In some string compactifications, for instance the recently proposed KKLT set-up, light moduli are stabilized by nonperturbative effects at supersymmetric AdS vacuum which is lifted to a dS vacuum by supersymmetry breaking uplifting potential. In such models, soft supersymmetry breaking terms are determined by a specific mixed modulusanomaly mediation in which the two mediations typically give comparable contributions to soft parameters. Similar pattern of soft terms can arise also in brane models to stabilize the radion by nonperturbative effects. We examine some phenomenological consequences of this mixed modulus-anomaly mediation, including the pattern of low energy sparticle spectrum and the possibility of electroweak symmetry breaking. It is noted that adding the anomaly-mediated contributions at M GU T amounts to replacing the messenger scale of the modulus mediation by a mirage messenger scale (m 3/2 /M P l ) α/2 M GU T where α = m 3/2 /[M 0 ln(M P l /m 3/2 )] for M 0 denoting the modulus-mediated contribution to the gaugino mass at M GU T . The minimal KKLT set-up predicts α = 1. As a consequence, for α = O(1), the model can lead to a highly distinctive pattern of sparticle masses at TeV scale, particularly when α = 2.

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.Comment: revtex4, 16 page

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TeV scale mirage mediation has been proposed as a supersymmetry breaking scheme reducing the fine tuning for electroweak symmetry breaking in the minimal supersymmetric extension of the standard model. We discuss a moduli stabilization set-up for TeV scale mirage mediation which allows an extra-dimensional interpretation for the origin of supersymmetry breaking and naturally gives an weak-scale size of the Higgs B-parameter. The set-up utilizes the holomorphic gauge kinetic functions depending on both the heavy dilaton and the light volume modulus whose axion partners are assumed to be periodic fields. We also examine the low energy phenomenology of TeV scale mirage mediation, particularly the constraints from electroweak symmetry breaking and FCNC processes.

We argue that the QCD axion can arise from many aligned axions with decay constants much smaller than the conventional axion window. If the typical decay constant is of O(100) GeV to 1 TeV, one or more of the axions or saxions may account for the recently found diphoton excess at ∼ 750 GeV. Our scenario predicts many axions and saxions coupled to gluons with decay constants of order the weak scale, and therefore many collider signatures by heavy axions and saxions will show up at different energy scales. In particular, if the inferred broad decay width is due to multiple axions or saxions, a non-trivial peak structure may become evident when more data is collected.We also discuss cosmological implications of the aligned QCD axion scenario. In the Appendix we give a possible UV completion and argue that the high quality of the Peccei-Quinn symmetry is naturally explained in our scenario.