Search for Associated Production of $Z$ and Higgs Bosons in $e^+e^-b\bar{b}$ final states

Studies are presented of the search for a light Standard Model Higgs boson produced in association with a $Z$ boson in the $Z \rightarrow e^+e^-$ and $h \rightarrow b\bar{b}$ decay channel using Run II data collected by the D\O\ detector at the Fermilab $p\bar{p}$ collider at $\sqrt{s} = 1.96$ TeV. A preliminary measurement of the cross section of the $Z$-boson associated production with jets is also presented.