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We present a search for the Higgs boson in the process $q\bar{q} \to ZH \to\ell^+\ell^- b\bar{b}$. The analysis uses an integrated luminosity of 1fb$^{-1}$ of $p\bar{p}$ collisions produced at $\sqrt{s} =$ 1.96 TeV andaccumulated by the upgraded Collider Detector at Fermilab (CDF II). We employartificial neural networks both to correct jets mismeasured in the calorimeter,and to distinguish the signal kinematic distributions from those of thebackground. We see no evidence for Higgs boson production, and set 95% CL upperlimits on $\sigma_{ZH} \cdot {\cal B}(H \to b\bar{b}$), ranging from 1.5 pb to1.2 pb for a Higgs boson mass ($m_H$) of 110 to 150 GeV/$c^2$.

Search for the Higgs boson produced with $Z \to \ell^+\ell^-$ in $p\bar{p}$ collisions at $\sqrt{s}=$ 1.96 TeV