Little SUSY hierarchy in mixed modulus-anomaly mediation

Motivated by the KKLT string compactification involving a supersymmetry-breaking uplifting potential, we examine 4D effective supergravity with a generic form of uplifting potential, focusing on the possibility that the resulting mixed modulus-anomaly mediated soft terms realize the little hierarchy between the Higgs boson masses m_H and the sparticle masses mSUSY. It is noted that for some type of uplifting potential, the anomaly-mediated contribution to m_H² at M_GUT can cancel the subsequent renormalization group evolution of m_H ² down to TeV scale, thereby the model can naturally realize the little hierarchy m_H²∼m_SUSY ²/8π² which is desirable for the lightest Higgs boson mass to satisfy the experimental bound. In such models, the other Higgs mass parameters μ and B can have the desirable size μ∼B∼m_H without severe fine-tuning of parameters, although the gravitino is much heavier than the Higgs boson. Those models for the little hierarchy avoid naturally the dangerous SUSY flavor and CP violations, and predict nearly degenerate low energy gaugino masses, pure Higgsino LSP, and also a specific relation between the stop and gaugino masses.