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

F. Jegerlehner; K. Kołodziej

doi:doi:10.1007/s100529900202

2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 12, 77-86
DOI 10.1007/s100529900202

The hard bremsstrahlung correction to $e^+ e^- \rightarrow4f$
with finite fermion masses: results for $e^+ e^- \rightarrow u \bar{d} \mu^- \bar{\nu}_{\mu}$

F. Jegerlehner¹ - K. Ko $\l$ odziej²

¹ Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15768 Zeuthen, Germany
² Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40007 Katowice, Poland

Received: 5 July 1999 / Published online: 16 November 1999

Abstract
An improved efficient method of calculating the hard bremsstrahlung correction to $e^+ e^- \rightarrow4f$ for non-zero fermion masses is presented. The non-vanishing fermion masses allow us to perform the phase space integrations to the very collinear limit. We therefore can calculate cross sections independent of angular cuts. Such calculations are important for background studies. Results are presented for the total and some differential cross sections for $e^+ e^- \rightarrow u \bar{d} \mu^- \bar{\nu}_{\mu}$ and the corresponding hard bremsstrahlung process. The latter is of particular interest for a detailed investigation of the effects of final state radiation. In principle, the process $e^+ e^- \rightarrow u \bar{d} \mu^- \bar{\nu}_{\mu}\gamma$ is also interesting since it helps to set bounds on possible anomalous triple and quartic gauge boson couplings involving photons. The size of mass effects is illustrated by comparing the final states $u \bar{d} \mu^- \bar{\nu}_{\mu}(\gamma)$ , $c \bar{s} \mu^- \bar{\nu}_{\mu}(\gamma)$ and $u \bar{d} \tau^- \bar{\nu}_{\tau}(\gamma)$ .