Hadron Radiation in Leptonic $Z$ Decays

Abstract

The rate for the final state radiation of hadrons in leptonic $Z$ decays is evaluated, using as input experimental data for $\sigma (e^+e^-\to hadrons)$ in the low energy region. Configurations with a lepton pair of large and a hadronic state of low invariant mass are dominant. A relative rate $\Gamma_{l\bar l had}/\Gamma_{l\bar l}=6.3\times 10^{-4}$ is calculated. This result is about twice the prediction based on a parton model calculation with a quark mass of $300$ MeV. The rate for secondary production of heavy quarks is calculated in the same formalism.