The $\rho$ parameter at three loops and elliptic integrals
Abstract
We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the parameter. In particular, we present the calculation of the master integrals for which the corresponding differential equations do not factorize to first order. The homogeneous solutions to these differential equations are obtained in terms of hypergeometric functions at rational argument. These hypergeometric functions can further be mapped to complete elliptic integrals, and the inhomogeneous solutions are expressed in terms of a new class of integrals of combined iterative non-iterative nature.
Cite
@article{arxiv.1807.05287,
title = {The $\rho$ parameter at three loops and elliptic integrals},
author = {J. Blümlein and A. De Freitas and M. van Hoeij and E. Imamoglu and P. Marquard and C. Schneider},
journal= {arXiv preprint arXiv:1807.05287},
year = {2018}
}
Comments
14 pages Latex, 7 figures, to appear in the Proceedings of "Loops and Legs in Quantum Field Theory - LL 2018", 29 April - 4 May 2018, PoS