Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
NNLO fermionic corrections to the charm quark mass dependent matrix elements in B -> X_s gamma
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abstract
We compute the virtual O(alpha_s^2) fermionic contributions to the charm quark mass dependent matrix elements of the B -> X_s gamma decay. In the case of a massless quark loop insertion into the gluon propagator, our result obtained as an expansion in z=m_c^2/m_b^2 and an exact expression in terms of multi-fold MB integrals, confirms the findings of Bieri, Greub and Steinhauser [19]. We observe, however, large deviations in the case of a b-quark loop insertion.The charm quark loop shows smaller, but still noticeable differences.
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hep-ph 4representative citing papers
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Tensor decomposition of $e^+e^-\to\pi^+\pi^-\gamma$ to higher orders in the dimensional regulator
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Solution of Canonical Differential Equations for Integrals on Arbitrary Geometries
A strategy is introduced to solve canonical differential equations for Feynman master integrals on arbitrary geometries by reducing numerical evaluation to an enlarged system of rational differential equations.
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AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.