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We present a search for associated production of the standard model (SM)Higgs boson and a $Z$ boson where the $Z$ boson decays to two leptons and theHiggs decays to a pair of $b$ quarks in $p\bar{p}$ collisions at the FermilabTevatron. We use event probabilities based on SM matrix elements to construct alikelihood function of the Higgs content of the data sample. In a CDF datasample corresponding to an integrated luminosity of 2.7 fb$^{-1}$ we see noevidence of a Higgs boson with a mass between 100 GeV$/c^2$ and 150 GeV$/c^2$.We set 95% confidence level (C.L.) upper limits on the cross-section for $ZH$production as a function of the Higgs boson mass $m_H$; the limit is 8.2 timesthe SM prediction at $m_H = 115$ GeV$/c^2$.

A Search for the Higgs Boson Produced in Association with $Z\to \ell^+\ell^-$ Using the Matrix Element Method at CDF II