A New Method to Measure the Ratio of~$W$ and~$Z$ Cross Sections

We present a new method for measuring the ratio, $R$, of the cross sections for~$W$ and~$Z$ production in $p\bar{p}$~collisions at the Fermilab Tevatron. A combined sample of $W$ and $Z$ boson candidates is selected by requiring at least one charged lepton and low net hadronic activity. The~$p_T$ spectrum of the leptons is used to infer the relative rate of $W$ and $Z$ production. We obtain a preliminary measurement of~$R$ using data collected with the CDF~II detector corresponding to an integrated luminosity of approximately $350$~pb$^{-1}$ and extract an indirect value for the width of the $W$~boson.