Effects of the 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-tau and b-tau Yukawa unification. The former is allowed only for moderate values of the D-term, if very precise (less than or equal to5%) 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). The common trilinear coupling A(0) plays a significant role in constraining the APS. For very precise t-b-tau Yukawa unification, -m(16) less than or similar to A(0) less than or equal to m(16) can be probed at the LHC, where m(16) is the common soft breaking mass for the sfermions. 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 m(16) is not the same as the soft breaking mass m(10) for the Higgs sector. In b-tau unification models with D-terms, the APS consistent with Yukawa unification and radiative electroweak symmetry breaking, increases as the UFB1 constraint becomes weaker. However, for A(0) less than or similar to 0, a stronger UFB3 condition still puts, for a given m(16), a stringent upper bound on the common gaugino mass (m(1/2)) and a lower bound on m(16) for a given m(1/2). The effects of sign of mu on Yukawa unification and UFB constraints are also discussed.