Two-loop integrals for t t̅ +jet production at hadron colliders in the leading colour approximation
arxiv(2024)
摘要
We compute the differential equations for the two remaining integral
topologies contributing to the leading colour two-loop amplitudes for pp
→ tt̅j. We derive differential equations for the master
integrals by solving the integration-by-parts identities over finite fields. Of
the two systems of differential equations, one is presented in canonical 'dlog' form, while the other is found to have an elliptic sector. For the
elliptic topology we identify the relevant elliptic curve, and present the
differential equations in a more general form which depends quadratically on
ϵ and contains non-logarithmic one-forms in addition to the canonical
dlog's. We solve the systems of differential equations numerically
using generalised series expansions with the boundary terms obtained using the
auxiliary mass flow method. A summary of all one-loop and two-loop planar
topologies is presented including the list of alphabet letters for the 'dlog' form systems and high-precision boundary values.
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