Abstract
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 mH and the sparticle masses mSUSY. It is noted that for some type of uplifting potential, the anomaly-mediated contribution to mH2 at MGUT can cancel the subsequent renormalization group evolution of mH2 down to TeV scale, thereby the model can naturally realize the little hierarchy mH2∼mSUSY2/8π2 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∼mH 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.
Highlights
Low-energy supersymmetry (SUSY) is one of primary candidates for physics beyond the standard model (SM) above the weak scale [1]
One of the most important motivations for supersymmetric extension of the SM is to solve the hierarchy problem between the weak scale and GUT/Planck scale, The minimal supersymmetric extension of the standard model is important from the viewpoint of its minimality as well as the realization of gauge coupling unification at MGUT ∼ 2 ×1016 GeV
The little SUSY hierarchy problem is caused by the combination of the following aspects of the minimal supersymmetric standard model (MSSM)
Summary
Where γi(μ) denote the running anomalous dimensions at μ and Yi is the U(1)Y hypercharge of Φi. The results of (21) and (23) show an interesting feature: when i m 2i Yi = 0 and the condition (22) is satisfied, the low energy soft masses in the mixed modulus-anomaly mediation with messenger scale MGUT are same as the low energy soft masses in the pure modulusmediation started from the mirage messenger scale Λm ≈ (m3/2/MP l)α/2MGUT. Note that under the assumption that n0, ni and nP are rational numbers, the conditions of (24) are not a parameter fine-tuning, but correspond to a restriction to the specific class of models. For these models, the low energy expressions (21) and (23) are applicable. The low energy expressions (21) and (23) are applicable.
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