Fuchsia and master integrals for splitting functions from differential equations in QCD

Gituliar, O.; Magerya, Vitaly

doi:10.22323/1.260.0030

Cited by 18 publications

(22 citation statements)

References 15 publications

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“…In the following we do not explicitly show the ǫ dependence of the functions in the arguments 3. Meanwhile there are two public computer implementations of this algorithm, see Refs [36][37][38][39]…”

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confidence: 99%

Four-loop quark form factor with quartic fundamental colour factor

Lee

Smirnov

et al. 2019

J. High Energ. Phys.

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We analytically compute the four-loop QCD corrections for the colour structure (d abcd F ) 2 to the massless non-singlet quark form factor. The computation involves non-trivial non-planar integral families which have master integrals in the top sector. We compute the master integrals by introducing a second mass scale and solving differential equations with respect to the ratio of the two scales. We present details of our calculational procedure. Analytical results for the cusp and collinear anomalous dimensions, and the finite part of the form factor are presented. We also provide analytic results for all master integrals expanded up to weight eight.

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confidence: 99%

Four-loop quark form factor with quartic fundamental colour factor

Lee

Smirnov

et al. 2019

J. High Energ. Phys.

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“…For differential equations depending on one variable, an algorithm to compute a transformation to a canonical basis has been described in detail by Lee [137]. Most of the aforementioned approaches lack such a detailed algorithmic description, which is reflected by the fact that Lee's algorithm is the only one with publicly available implementations [139][140][141]. Since Lee's algorithm can only compute transformations depending on one variable, the range of processes it can be used for is severely restricted.…”

Section: Determination Of Boundary Conditionsmentioning

confidence: 99%

“…Most of the other methods do not rise to the same level in terms of their algorithmic description, but rather represent recipes for specific cases. This is also reflected by the fact that Lee's algorithm is the only one with publicly available implementations [139][140][141]. The main drawback of Lee's algorithm is that it 1 Introduction is only applicable to differential equations depending on one variable, which severely restricts the range of processes it can be applied to.…”

Section: Introductionmentioning

confidence: 99%

Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA

Meyer¹

2018

Computer Physics Communications

119

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The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica package CANONICA, which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations.

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“…This is in contrast to N = 4 super-Yang-Mills theory, where analytical expressions for the NLO corrections have recently been derived [4] and one expects that the latter results correspond to those in QCD (after the usual identification of color factors) as far as the polylogarithms of highest weight are concerned. Second, we wish to extend the application of Lee's algorithm [5] and the Fuchsia program [6,7] beyond univariate problems. To our knowledge, there are no examples of such usage in the literature so far while the method is not limited to univariate problems only.…”

Section: Introductionmentioning

confidence: 99%

Fuchsia and Master Integrals for Energy-Energy Correlations at NLO in QCD

Gituliar¹,

Moch²

2018

Proceedings of 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) —

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In this talk we discuss some aspects of the analytical calculation of energy correlations in electronpositron annihilation at a next-to-leading order in QCD. Our primary focus is on the most difficult task: the calculation of master integrals for real-emission contributions, which are functions of two dimensionless variables and the dimensional regulator. We use a method of differential equations and their so-called epsilon-form which is constructed with the help of the FUCHSIA program based on Lee's algorithm.13th International Symposium on Radiative Corrections

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Fuchsia and master integrals for splitting functions from differential equations in QCD

Cited by 18 publications

References 15 publications

Four-loop quark form factor with quartic fundamental colour factor

Four-loop quark form factor with quartic fundamental colour factor

Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA

Fuchsia and Master Integrals for Energy-Energy Correlations at NLO in QCD

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