Speaker
Description
We complete the calculation of the two-loop Feynman integrals required to obtain next-to-next-to-leading order (NNLO) QCD predictions for on-shell top-antitop production in association with a photon at hadron colliders in the leading-colour approximation.
The integrals computed here are also relevant to the subleading-colour contributions to top-antitop production in association with a jet.
Due to the complex kinematic structure of the process, involving six independent kinematic invariants, and the appearance of up to three massive propagators in the master integrals, the algebraic complexity of the latter increases dramatically, giving rise to sectors containing nested square roots and elliptic integrals.
To address these challenges and compute the master integrals using the method of differential equations (DEs), we employ finite-field techniques for the reconstruction of the connection matrix entries and construct suitable bases for each family, avoiding the introduction of transcendental functions in their definition. In these bases, the DEs are $\varepsilon$-factorised in the logarithmic sectors, linear in $\varepsilon$ for sectors with nested square roots, and quadratic in $\varepsilon$ for the elliptic sectors.
We perform the Laurent expansion in terms of a potentially overcomplete set of special functions, evaluated through numerical solution of DEs.