Three loop top quark contributions to the ρ parameter

Abstract

We present results for the three-loop top quark contributions to the ρ parameter in the limit of large top quark mass. The simultaneous dependence on the mass of the Higgs boson M H and the mass of the top quark m t is obtained from expansions in the range of M H around m t and in the limit M H ⪢ m t . In combination with the previous result for M H =0 the dependence of the ρ parameter on the leading Yukawa contributions, i.e., on m t and M H , is well under control for all mass values of practical importance. The effects lead to a shift in the W mass in the order of 5 MeV and are relevant for precision measurements at TESLA.