Three-loop master integrals for the Higgs boson self-energy with internal top-quarks and W-bosons

We consider the full set of master integrals with internal top-and $W$-propagators contributing to the three-loop Higgs self-energy diagrams of order $\mathcal{O}({\alpha }^2{\alpha }_s)$. We split the master integrals into a system relevant to the Feynman diagrams proportional to the product of Yukawa couplings $y_b{y}_t$ and the complement. For both systems we define master integrals of uniform weight, such that the associated differential equation is in $\epsilon$-factorised form. The occurring square roots are rationalised and all master integrals are expressible in multiple polylogarithms.