Non-invariant two-loop counterterms for the three-gauge-boson vertices

Some practical applications of algebraic renormalization are discussed. In particular we consider the two-loop QCD corrections to the three-gauge-boson vertices involving photons, Z and W bosons. For this purpose also the corresponding two-point functions have to be discussed. A recently developed procedure is used to analyze the breaking terms of the functional identities and explicit formulae for the universal counterterms are provided. Special attention is devoted to the treatment of infra-red divergences.Comment: Some minor corrections and improved discussion in the one-loop sectio

Width and partial widths of unstable particles

In the gauge theory context, a definition of branching ratios and partial widths of unstable particles is proposed that satisfies the basic principles of additivity and gauge independence. The difference between the new, gauge-independent formulation and the conventional one reflects the fact that unstable particles are not asymptotic states. Aside from restoring the crucial property of gauge independence, the new formulation avoids well-known pitfalls of the conventional approach. (orig.)18 refs.Available from TIB Hannover: RA 2999(00-074) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Width and partial widths of unstable particles in the light of the Nielsen identities

Fundamental properties of unstable particles, including mass, width, and partial widths, are examined on the basis of the Nielsen identities (NI) that describe the gauge dependence of Green functions. In particular, we prove that the pole residues and associated definitions of branching ratios and partial widths are gauge independent to all orders. A simpler, previously discussed definition of branching ratios and partial widths is found to be gauge independent through next-to-next-to-leading order. It is then explained how it may be modified in order to extend the gauge independence to all orders. We also show that the physical scattering amplitude is the most general combination of self-energy, vertex, and box contributions that is gauge independent for arbitrary s, discuss the analytical properties of the NI functions, and exhibit explicitly their one-loop expressions in the Z-#gamma# sector of the Standard Model. (orig.)Available from TIB Hannover: RA 2999(01-120) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

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 noninvariant 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#->#s#gamma#. (orig.)Available from TIB Hannover: RA 2999(01-008) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman