Higgs funnel region of supersymmetric dark matter for smalltan βand renormalization group effects on pseudoscalar Higgs boson with scalar mass nonuniversality

A nonuniversal scalar mass supergravity type of model is explored where the first two generations of scalars and the third generation of sleptons may be very massive. The lighter or vanishing third generation of squarks as well as Higgs scalars at the unification scale cause the radiative electroweak symmetry breaking constraint to be less prohibitive. Thus, both flavor-changing neutral-current/$CP$-violation problems as well as the naturalness problem are within control. We identify a large slepton mass effect in the renormalization group equations of ${m}_{{H}_{D}}^{2}$ (for the down type of Higgs) that may turn the latter negative at the electroweak scale even for a small $\mathrm{tan} \ensuremath{\beta}$. A hyperbolic branch/focus pointlike effect is found for ${m}_{A}^{2}$ that may result in very light Higgs spectra. The lightest stable particle is dominantly a $b$-ino that pair annihilates via Higgs exchange, giving rise to a Wilkinson Microwave Anisotropy Probe satisfied relic density region for all $\mathrm{tan} \ensuremath{\beta}$. Detection prospects of such lightest stable particles in the upcoming dark matter experiments both of direct and indirect types (photon flux) are interesting. The Higgs bosons and the third generation of squarks are light in this scenario and these may be easily probed besides charginos and neutralinos in the early runs of the Large Hadron Collider.