First Measurement of the $W$ Boson Mass with CDF in Run II

We describe a measurement of the $W$ boson mass $m_W$ using $\approx$200 pb$^{-1}$ of $\sqrt{s}$=1.96 TeV $p\bar{p}$ collision data from the Fermilab Tevatron collected with the CDF II detector. Using 63,964 $W\rightarrow e\nu$ candidates and 51,128 $W\rightarrow \mu\nu$ candidates, we measure $m_W = 80.413 \pm 0.034~{\rm (stat)} \pm 0.034~{\rm (sys)}$ GeV/$c^2$. With a total uncertainty of 0.048 GeV/$c^2$, this is the single most precise $m_W$ measurement to date.