Canonical differential equations for the elliptic two-loop five-point integral family relevant to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>t</mml:mi> <mml:mover accent="true"> <mml:mi>t</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> <mml:mo>+</mml:mo> <mml:mtext>jet</mml:mtext> </mml:math> production at leading color
Matteo Becchetti, Christoph Dlapa, Simone Zoia
Abstract
We complete the construction of canonical differential equations (DEs) for all families of Feynman integrals appearing in the two-loop leading-color QCD amplitude for top-pair production in association with a jet at hadron colliders. This allows us to obtain analytic results for all required Feynman integrals in terms of iterated integrals with closed-form kernels. To achieve this, we study the two-loop five-point integral family for which canonical DEs were previously unavailable due to the appearance of elliptic functions and nested square roots. In addition to marking a significant step toward next-to-next-to-leading-order QCD predictions for a high-priority LHC process, this is the first time that canonical DEs are obtained for Feynman integrals where elliptic functions appear in conjunction with the high algebraic complexity of a process with more than four particles. Our results also reveal a number of new interesting analytic features, such as a “duplet” structure that generalizes the even/odd parity of square roots to nested square roots.