Bananas of equal mass: any loop, any order in the dimensional regularisation parameter

Understand

We describe a systematic approach to cast the differential equation for the $l$-loop equal mass banana integral into an $\varepsilon$-factorised form.

• With the known boundary value at a specific point we obtain systematically the term of order $j$ in the expansion in the dimensional regularisation parameter $\varepsilon$ for any loop $l$.
• The approach is based on properties of Calabi-Yau operators, and in particular on self-duality.