Three Loop Top Quark Contributions to the rho Parameter

Abstract

We present results for the three-loop top quark contributions to the rho 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 rho 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.

15 pages, 8 figures; Eqs. 8, 9, 11, 12, 20, and 21, relevant for the limit of large M_H, are modified. Numerical results, figures, and conclusion remain unaffected

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