Hypergeometric representation of the two - loop equal mass sunrise diagram

نویسنده

  • O. V. Tarasov
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.

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تاریخ انتشار 2006