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Coherent Exclusive Exponentiation For Precision Monte Carlo Calculations

We present the new Coherent Exclusive Exponentiation (CEEX), the older Exclusive Exponentiation (EEX) and the semi-analytical Inclusive Exponentiation (IEX) for the process $e^+e^-\to f\bar{f} +nγ$, $f=μ,τ,d,u,s,c,b$ with validity for centre of mass energies from $τ$ lepton threshold to 1TeV, that is for LEP1, LEP2, SLC, future Linear Colliders, $b,c,τ$-factories etc. They are based on Yennie-Frautschi-Suura exponentiation. In CEEX 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 in first-order, at the amplitude level. Beams can be polarized longitudinally and transversely, and all spin correlations are incorporated in an exact manner. EEX is more primitive, lacks initial-final interferences, but it is valuable for testing the newer CEEX. IEX provides us set of a sophisticated semi-analytical formulas for the total cross section and selected inclusive distributions which are mainly used for cross-checks of the MC results. We analyse numerical results at the Z-peak 189 GeV and 500 GeV for simple kinematical cuts (comparisons with IEX) and for realistic experimental cuts. Physical precision and technical precision are determined for the total cross section and for the charge asymmetry.