Strategy for discovering a low-mass Higgs boson at the Fermilab Tevatron

We have studied the potential of the CDF and DZero experiments to discover a low-mass Standard Model Higgs boson, during Run II, via the processes $p\bar{p}$ -> WH -> $\ell\nu b\bar{b}$, $p\bar{p}$ -> ZH -> $\ell^{+}\ell^{-}b\bar{b}$ and $p\bar{p}$ -> ZH ->$\nu \bar{\nu} b\bar{b}$. We show that a multivariate analysis using neural networks, that exploits all the information contained within a set of event variables, leads to a significant reduction, with respect to {\em any} equivalent conventional analysis, in the integrated luminosity required to find a Standard Model Higgs boson in the mass range 90 GeV/c**2 < M_H < 130 GeV/c**2. The luminosity reduction is sufficient to bring the discovery of the Higgs boson within reach of the Tevatron experiments, given the anticipated integrated luminosities of Run II, whose scope has recently been expanded.