Coherent exclusive exponentiation for precision Monte Carlo calculations

We present the new coherent exclusive exponentiation (CEEX), the older exclusive exponentiation (EEX), and the semianalytical inclusive exponentiation (IEX) for the process ${e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}f\overline{f}+n\ensuremath{\gamma},$ where $f=\ensuremath{\mu},\ensuremath{\tau},d,u,s,c,b,$ which are valid for center-of-mass energies from the $\ensuremath{\tau}$ lepton threshold to 1 TeV, that is, for CERN LEP1, LEP2, the SLC, future linear colliders, and $b,c,\ensuremath{\tau}$ 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 exponentiation) and for realistic experimental cuts. The physical precision and technical precision are determined for the total cross section and for the charge asymmetry.