Hypergeometric representation of the two-loop equal mass sunrise diagram

Preprint

28 March 2006

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.hep-ph/0603227

Abstract

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' 2F1 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 2F1 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 3F2 of argument -1/3 is given.

Keywords

HYPERGEOMETRIC REPRESENTATION
SUNRISE DIAGRAMS
THRESHOLD VALUE
MASS SUNRISE
LOOP EQUAL
EQUAL MASS
CUBIC FORM
TWO LOOP

All Related Versions

Version 1, 2006-03-28, ArXiv
Published version: Physics Letters B, 638 (2-3), 195.

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