If the Higgs boson indeed weighs about 114 to 115 GeV, there must be new
physics beyond the Standard Model at some scale \la 10^6 GeV. The most
plausible new physics is supersymmetry, which predicts a Higgs boson weighing
\la 130 GeV. In the CMSSM with R and CP conservation, the existence, production
and detection of a 114 or 115 GeV Higgs boson is possible if \tan\beta \ga 3.
However, for the radiatively-corrected Higgs mass to be this large, sparticles
should be relatively heavy: m_{1/2} \ga 250 GeV, probably not detectable at the
Tevatron collider and perhaps not at a low-energy e^+ e^- linear collider. In
much of the remaining CMSSM parameter space, neutralino-stau coannihilation is
important for calculating the relic neutralino density, and we explore
implications for the elastic neutralino-nucleon scattering cross section.Comment: 17 pages, 5 eps figure
