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Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
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abstract
We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a $W$ boson at hadron colliders in the leading colour approximation. These Feynman integrals also contribute to Higgs or $Z$-boson production in association with a top pair. We employ the method of differential equations (DEs), facilitated by the use of finite field methods to handle the algebraic complexity stemming from the seven-scale kinematics. The presence of the top quark in the virtual propagators, in addition to the mass of the external $W$ boson, gives rise to nested square roots and three elliptic curves. We obtain DEs that depend at most quadratically on the dimensional regulator $\epsilon$ for sectors where these analytic structures appear, and are $\epsilon$-factorised otherwise. We express the DEs in terms of a minimal set of differential one-forms, separating the logarithmic ones. We solve the DEs numerically in the physical kinematic region, with the method of generalised power series expansions.
Forward citations
Cited by 5 Pith papers
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Planar two-loop four-point master integrals for massive radiative-return QED, including elliptic and nested-root sectors, are reduced to polynomial-in-ε differential equations that evaluate stably in the physical region.
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Multi-scale improved predictions for $\boldsymbol{pp \to t\bar{t}W^+ +X}$
MiNLO yields NLO predictions for full off-shell pp o ttW+(j/jj) that agree with fixed-order results while reducing scale dependence for multi-jet samples, and merging improves the inclusive ttW+ description.
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