Effects of SO(10) D-Term on Yukawa Unification and Unstable Minima of the Supersymmetric Scalar Potential

We study the effects of SO(10) D-terms on the allowed parameter space ( APS ) in models with t− b− τ and b− τ Yukawa unifiction. The former is allowed only for moderate values of the D-term, if very precise ( ≤ 5% ) unification is required. Next we constrain the parameter space by looking for different dangerous directions where the scalar potential may be unbounded from below ( UFB1 and UFB3 ) constraints. The common trilinear coupling A0 plays a significant role in constraing the APS. For very precise t− b− τ Yukawa unification, −m16 <∼ A0 <∼ m16 can be probed at the LHC. Moreover, an interesting mass hierarchy with very heavy sfermions but light gauginos, which is strongly disfavoured in models without D-terms, becomes fairly common in the presence of the D-terms. The APS exhibits interesting characteristics if the common sfermion soft mass m16 is not the same with the soft mass m10 for Higgs sector. In b− τ unification models with D-terms, the APS allowed by Yukawa unification and REWSB increases and UFB1 constraint become weaker. However for A0 <∼ 0, a stronger UFB3 condition still puts, for a given m16, a stringent upper bound on the common gaugino mass and a lower bound on the common soft breaking scalar mass for for a given m1/2. PACS no: 12.60.Jv, 14.80.Ly, 14.80.Cp ∗Electronic address: [email protected] †On leave of absence from Jadavpur University. ‡Electronic address: [email protected]