Measurement of W and Z boson production cross sections in $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}$ TeV

DØ has measured the inclusive production cross section of W and Z bosons in a sample of 13 ${\mathrm{pb}}^{-1}$ of data collected at the Fermilab Tevatron. The cross sections, multiplied by their leptonic branching fractions, for production in $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}$ TeV are ${\sigma }_W\mathrm{B}\left(\overrightarrow{W}e\nu \right)=2.36\mathrm{}\pm 0.02\pm 0.08\pm 0.13\mathrm{}\mathrm{nb},$ ${\sigma }_W\mathrm{B}\left(\overrightarrow{W}\mu \nu \right)=2.09\mathrm{}\pm 0.06\pm 0.22\pm 0.11\mathrm{}\mathrm{nb},$ ${\sigma }_Z\mathrm{B}\left(\overrightarrow{Z}{e}^{+}{e}^{-}\right)=0.218\mathrm{}\pm 0.008\pm 0.008\pm 0.012\mathrm{}\mathrm{nb}$, and ${\sigma }_Z\mathrm{B}\left(\overrightarrow{Z}{\mu }^{+}{\mu }^{-}\right)=0.178\mathrm{}\pm 0.022\pm 0.021\pm 0.009\mathrm{}\mathrm{nb}$, where the first uncertainty is statistical and the second systematic; the third reflects the uncertainty in the integrated luminosity. For the combined electron and muon analyses, we find ${\sigma }_W\mathrm{B}\left(\overrightarrow{W}l\nu \right)/{\sigma }_Z\mathrm{B}\left(\overrightarrow{Z}{l}^{+}{l}^{-}\right)=10.90\mathrm{}\pm 0.52$. Assuming standard model couplings, we use this result to determine the width of the W boson, and obtain $\Gamma \mathrm{}\left(W\right)=2.044\mathrm{}\pm 0.097\hspace{0.5em}\mathrm{GeV}$.