Harmonic Polylogarithms

Remiddi, E.; Vermaseren, J. A. M.

doi:10.1142/s0217751x00000367

Cited by 1,143 publications

(1,604 citation statements)

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“…From these functions the x-space expressions can be reconstructed algebraically [20,43] in terms of harmonic polylogarithms [41][42][43]. As in the case of F 2,L in electromagnetic DIS presented before [17,18], the exact third-order expressions are unpleasantly long in both N-space and x-space.…”

Section: Resultsmentioning

confidence: 99%

Third-order QCD corrections to the charged-current structure function

2009

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We compute the coefficient function for the charge-averaged W ± -exchange structure function F 3 in deep-inelastic scattering (DIS) to the third order in massless perturbative QCD. Our new threeloop contribution to this quantity forms, at not too small values of the Bjorken variable x, the dominant part of the next-to-next-to-next-to-leading order corrections. It thus facilitates improved determinations of the strong coupling α s and of 1/Q 2 power corrections from scaling violations measured in neutrino-nucleon DIS. The expansion of F 3 in powers of α s is stable at all values of x relevant to measurements at high scales Q 2 . At small x the third-order coefficient function is dominated by diagrams with the colour structure d abc d abc not present at lower orders. At large x the coefficient function for F 3 is identical to that of F 1 up to terms vanishing for x → 1.

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Section: Resultsmentioning

confidence: 99%

Third-order QCD corrections to the charged-current structure function

2009

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“…Only integrations with kernels 1/x, 1/(1 − x) and 1/(1 + x) are required, and the solutions can be written exclusively in terms of harmonic polylogarithms [29]. To fully determine the solution of the differential equations, we require the value of the master integrals at a certain kinematic point.…”

Section: Master Integralsmentioning

confidence: 99%

Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

Anastasiou

Beerli

Bucherer

et al. 2007

J. High Energy Phys.

185

233

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Abstract:We compute all two-loop master integrals which are required for the evaluation of next-to-leading order QCD corrections in Higgs boson production via gluon fusion. Many two-loop amplitudes for 2 → 1 processes in the Standard Model and beyond can be expressed in terms of these integrals using automated reduction techniques. These integrals also form a subset of the master integrals for more complicated 2 → 2 amplitudes with massive propagators in the loops. As a first application, we evaluate the two-loop amplitude for Higgs boson production in gluon fusion via a massive quark. Our result is the first independent check of the calculation of Spira, Djouadi, Graudenz and Zerwas. We also present for the first time the two-loop amplitude for gg → h via a massive squark.

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“…In [4] that analytic integration of the dispersion relations could at last be performed, expressing the real parts of the 2-loop form factors in terms of the 1-dimensional harmonic polylogarithms (HPLs), introduced in the meanwhile [5,6], of maximum weight w = 4.…”

Section: Introductionmentioning

confidence: 99%

QED vertex form factors at two loops

Bonciani¹,

Mastrolia²,

Remiddi³

2004

Nuclear Physics B

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We present the closed analytic expression of the form factors of the twoloop QED vertex amplitude for on-shell electrons of finite mass m and arbitrary momentum transfer S = −Q 2 . The calculation is carried out within the continuous D-dimensional regularization scheme, with a single continuous parameter D, the dimension of the space-time, which regularizes at the same time UltraViolet (UV) and InfraRed (IR) divergences. The results are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.

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Harmonic Polylogarithms

Cited by 1,143 publications

References 10 publications

Third-order QCD corrections to the charged-current structure function

Third-order QCD corrections to the charged-current structure function

Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

QED vertex form factors at two loops

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