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We present analytic results for all the Feynman integrals relevant for${\mathcal O}(\alpha \alpha_s)$ virtual corrections to $H \rightarrow ZZ^*$decay. We use the method of differential equations to solve the masterintegrals while keeping the full dependence on the masses of all the particlesincluding internal propagators. Due to the presence of four mass scales weencounter multiple square roots. We argue that all the occurring square rootscan not be rationalized at the same time as a simultaneous rationalizationbrings us to integrals over $CY_3$ manifolds. Hence we rationalize only threesquare roots simultaneously and construct suitable ans\"atze to obtaindlog-forms containing the square root, after obtaining an epsilon-factorisedform for the differential equations. We present the alphabet and the analyticform of all the boundary constants that appear in the solutions of thedifferential equations. The results for master integrals are expressed in termsof Chen's iterated integrals with dlog one-forms.

Master integrals for ${\cal O}(\alpha \alpha_s)$ corrections to $H \to ZZ^*$