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

A bstract We consider the three-loop mixed strong-electroweak $$\left(\mathcal{O}\left(\alpha {\alpha }_{s}^{2}\right)\right)$$ 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.