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
ppΛβ -> WH -> βΞ½bbΛ, ppΛβ -> ZH ->
β+ββbbΛ and ppΛβ -> ZH ->Ξ½Ξ½ΛbbΛ. 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.Comment: 26 pages, 8 figures, 7 tables, to appear in Physical Review D, Minor
fixes and revision