Extraction of the width of the W boson from measurements of $\sigma (p\overline{p}\to W+X)\times B\left(\overrightarrow{W}e\nu \right)$ and $\sigma (p\overline{p}\to Z+X)\times B\left(\overrightarrow{Z}ee\right)$ and their ratio

We report on measurements on inclusive cross sections times branching fractions into electrons for W and Z bosons produced in $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}\mathrm{TeV}.$ From an integrated luminosity of 84.5 ${\mathrm{pb}}^{\mathrm{-}1}$ recorded in 1994–1995 using the DØ detector at the Fermilab Tevatron, we determine $\sigma (p\overline{p}\to W+X)\times B\left(\overrightarrow{W}e\nu \right)=2310\mathrm{}\pm 10\mathrm{}\left(\mathrm{stat}\right)\mathrm{}\pm 50\mathrm{}\left(\mathrm{syst}\right)\mathrm{}\pm 100\mathrm{}\left(\mathrm{lum}\right)\mathrm{pb}$ and $\sigma (p\overline{p}\to Z+X)\times B\left(\overrightarrow{Z}ee\right)=221\mathrm{}\pm 3\mathrm{}\left(\mathrm{stat}\right)\mathrm{}\pm 4\mathrm{}\left(\mathrm{syst}\right)\mathrm{}\pm 10\mathrm{}\left(\mathrm{lum}\right)\mathrm{pb}.$ From these, we derive $\sigma (p\overline{p}\to W+X)\times B\left(\overrightarrow{W}e\nu \right)/\sigma (p\overline{p}\to Z+X)\times B\left(\overrightarrow{Z}ee\right)=10.43\mathrm{}\pm 0.15\mathrm{}\left(\mathrm{stat}\right)\mathrm{}\pm 0.20\mathrm{}\left(\mathrm{syst}\right)\mathrm{}\pm 0.10\mathrm{}\left(\mathrm{NLO}\right)\mathrm{},$ $B\left(\overrightarrow{W}e\nu \right)=0.1044\mathrm{}\pm 0.0015\mathrm{}\left(\mathrm{stat}\right)\mathrm{}\pm 0.0020\mathrm{}\left(\mathrm{syst}\right)\mathrm{}\pm 0.0017\mathrm{}\left(\mathrm{theory}\right)\mathrm{}\pm 0.0010\mathrm{}\left(\mathrm{NLO}\right)\mathrm{},$ and ${\Gamma }_W=2.169\mathrm{}\pm 0.031\mathrm{}\left(\mathrm{stat}\right)\mathrm{}\pm 0.042\mathrm{}\left(\mathrm{syst}\right)\mathrm{}\pm 0.041\mathrm{}\left(\mathrm{theory}\right)\mathrm{}\pm 0.022\mathrm{}\left(\mathrm{NLO}\right)\mathrm{GeV}.$ We use the latter to set a 95% confidence level upper limit on the partial decay width of the W boson into nonstandard model final states, ${\Gamma }_W^{\mathrm{inv}},$ of 0.213 GeV. Combining these results with those from the 1992–1993 data gives $\sigma (p\overline{p}\to W+X)\times B\left(\overrightarrow{W}e\nu \right)/\sigma (p\overline{p}\to Z+X)\times B\left(\overrightarrow{Z}ee\right)=10.51\mathrm{}\pm 0.25,$