Massive 3-loop Feynman diagrams reducible to SC
                $^*$
               primitives of algebras of the sixth root of unity

Broadhurst, David J.

doi:10.1007/s100529900935

Cited by 202 publications

(137 citation statements)

References 28 publications

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“…Evidently, eq. (5.1) is divergent, but one can arrive at a finite integral by considering the difference between the general U 6 integral and a simpler U 6 with only one independent mass scale: The special case of U 6 with identical masses in all six propagators is known analytically [9],…”

Section: Umentioning

confidence: 99%

Three-loop vacuum integrals with arbitrary masses

Freitas

2016

J. High Energ. Phys.

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Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, analytical results for integrals with only one and two independent mass scales are known, but in the electroweak Standard Model and many extensions thereof, one often encounters more mass scales of comparable magnitude. For this reason, a numerical approach for the evaluation of three-loop vacuum integrals with arbitrary mass pattern is proposed here. Concretely, one can identify a basic set of three master integral topologies. With the help of dispersion relations, each of these can be transformed into one-dimensional or, for the most complicated case, two-dimensional integrals in terms of elementary functions, which are suitable for efficient numerical integration.

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Section: Umentioning

confidence: 99%

Three-loop vacuum integrals with arbitrary masses

Freitas

2016

J. High Energ. Phys.

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“…The transcendental functions appearing in the results are one-and two-dimensional harmonic polylogarithms (HPLs) [107,108,[114][115][116][117][118][119][120][121][122][123] of maximum weight four. All of the HPLs appearing in the analytic expression of the coefficient A can be evaluated numerically with arbitrary precision by employing the methods and codes described in [120].…”

Section: Jhep01(2011)102mentioning

confidence: 99%

Two-loop leading color corrections to heavy-quark pair production in the gluon fusion channel

Bonciani

Ferroglia

Gehrmann

et al. 2011

J. High Energ. Phys.

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Abstract:We evaluate the two-loop QCD diagrams contributing to the leading color coefficient of the heavy-quark pair production cross section in the gluon fusion channel. We obtain an analytic expression, which is valid for any value of the Mandelstam invariants s and t and of the heavy-quark mass m. Our findings agree with previous analytic results in the small-mass limit and with recent results for the coefficients of the IR poles.

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“…16 15 Using the results of the all-order ε-expansion for Gauss hypergeometric functions [13,29] we could consider a series of type (2.1). 16 In particular, all sums presented in ref. [46] are reducible in terms of our basis sums or sums studied in ref.…”

Section: Jhep10(2007)048mentioning

confidence: 99%

“…This gives an explanation of the proper "basis of transcendental constants" constructed in refs. [52] and [10], and its difference from the proper basis of Broadhurst [16]. Of course, for numerical evaluation of harmonic polylogarithms of complex argument, only a series representation is necessary.…”

Section: Jhep10(2007)048mentioning

confidence: 99%