We present the Monte Carlo event generator KK version 4.13 for precision predictions of the Electroweak Standard Model for the process e + e − → ff + nγ, f = µ, τ, d, u, s, c, b, at centre-of-mass energies from τ lepton threshold to 1 TeV, that is for LEP, SLC, future Linear Colliders, b, c, τ -factories, etc. Effects due to photon emission from initial beams and outgoing fermions are calculated in QED up to second order, including all interference effects, within Coherent Exclusive Exponentiation (CEEX), which is based on Yennie-Frautschi-Suura exponentiation. Electroweak corrections are included in first order, with higher-order extensions, using the DIZET 6.21 library. Final-state quarks hadronize according to the parton shower model using JETSET. Beams can be polarized longitudinally and transversely. Decay of the τ leptons is simulated using the TAUOLA library, taking into account spin polarization effects as well. In particular the complete spin correlations density matrix of the initial-state beams and final state τ 's is incorporated in an exact manner. Effects due to beamstrahlung are simulated in a realistic way. The main improvements with respect to KORALZ are: (a) inclusion of the initial-final state QED interference, (b) inclusion of the exact matrix element for two photons, and (c) inclusion of the transverse spin correlations in τ decays (as in KORALB). To appear in Computer Physics Nature of the physical problem:The fermion pair production is and will be used as an important data point for precise tests of the standard electroweak theory at LEP and future linear colliders at higher energies. QED corrections to fermion pair production (especially τ leptons) at c-quark and b-quark factories has to be known to second order, including spin polarization effects. The Standard Model predictions at the per mille precision level, taking into account multiple emission of photons for realistic experimental acceptance, can only be obtained using a Monte Carlo event generator. Method of solution:The Monte Carlo methods are used to simulate most of the twofermion final-state processes in e + e − collisions in the presence of multiphoton initial-state radiation. The latter is described in the framework of exclusive coherent exponentiation (CEEX) based on Yennie-Frautschi-Suura exclusive exponentiation (YFS/EEX). CEEX treats correctly to infinite order not only infrared cancellations but also QED interferences and narrow resonances. The matrix element according to standard YFS exponentiation is also provided for tests. For quarks and τ leptons, the appropriate simulation of hadronization or decay is included. Beam polarization and spin effects, both longitudinal and transverse, in tau decays are properly taken into account. Restrictions on the complexity of the problem: In the present version, electron (Bhabha), neutrino and top quark final states are not included (they will be in a future version). Additional fermion pair production is not included. Third-order QED corrections in leading-logarithmic ap...

This paper documents an update of the PHOTOS algorithm, by E. Barberio, B. van Eijk and Z. Was, for the Monte Carlo simulation of QED photon radiative corrections in decays. The algorithm is implemented as an independent package written in FORTRAN 77. The program is universal, i.e. it allows for easy interface with \any" program generating decays of \any" particle. The program can be used to estimate the size of the QED bremsstrahlung in the leading-logarithmic (collinear) approximation, but it provides nal states with their full topology, including kinematical e ects due to massive particles. The proper soft photon behaviour is also reproduced. The algorithm is designed in such a w a y that the inclusion (if necessary) of the exact, process-dependent, matrix element subgenerator is possible and straightforward. This update of PHOTOS provides new options to improve the performances of the program in some speci c cases: the interference for two-body particle-antiparticle decays, the double bremsstrahlung, and re nements important for the decays into massive non-relativistic decay products. leptons, resonances, particle decays, Monte Carlo simulation, quantum electrodynamics, leading-log approximations. Nature of physical problem: Most of the decay modes of particles or resonances are accompanied by the QED real photon corrections. The presence of (a) hard photon(s) may a ect the shape of the measured distributions, detection e ciencies and/or experimental selection criteria. Method of solution: The Monte Carlo simulation is best suited for studying the combined process of production and decay of unstable particles, including QED corrections and detector e ciencies. Restrictions on the complexity of the problem: The QED O( ) and O( 2 ) corrections are implemented in the leading-logarithm approximation with the proper soft photon behaviour. Emission of non-collinear hard photons is simulated, but the validity of distribution may be restricted.Typical running time: 500 events/sec (VAX station 4000-90) for the Z ! + decay mode.

We present a discussion of the precision for the PHOTOS Monte Carlo algorithm, with improved implementation of QED interference and multiple-photon radiation. The main application of PHOTOS is the generation of QED radiative corrections in decays of any resonances, simulated by a "host" Monte Carlo generator. By careful comparisons automated with the help of the MC-TESTER tool specially tailored for that purpose, we found that the precision of the current version of PHOTOS is of 0.1% in the case of Z and W decays. In the general case, the precision of PHOTOS was also improved, but this will not be quantified here.To be submitted to EPJC

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We present the new coherent exclusive exponentiation ͑CEEX͒, the older exclusive exponentiation ͑EEX͒, and the semianalytical inclusive exponentiation ͑IEX͒ for the process e Ϫ e ϩ → f fϩn␥, where f ϭ , ,d,u,s,c,b, which are valid for center-of-mass energies from the lepton threshold to 1 TeV, that is, for CERN LEP1, LEP2, the SLC, future linear colliders, and b,c, factories, etc. The approaches are based on Yennie-Frautschi-Suura exponentiation. In CEEX, the effects due to photon emission from initial beams and outgoing fermions are calculated in QED up to second order, including all interference effects. Electroweak corrections are included to first order, at the amplitude level. Beams can be polarized longitudinally and transversely, and all spin correlations are incorporated in an exact manner. The EEX is more primitive, lacks initial-final interferences, but it is valuable for testing the newer CEEX. The IEX provides us with a set of sophisticated semianalytical formulas for the total cross section and selected inclusive distributions, which are mainly used for cross-checks of the Monte Carlo results. We analyze numerical results at the Z peak, 189 GeV and 500 GeV for simple kinematical cuts ͑comparisons with inclusive exponentiation͒ and for realistic experimental cuts. The physical precision and technical precision are determined for the total cross section and for the charge asymmetry.

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