The unequal mass sunrise integral expressed through iterated integrals on $\overline{\mathcal M}_{1,3}$

Understand

We solve the two-loop sunrise integral with unequal masses systematically to all orders in the dimensional regularisation parameter $\varepsilon$.

• In order to do so, we transform the system of differential equations for the master integrals to an $\varepsilon$-form.
• The sunrise integral with unequal masses depends on three kinematical variables.
• We perform a change of variables to standard coordinates on the moduli space ${\mathcal M}_{1,3}$ of a genus one Riemann surface with three marked points.