3-Loop Corrections to the Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

Bluemlein, Johannes

doi:10.22323/1.234.0504

Cited by 1 publication

(4 citation statements)

References 59 publications

(79 reference statements)

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“…As a starting point the master integrals all have to be solved in analytic form in terms of the auxiliary variable t, including also eventual non first-order factorizing cases, which leads to iterated non-iterative integrals, see refs. [34][35][36] in general. Integrals of this kind are iterations over letters, which are given as integrals in which the integration variable cannot be JHEP06(2023)062 transferred to the integral boundaries only.…”

Section: Jhep06(2023)062mentioning

confidence: 99%

“…In section 3 we show how to use our proposed method on different classes of iterated integrals, such as harmonic polylogarithms [64], generalized harmonic polylogarithms [65][66][67], cyclotomic harmonic polylogarithms [68], and iterated integrals containing square root valued letters [69]. In section 4 we investigate the case where also iterated non-iterative integrals are present, [34][35][36]. In section 5 we comment on ways of efficient numerical representations of the results in x-space and section 6 contains the conclusions.…”

Section: Jhep06(2023)062mentioning

confidence: 99%

“…Here W µν is the hadronic tensor. For the present application W µν is the final function depending on the Bjorken variable x, while T µν contains the variable t. The imaginary part in (2.9) results from the monodromy of the iterated, or iterated non-iterative integrals [34,35] around t = 1, t = −1, and complex valued contributions of other kind by setting…”

Section: Jhep06(2023)062mentioning

confidence: 99%

“…In the case we consider in the following it turns out that the hierarchy of master integrals is such that the 2 F 1 -solutions occur only in the seeds and the other master integrals are given by first-order iterations over them. For this reason we called these integrals iterated non-iterative integrals [34,35]. This class also covers a wide range of concrete cases which occur in Feynman diagram calculations such as Abel integrals [142], K3 surfaces [143,144], and Calabi-Yau motives [145,146], see also refs.…”

Section: Iterated Non-iterative Integralsmentioning

confidence: 99%

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The inverse Mellin transform via analytic continuation

Behring

Blümlein

Schönwald

2023

J. High Energ. Phys.

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We present a method to calculate the x-space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin index N, directly, without computing the Mellin-space expressions in explicit form analytically. Here N belongs 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. The x-space expressions are needed to derive the small-x behaviour of the respective quantities, which usually cannot be accessed in N-space. We illustrate the method for different (iterated) alphabets, including non-iterative 2F1 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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Section: Jhep06(2023)062mentioning

confidence: 99%