Three-Loop Heavy Quark Form Factors and Their Asymptotic Behavior

Abstract

A summary of the calculation of the color-planar and complete light quark contributions to the massive three-loop form factors is presented. Here a novel calculation method for the Feynman integrals is used, solving general univariate first order factorizable systems of differential equations. We also present predictions for the asymptotic structure of these form factors.

Numerical implementation of harmonic polylogarithms to weight w = 8

“…We briefly commented on the numerical implementation of cyclotomic harmonic polylogarithms, which are important in massive higher loop calculations, as e.g. for the massive Formfactors from 3-loop order [24,25,32]. Here, precise Taylor series around x = 0, 1, −1 providing sufficient convergence in a circle of radius ρ = 1/2 within x ∈ [−1, 1] serve the purpose.…”

“…Ref. [24,25]. One possibility is given by Taylor series in x around x = 0, 1 and x = −1, which can be calculated analytically using the command…”

“…The function is graphically illustrated in Figure 1. In case of the planar contributions to the 3-loop massive Formfactors [24,25] 206 real-valued cyclotomic polylogarithms up to w=6 contribute. Their numerical representation is given in Ref.…”

“…to weight w = 6 in Refs. [23][24][25], which were given in [26]. Numerical implementations of the analytic continuation of harmonic sums to complex arguments have been given in [27].…”