# The $\rho$ parameter at three loops and elliptic integrals

@article{Blumlein2018TheP,
title={The \$\rho\$ parameter at three loops and elliptic integrals},
author={J. Blumlein and A. Freitas and M. V. Hoeij and E. Imamoglu and P. Marquard and C. Schneider},
journal={arXiv: High Energy Physics - Phenomenology},
year={2018}
}
• J. Blumlein, +3 authors C. Schneider
• Published 2018
• Physics, Mathematics
• arXiv: High Energy Physics - Phenomenology
• We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ 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… CONTINUE READING
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