A systematic method for optimizing multivariate discriminants is developed
and applied to the important example of a light Higgs boson search at the
Tevatron and the LHC. The Significance Improvement Characteristic (SIC),
defined as the signal efficiency of a cut or multivariate discriminant divided
by the square root of the background efficiency, is shown to be an extremely
powerful visualization tool. SIC curves demonstrate numerical instabilities in
the multivariate discriminants, show convergence as the number of variables is
increased, and display the sensitivity to the optimal cut values. For our
application, we concentrate on Higgs boson production in association with a W
or Z boson with H -> bb and compare to the irreducible standard model
background, Z/W + bb. We explore thousands of experimentally motivated,
physically motivated, and unmotivated single variable discriminants. Along with
the standard kinematic variables, a number of new ones, such as twist, are
described which should have applicability to many processes. We find that some
single variables, such as the pull angle, are weak discriminants, but when
combined with others they provide important marginal improvement. We also find
that multiple Higgs boson-candidate mass measures, such as from mild and
aggressively trimmed jets, when combined may provide additional discriminating
power. Comparing the significance improvement from our variables to those used
in recent CDF and DZero searches, we find that a 10-20% improvement in
significance against Z/W + bb is possible. Our analysis also suggests that the
H + W/Z channel with H -> bb is also viable at the LHC, without requiring a
hard cut on the W/Z transverse momentum.Comment: 41 pages, 5 tables, 29 figure