Higher Order Corrections to the Hadronic Higgs Decay

A Higgs boson in the intermediate mass range is considered. An effective Lagrangian approach is used in order to evaluate the top-induced QCD corrections of order $\alpha_s^3$ to the decay into light quarks and $O(\alpha_s^4)$ corrections to the gluonic decay mode. The connection to the decoupling relations for $\alpha_s$ and the light quark masses is discussed.Comment: 5 pages (Latex), 5 figures (Postscript), to appear in the Proceedings of the International Europhysics Conference on High Energy Physics, Jerusalem, Israel, 19 - 26 August 199

Short Distance Mass of a Heavy Quark at Order \alpha_s^3

The relation between the on-shell quark mass and the mass defined in the modified minimal subtraction scheme is computed up to order \alpha_s^3. Implications for the numerical values of the top and bottom quark masses are discussed. We show that the new three-loop correction significantly reduces the theoretical uncertainty in the determination of the quark masses.Comment: Latex, 5 page

The Algebraic Method

Combining the effect of an intermediate renormalization prescription (zero momentum subtraction) and the background field method (BFM), we show that the algebraic renormalization procedure needed for the computation of radiative corrections within non-invariant regularization schemes is drastically simplified. The present technique is suitable for gauge models and, here, is applied to the Standard Model. The use of the BFM allows a powerful organization of the counterterms and avoids complicated Slavnov-Taylor identities. Furthermore, the Becchi-Rouet-Stora-Tyutin (BRST) variation of background fields plays a special role in disentangling Ward-Takahashi identities (WTI) and Slavnov-Taylor identities (STI). Finally, the strategy to be applied to physical processes is exemplified for the process $b\to s\gamma$.Comment: Latex, 38 page

High energy behaviour of form factors

We solve renormalization group equations that govern infrared divergences of massless and massive form factors. By comparing to recent results for planar massive three-loop and massless four-loop form factors in QCD, we give predictions for the high-energy limit of massive form factors at the four- and for the massless form factor at five-loop order. Furthermore, we discuss the relation which connects infrared divergences regularized dimensionally and via a small quark mass and extend results present in the literature to higher order.Comment: 21 page

Second Order Corrections to the Muon Lifetime and the Semileptonic B Decay

In this article two-loop QED corrections to the muon decay and corrections of order $\alpha_s^2$ to the semileptonic decay of the bottom quark are considered. We compute the imaginary part of the four-loop diagrams contributing to the corresponding fermion propagator in the limit of small external momentum. The on-shell condition is obtained with the help of a conformal mapping and Pad\'e approximation. Via this method we confirm the existing results by an independent calculation.Comment: LaTeX, 11 pages, 1 figur