Three loop master integrals for $\mathcal{O}(\alpha {\alpha }_s^2)$ corrections to quark form factor

We consider the three-loop mixed strong-electroweak ($\mathcal{O}(\alpha {\alpha }_s^2)$) corrections to the quark form factor. We compute the master integrals which are appearing in the Feynman diagrams containing a single massive boson in the loop. We use the state-of-the-art method of differential equations to compute all 303 of them, expressing the results in terms of generalized polylogarithms. We encounter multiple square roots that cannot be simultaneously rationalized using a single transformation. Applying concurrent transformations allows us to express the results through generalized polylogarithms with a simple alphabet, but with multiple interdependent arguments.