Working out some quantum field theory computations, I have to find out the value of the two-loop Feynman integral I(p)=∫d4p1(2π)4d4p2(2π)41(p21+m21)(p2+m22)[(p−p1−p2)2+m23].
Thanks beforehand.
Answer
In the case of equal masses, there is an analytical solution (of this diagram known by the name "the two loop sunrise diagram" for the obvious reason) in terms of hypergeometric functions given by O.V. Tarasov (equation 4.32). There is also a numerical method given by: Pozzorini and Remiddi.
In the case of unequal masses Müller-Stach, Weinzierl and Zayadeh were able to obtain a second order differential equation for this graph.
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