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=4−2ε and d=2−2ε dimensions together with differential equations for considered kite master integrals in A+Bε form. The obtained results can be easily generalized to all orders in ε-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.
Highlights
We have seen a lot of progress in the evaluation of multiloop Feynman diagrams, in particular those with masses
The most impressive results in the realm of massive Feynman diagrams were obtained with the use of differential equation method [1,2,3,4,5]
To be able to write down results for kite diagrams in a chosen class of functions we used new integral representations for sunset subgraphs in d = 4 − 2ε and d = 2 − 2ε dimensions
Summary
We have seen a lot of progress in the evaluation of multiloop Feynman diagrams, in particular those with masses. As a particular example we consider three different two-loop massive kite diagrams, which contain elliptics Among these kite diagrams only one, the one with two massless lines, can be written in terms of elliptic polylogarithms, while the other two require introduction of more complicated structures, which we can call hyperelliptic polylogarithms. To be able to write down results for kite diagrams in a chosen class of functions we used new integral representations for sunset subgraphs in d = 4 − 2ε and d = 2 − 2ε dimensions. We have prepared Mathematica notebook with all required details of calculation and results
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