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An improved efficient method of calculating the hard bremsstrahlungcorrection to e^+ e^- -> 4f for non-zero fermion masses is presented. Thenon-vanishing fermion masses allow us to perform the phase space integrationsto the very collinear limit. We therefore can calculate cross sectionsindependent of angular cuts. Such calculations are important for backgroundstudies. Results are presented for the total and some differential crosssections for e^+ e^- -> u d-bar mu^- nu and the corresponding hardbremsstrahlung process. The latter is of particular interest for a detailedinvestigation of the effects of final state radiation. In principle, theprocess e^+ e^- -> u d-bar mu^- nu gamma is also interesting since it helps toset bounds on possible anomalous triple and quartic gauge boson couplingsinvolving photons. The size of mass effects is illustrated by comparing thefinal states u d-bar mu^- nu (gamma), c s-bar mu^- nu (gamma) and u d-bar tau^-nu(gamma).Comment: 18 pages, 6 figure

The hard bremsstrahlung correction to $e^+ e^- \to 4f$ with finite fermion masses: results for $e^+ e^- \to u \bard} \mu^- \bar{\nu}_{\mu}$