MS vs. Pole Masses of Gauge Bosons: Electroweak Bosonic Two-Loop Corrections

Abstract

The relationship between MS and pole masses of the vector bosons Z and W is calculated at the two-loop level in the Standard Model. We only consider the purely bosonic contributions which represents a gauge invariant subclass of diagrams. All calculations were performed in the linear $R_{\xi }$ gauge with three arbitrary gauge parameters utilizing the method of asymptotic expansions. The results are presented in analytic form as series in the small parameters ${\sin }^2{\theta }_W$ and mass ratio $m_Z^2/m_H^2$. As a byproduct we obtain the bosonic two-loop contributions to the renormalization of the weak mixing parameter ${\sin }^2{\theta }_W$ and of the Fermi constant. The running of Fermi constant will become important at high energy colliders.

LaTeX, 36 p., 10 fig.; in v3 more technical details about renormalization procedure are added

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