Speaker
Sara Maggio
Description
The three-loop banana integral with three equal masses in two dimensions is related to a two-parameter family of K3 surfaces. First, I will show that the periods and the mirror map can be expressed in terms of ordinary modular forms and functions. As a result, its maximal cuts can be written as a product of two copies of the maximal cuts of the two-loop equal-mass sunrise integral. Secondly, I will show how to get an eps-factorised differential equation for integrals with un underlying K3 surface. Finally, combining these two steps, I will indicate how to derive an analytic solution for this three-loop integral dependent on two kinematic scales.
