Massive kite diagrams with elliptics

TL;DR

This paper derives explicit two-loop massive kite master integrals involving elliptic functions, using new integral representations and differential equations, demonstrating the broad applicability of iterated integrals with algebraic kernels in quantum field theory calculations.

Contribution

It introduces novel integral representations and differential equations for massive kite integrals with elliptics, enabling generalization to all orders in epsilon expansion.

Findings

Results expressed in terms of iterated integrals with algebraic kernels

Method applicable to a wide class of massive Feynman diagrams

Potential for simplifying complex multi-loop calculations

Abstract

We present the results for two-loop massive kite master integrals with elliptics in terms of iterated integrals with algebraic kernels. The key ingredients are new integral representations for sunset subgraphs in $d=4-2\epsilon$ and $d=2-2\epsilon$ dimensions together with differential equations for considered kite master integrals in $A+B\epsilon$ form. The obtained results can be easily generalized to all orders in $\epsilon$-expansion and show that the class of functions defined as iterated integrals with algebraic kernels may be large enough for writing down results for a large class of massive Feynman diagrams.