283 research outputs found
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
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