We consider two classes of supersymmetric models with nonuniversal gaugino masses at M_GUT in an attempt to resolve the apparent muon g-2 anomaly encountered in the Standard Model. We explore two distinct scenarios, one in which all gaugino masses ha
ve the same sign at M_GUT, and a second case with opposite sign gaugino masses. The sfermion masses in both cases are assumed to be universal at M_GUT. We exploit the non universality among gaugino masses to realize large mass splitting between the colored and non-colored sfermions. Thus, the sleptons can have masses in the few hundred GeV range, whereas the colored sparticles turn out to be an order of magnitude or so heavier. In both models the resolution of the muon g-2 anomaly is compatible, among other things, with a 125-126 GeV Higgs boson mass and the WMAP dark matter bounds.
We demonstrate that natural supersymmetry is readily realized in the framework of SU(4)_c times SU(2)_L times SU(2)_R with non-universal gaugino masses. Focusing on ameliorating the little hierarchy problem, we explore the parameter space of this mod
el which yields small fine-tuning measuring parameters (natural supersymmetry) at the electroweak scale (Delta_{EW}) as well as at high scale (Delta_{HS}). It is possible to have both Delta_{EW} and Delta_{HS} less than 100 in these models, (2 % or better fine-tuning), while keeping the light CP-even (Standard Model-like) Higgs mass in the 123 GeV-127 GeV range. The light stop quark mass lies in the range 700 GeV <m_{tilde{t}_{1}}< 1500 GeV, and the range for the light stau lepton mass is 900 GeV <m_{tilde{tau}_{1}}< 1300 GeV. The first two family squarks are in the mass range 3000 GeV <m_{tilde{t}_{1}}< 4500 GeV, and for the gluino we find 2500 GeV <m_{tilde{g}_{1}}< 3500 GeV. We do not find any solution with natural supersymmetry which yields significant enhancement for Higgs production and decay in the diphoton channel.
