Optimal Belief Approximation

In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a loss function that quantifies how "embarrassing" it is to communicate a given approximation. We reproduce and discuss an old proof showing that there is only one ranking under the requirements that (1) the best ranked approximation is the non-approximated belief and (2) that the ranking judges approximations only by their predictions for actual outcomes. The loss function that is obtained in the derivation is equal to the Kullback-Leibler divergence when normalized. This loss function is frequently used in the literature. However, there seems to be confusion about the correct order in which its functional arguments, the approximated and non-approximated beliefs, should be used. The correct order ensures that the recipient of a communication is only deprived of the minimal amount of information. We hope that the elementary derivation settles the apparent confusion. For example when approximating beliefs with Gaussian distributions the optimal approximation is given by moment matching. This is in contrast to many suggested computational schemes.Comment: made improvements on the proof and the languag

ZZ' Mixing in Presence of Standard Weak Loop Corrections

We derive a method for a common treatment of Z' exchange, QED corrections, and weak loops. It is based on the form factor approach to the description of weak loop corrections to partial Z widths and cross sections. Problems connected with ZZ' mixing are discussed with special care. Our theoretical results are applied to the package ZFITTER. We demonstrate two different ways to the data analysis - one based on an extension of the standard model cross sections, the other on model-independent formulae together with the Z width calculations in presence of a Z'. With the resulting package ZEFIT+ZFITTER, LEP1 data from fermion pair production, including Bhabha scattering, can be analysed on, but also off the Z peak. Further, the code may be used at very high energies, e.g. in the region of a possible future linear e+e- collider.Comment: Latex, 24 pages, a typo in eqs. 23,24 correcte

Elektroweak one-loop corrections for e^+e^- annihilation into t\bar{t} including hard bremsstrahlung

We present the complete electroweak one-loop corrections to top-pair production at a linear e^+e^- collider in the continuum region. Besides weak and photonic virtual corrections, real hard bremsstrahlung with simple realistic kinematical cuts is included. For the bremsstrahlung we advocate a semi-analytical approach with a high numerical accuracy. The virtual corrections are parametrized through six independent form factors, suitable for Monte-Carlo implementation. Alternatively, our numerical package topfit, a stand-alone code, can be utilized for the calculation of both differential and integrated cross sections as well as forward--backward asymmetries.Comment: 34 page

Status of Electroweak Corrections to Top Pair Production

We review the status of electroweak radiative corrections to top-pair production at a Linear Collider well above the production threshold. We describe the Fortran package topfit and present numerical results at sqrt(s) = 500 GeV, 1 TeV, and 3 TeV.Comment: 6 pages, LaTex, 2 tables, 1 figure, talk presented by T.R. at the Int. Workshop on Linear Colliders (LCWS 2002), 26-30 Aug 2002, Jeju Island, Kore