Abstract
We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order differential equations for one- and two-loop sunrise diagrams that have recently been discussed in the literature.
Highlights
IntroductionThe paper is organized as follows: In Sect. 2 we introduce the configuration space techniques which will be used in Sect. 3 to check the differential equations for one-loop sunrise-type diagrams
We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams which we use to numerically check on the correctness of the second order differential equations for one- and two-loop sunrise diagrams that have recently been discussed in the literature
The paper is organized as follows: In Sect. 2 we introduce the configuration space techniques which will be used in Sect. 3 to check the differential equations for one-loop sunrise-type diagrams
Summary
The paper is organized as follows: In Sect. 2 we introduce the configuration space techniques which will be used in Sect. 3 to check the differential equations for one-loop sunrise-type diagrams. The paper is organized as follows: In Sect. we introduce the configuration space techniques which will be used in Sect. to check the differential equations for one-loop sunrise-type diagrams. we check the differential equations for the two-loop sunrise diagrams for the equal mass case, while in Sect. we will deal with nondegenerate cases. Our conclusions can be found in Sect. 6. Even though the configuration space techniques are well suited to treat general D = 4 space-time dimensions, we will mainly deal with the case of D = 2 space-time dimensions in this paper. Throughout this paper we work in the Euclidean domain. The transition to the Minkowskian domain can be obtained as usual by a Wick rotation (or, equivalently, by replacing p2 → −p2)
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