Search for Standard Model Higgs Boson Production in Association with $W^{\pm}$ Bosons at CDF

We present a search for the Standard Model Higgs boson decaying into $b\bar{b}$ after being produced in association with a $W^{\pm}$ boson in the $p\bar{p}$ collisions at $\sqrt{s}=1.96$~TeV. The search uses the data collected up to fall 2005 using the CDF detector, which corresponds to an integrated luminosity of about 700~$pb^{-1}$. Events with an electron or muon, large missing transverse energy and jets are selected using an advanced multivariate technique and at least one of the jets is required to be $b$-tagged for further reduction of the large $W^{\pm}+$jet background. We set a limit on the $p\bar{p}\rightarrow W^{\pm}H$ production cross section.