Measurement of $\sigma B(W\to e\nu )$ and $\sigma B(Z^0\to e^{+}{e}^{-})$ in $\overline{p}p$ collisions at $\sqrt{s}=1800\mathrm{}$ GeV

An analysis of high-transverse-momentum electrons using data from the Collider Detector at Fermilab (CDF) of $\overline{p}p$ collisions at $\sqrt{s}=1800\mathrm{}$ GeV yields values of the production cross section times branching ratio for $W$ and $Z^0$ bosons of $\sigma (\overline{p}p\to \mathrm{WX}\to e\nu X)=2.19\mathrm{}\pm 0.04\left(\mathrm{stat}\right)\pm 0.21\left(\mathrm{syst}\right)$ nb and $\sigma (\overline{p}p\to Z^{0}X\to e^{+}{e}^{-}X)=0.209\mathrm{}\pm 0.013\left(\mathrm{stat}\right)\pm 0.017\left(\mathrm{syst}\right)$ nb. Detailed descriptions of the CDF electron identification, background, efficiency, and acceptance are included. Theoretical predictions of the cross sections that include a mass for the top quark larger than the $W$ mass, current values of the $W$ and $Z^0$ masses, and higher-order QCD corrections are in good agreement with these measured values.