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 $m_{SUSY}$. It is noted that for some type of uplifting potential, the anomaly-mediated contribution to $m_H^2$ 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 $m_H^2\sim m_{SUSY}^2/8\pi^2$ which is desirable for the lightest Higgs boson mass to satisfy the experimental bound. In such models, the other Higgs mass parameters $\mu$ and $B$ can have the desirable size $\mu \sim B \sim m_H$ 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.