or odd positive integers. The method is based on the resummation of the operators into effective propagators and relies on an analytic continuation between two continuous variables. We apply it to iterated integrals as well as to the more general case of iterated non-iterative integrals, generalizing the former ones. Thex-space expressions are needed to derive the small-xbehaviour of the respective quantities, which usually cannot be accessed inN-space. We illustrate the method for different (iterated) alphabets, including non-iterative$_{2}$F$_{1}$and elliptic structures, as examples. These structures occur in different massless and massive three-loop calculations. Likewise the method applies even to the analytic closed form solutions of more general cases of differential equations which do not factorize into first-order factors.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Nuclear and High Energy Physics
Uncontrolled Keywords:Nuclear and High Energy Physics
Language:English
Date:12 June 2023
Deposited On:04 Jan 2024 12:31
Last Modified:28 Jun 2024 03:33
Publisher:Springer
ISSN:1029-8479
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/jhep06(2023)062
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)