An Improved W Boson Mass Measurement using the Collider Detector at Fermilab

The mass of the $W$ boson is one of the most important parameters in the

Standard Model. A precise measurement of the $W$ boson mass, together

with a precise measurement of the top quark mass, can constrain the

mass of the undiscovered Higgs boson within the Standard Model

framework or give a hint for physics beyond the Standard Model.

This dissertation describes a measurement of the $W$ boson mass

through its decay into a muon and a neutrino using

$\approx$ 2.2 fb$^{-1}$ of $\sqrt{s} = 1.96$ TeV $p\bar{p}$ data taken

with the CDF II detector at Fermilab. We measure the $W$ boson mass

to be ($80.374 \pm 0.015_{\rm stat.} \pm 0.016_{\rm syst.}$)

GeV/c$^2$. This result, when combined with the $W$ mass

measurement in the electron channel, leads to the single most

precise $m_W$ value and greatly constrains the possible mass

range of the undiscovered Higgs boson.