Two-loop light-quark Electroweak corrections to Higgs boson pair production in gluon fusion

We compute two-loop electroweak corrections to double Higgs boson production in gluon fusion mediated by light quarks in a fully analytical way. We determine a basis of master integrals satisfying canonical differential equations in dlog form, enhanced by subsequent rotations to remove unnecessary functions that do not appear in the analytic expressions of the amplitudes. We determine the integration constants by matching our expressions to the large mass expansion limit of the canonical integrals. We express the solution of differential equations in terms of Chen iterated integrals up to transcendental weight six over logarithmic kernels with algebraic arguments, and further decompose them by employing a basis of uniform weight functions. By deriving differential equations for such basis, we provide numerical results as well as routines for optimised numerical evaluations.