Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d=2 and d=4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10^{15} is achieved for arbitrary real values of the momentum transfer.Comment: 11 pages, LaTeX. The complete paper is also available via the www at http://www-ttp.physik.uni-karlsruhe.de/Preprints/ and the program can be downloaded from http://www-ttp.physik.uni-karlsruhe.de/Progdata

Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves

We show that for a class of two-loop diagrams, the on-shell part of the integration-by-parts (IBP) relations correspond to exact meromorphic one-forms on algebraic curves. Since it is easy to find such exact meromorphic one-forms from algebraic geometry, this idea provides a new highly efficient algorithm for integral reduction. We demonstrate the power of this method via several complicated two-loop diagrams with internal massive legs. No explicit elliptic or hyperelliptic integral computation is needed for our method.Comment: minor changes: more references adde

Massive Feynman integrals and electroweak corrections

There are steady advances in the calculation of electroweak corrections to massive scattering problems at colliders, from the very beginning in the nineteen seventies until contemporary developments. Recent years brought a remarkable progress due to new calculational technologies. This was motivated by demands from phenomenological applications at particle accelerators: higher multiplicities of the final states, extreme kinematics, need of higher precision and thus of higher orders in perturbation theory. We describe selected contributions from the project "Massive particle production" of Sonderforschungsbereich/Transregio 9 of Deutsche Forschungsgemeinschaft.Comment: Material presented at the final Workshop of Sonderforschungsbereich Transregio 9 "Advances in Computational Physics" of Deutsche Forschungsgemeinschaft (DFG), 15-19 Sep 2014, Durbach, Germany, to appear in the proceedings, 16 pages, 16 figures, 3 tables; references added in v

The complete set of two-loop master integrals for Higgs + jet production in QCD

In this paper we complete the computation of the two-loop master integrals relevant for Higgs plus one jet production initiated in arXiv:1609.06685, arXiv:1907.13156, arXiv:1907.13234. We compute the integrals by defining differential equations along contours in the kinematic space, and by solving them in terms of one-dimensional generalized power series. This method allows for the efficient evaluation of the integrals in all kinematic regions, with high numerical precision. We show the generality of our approach by considering both the top- and the bottom-quark contributions. This work along with arXiv:1609.06685, arXiv:1907.13156, arXiv:1907.13234 provides the full set of master integrals relevant for the NLO corrections to Higgs plus one jet production, and for the real-virtual contributions to the NNLO corrections to inclusive Higgs production in QCD in the full theory.Comment: 32 pages, references added, minor revisio