Hypergeometric representation of the two - loop equal mass sunrise diagram
نویسنده
چکیده
A recurrence relation between equal mass two-loop sunrise diagrams differing in dimensionality by 2 is derived and it's solution in terms of Gauss' 2 F 1 and Appell's F 2 hypergeometric functions is presented. For arbitrary space-time dimension d the imaginary part of the diagram on the cut is found to be the 2 F 1 hypergeometric function with argument proportional to the maximum of the Kibble cubic form. The analytic expression for the threshold value of the diagram in terms of the hypergeometric function 3 F 2 of argument −1/3 is given.
منابع مشابه
The analytic value of the sunrise self - mass with two equal masses and the external invariant equal to the third squared mass
We consider the two-loop self-mass sunrise amplitude with two equal masses M and the external invariant equal to the square of the third mass m in the usual d-continuous dimensional regularization. We write a second order differential equation for the amplitude in x = m/M and show as solve it in close analytic form. As a result, all the coefficients of the Laurent expansion in (d − 4) of the am...
متن کاملar X iv : h ep - t h / 06 04 11 3 v 1 1 6 A pr 2 00 6 Dispersive calculation of the massless multi - loop sunrise diagram
The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.
متن کاملar X iv : h ep - t h / 06 04 11 3 v 2 2 M ay 2 00 6 Dispersive calculation of the massless multi - loop sunrise diagram
The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.
متن کاملDispersive calculation of the massless multi-loop sunrise diagram
The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and explained. The result displays the high energy behaviour of the massive sunrise diagrams, whose calculation is involved already for the two-loop case.
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