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.

Comments: 7 pages, LaTex (uses epsf.sty, 2 figures appended as uuencoded eps files). Errors of some numerical values corrected. Conclusions are not affected by these modifications