Upper and Lower Limits on Neutralino WIMP Mass and Spin--Independent Scattering Cross Section, and Impact of New (g-2)_(mu) Measurement

We derive the allowed ranges of the spin--independent interaction cross section $\sigsip$ for the elastic scattering of neutralinos on proton for wide ranges of parameters of the general Minimal Supersymmetric Standard Model. We investigate the effects of the lower limits on Higgs and superpartner masses from colliders, as well as the impact of constraints from $\bsgamma$ and the new measurement of $\gmtwo$ on the upper and lower limits on $\sigsip$. We further explore the impact of the neutralino relic density, including coannihilation, and of theoretical assumptions about the largest allowed values of the supersymmetric parameters. For $\mu>0$, requiring the latter to lie below $1\tev$ leads to $\sigsip\gsim 10^{-11}\pb$ at $\mchi\sim100\gev$ and $\sigsip\gsim 10^{-8}\pb$ at $\mchi\sim1\tev$. When the supersymmetric parameters are allowed above $1\tev$, for $440\gev \lsim \mchi\lsim 1020 \gev$ we derive a {\em parameter--independent lower limit} of $\sigsip \gsim 2\times 10^{-12}\pb$. (No similar lower limits can be set for $\mu<0$ nor for $1020\gev\lsim\mchi\lsim2.6\tev$.) Requiring $\abundchi<0.3$ implies a {\em parameter--independent upper limit} $\mchi\lsim2.6\tev$. The new $\epem$--based measurement of $(g-2)_{\mu}$ restricts $\mchi\lsim 350\gev$ at $1 \sigma$ CL and $\mchi\lsim515\gev$ at $2 \sigma$ CL, and implies $\mu>0$. The largest allowed values of $\sigsip$ have already become accessible to recent experimental searches.