CHAPLIN—Complex Harmonic Polylogarithms in Fortran
نویسندگان
چکیده
منابع مشابه
Harmonic Polylogarithms
The harmonic polylogarithms (hpl’s) are introduced. They are a generalization of Nielsen’s polylogarithms, satisfying a product algebra (the product of two hpl’s is in turn a combination of hpl’s) and forming a set closed under the transformation of the arguments x = 1/z and x = (1−t)/(1+t). The coefficients of their expansions and their Mellin transforms are harmonic sums. AMS(1991) subject cl...
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Oneand two-dimensional harmonic polylogarithms, HPLs and GPLs, appear in calculations of multi-loop integrals. We discuss them in the context of analytical solutions for two-loop master integrals in the case of massive Bhabha scattering in QED. For the GPLs we discuss analytical representations, conformal transformations, and also their transformations corresponding to relations between master ...
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The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index calss rather than on their value. We show how to find a basis of the associated algebra. The length of the basis l is found to be ≤ 1/d, where d is the depth of the su...
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We describe how to compute numerically in the complex plane a set of Generalized Harmonic Polylogarithms (GHPLs) with square roots in the weights, using the C++/GiNaC numerical routines of Vollinga and Weinzierl. As an example, we provide the numerical values of the NLO electroweak light-fermion corrections to the Higgs boson production in gluon fusion in the case of complex W and Z masses.
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The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin transforms of Poincaré– iterated integrals including denominators of higher cyclotomic polynomials. We derive the cyclotomic harmonic polylogarithms and harmo...
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ژورنال
عنوان ژورنال: Computer Physics Communications
سال: 2014
ISSN: 0010-4655
DOI: 10.1016/j.cpc.2014.05.022