The hard bremsstrahlung in e+e- → 4f with non-zero fermion masses

An efficient method for calculating polarized matrix elements of the four fermion reactions e(+)e(-) --> 4f and corresponding hard bremsstrahlung reactions with non-zero fermion masses is discussed. The numerical results for the total cross sections and some differential cross sections of e(+)e(-) -, u (d) over bar mu-<(nu)over bar>(mu) and e(+)e(-) --> u (d) over bar mu-<(nu)over bar>(mu)gamma are given. The dependence on the fermion masses is illustrated by comparing the hard bremsstrahlung corrections to different semi-leptonic channels.