Search for New Physics and the Higgs Boson in the $b\bar{b}$ plus Missing $E_T$ Signature

Using the data taken by the CDF detector in Run II of the Tevatron, we have analysed events containing two jets and missing transverse energy in order to estimate the possible presence of new physics. At least one of the jets is required to be tagged as originating from a b quark in order to enhance the presence of $b\bar{b}$ pairs. The analysis is optimized for the search for a light Higgs boson produced in association with a Z boson decaying into a pair of neutrinos. Preliminary results, based on an integrated luminosity of about $300$ pb$^{-1}$, are presented as well as future plans for the search for the Higgs boson in this channel.