CHAPLIN—Complex Harmonic Polylogarithms in Fortran

Self Cite

102

Abstract:We compute the contributions to the N 3 LO inclusive Higgs boson cross-section from the square of one-loop amplitudes with a Higgs boson and three QCD partons as external states. Our result is a Taylor expansion in the dimensional regulator ǫ, where the coefficients of the expansion are analytic functions of the ratio of the Higgs boson mass and the partonic center of mass energy and they are valid for arbitrary values of this ratio. We also perform a threshold expansion around the limit of soft-parton radiation in the final state. The expressions for the coefficients of the threshold expansion are valid for arbitrary values of the dimension. As a by-product of the threshold expansion calculation, we have developed a soft expansion method at the integrand level by identifying the relevant soft and collinear regions for the loop-momentum.

Section: Jhep12(2013)088mentioning

confidence: 99%

Real-virtual contributions to the inclusive Higgs cross-section at N3LO

Anastasiou

Duhr

Dulat

et al. 2013

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102

“…Furthermore, to cross-check our results, a second implementation was programmed in C++, where the convolutions of splitting kernels and partonic cross sections were performed numerically. For both codes, the numerical evaluation of HPLs was performed using the library Chaplin [60]. The two implementations agreed for all parameter configurations that were tested.…”

Section: Numerical Results For the Gluon Fusion Scale Variation At N mentioning

confidence: 99%

“…For more comprehensive information about harmonic polylogarithms, we refer to [54][55][56][57][58][59][60]. Any convolution involving a delta function trivially returns the other convolutant (whether it be another delta function, a plus distribution or a regular function),…”

Section: Computation Of the Convolutionsmentioning

confidence: 99%

Scale dependence and collinear subtraction terms for Higgs production in gluon fusion at N3LO

Buehler

Lazopoulos

2013

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The full, explicit, scale dependence of the inclusive N 3 LO cross section for single Higgs hadroproduction is obtained by calculating the convolutions of collinear splitting kernels with lower-order partonic cross sections. We provide results for all convolutions of splitting kernels and lower-order partonic cross sections to the order in ǫ needed for the full N 3 LO computation, as well as their expansions around the soft limit. We also discuss the size of the total scale uncertainty at N 3 LO that can be anticipated with existing information.

“…It was realised that many Feynman integrals can be evaluated in terms of multiple polylogarithms [1][2][3]. These functions are by now well understood, including their analytic continuation to arbitrary kinematic regions and their efficient numerical evaluation for arbitrary complex arguments [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Three-loop contributions to the ρ parameter and iterated integrals of modular forms

Abreu

Becchetti

Duhr

et al. 2020

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We compute fully analytic results for the three-loop diagrams involving two different massive quark flavours contributing to the ρ parameter in the Standard Model. We find that the results involve exactly the same class of functions that appears in the wellknown sunrise and banana graphs, namely elliptic polylogarithms and iterated integrals of modular forms. Using recent developments in the understanding of these functions, we analytically continue all the iterated integrals of modular forms to all regions of the parameter space, and in each region we obtain manifestly real and fast-converging series expansions for these functions.