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We use dimensional regularization to calculate the ${cal O}(ep^2)$ expansion of all scalar one-loop one-, two-, three- and four-point integrals that are needed in the calculation of hadronic heavy quark production. The Laurent series up to ${cal O}(ep^2)$ is needed as input to that part of the NNLO corrections to heavy flavor production at hadron colliders where the one-loop integrals appear in the loop-by-loop contributions. The four-point integrals are the most complicated. The ${cal O}(ep^2)$ expansion of the three- and four-point integrals contains in general polylogarithms up to ${rm Li}_4$ and functions related to multiple polylogarithms of maximal weight and depth four.
We present the public C++ library Ninja, which implements the Integrand Reduction via Laurent Expansion method for the computation of one-loop integrals. The algorithm is suited for applications to complex one-loop processes.
We present a new Fortran code to calculate the scalar one-loop four-point integral with complex internal masses, based on the method of t Hooft and Veltman. The code is applicable when the external momenta fulfill a certain physical condition. In par
We present a new method to evaluate the $alpha$-expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation o
We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an appropriate numer
Representations are derived for the basic scalar one-loop vertex Feynman integrals as meromorphic functions of the space-time dimension $d$ in terms of (generalized) hypergeometric functions $_2F_1$ and $F_1$. Values at asymptotic or exceptional kine