A basic inequality for submanifolds in a cosymplectic space form

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely squared mean curvature on the other side. Some applications including inequalities between the intrinsic invariant $\delta_{M}$ and the squared mean curvature are given. The equality cases are also discussedComment: Latex 9 page

Flavor and CP conserving moduli mediated SUSY breaking in flux compactification

In certain class of flux compactification, moduli mediated supersymmetry (SUSY) breaking preserves flavor and CP at leading order in the perturbative expansion controlled by the vacuum expectation value of the messenger modulus. Nevertheless there still might be dangerous flavor or CP violation induced by higher order K\"ahler potential. We examine the constraints on such SUSY breaking scheme imposed by low energy flavor and/or CP violating observables. It is found that all phenomenological constraints can be satisfied even for generic form of higher order K\"ahler potential and sparticle spectra in the sub-TeV range, under plausible assumptions on the size of higher order correction and flavor mixing angles. This implies for instance that mirage mediation scheme of SUSY breaking, which involves such modulus mediation together with an anomaly mediation of comparable size, and also the modulus-dominated mediation realized in flux compactification can be free from the SUSY flavor and CP problems, while giving gaugino and sfermion masses in the sub-TeV range.Comment: 27 pages; corrected typos, added reference

Diluting the inflationary axion fluctuation by a stronger QCD in the early Universe

We propose a new mechanism to suppress the axion isocurvature perturbation, while producing the right amount of axion dark matter, within the framework of supersymmetric axion models with the axion scale induced by supersymmetry breaking. The mechanism involves an intermediate phase transition to generate the Higgs \mu-parameter, before which the weak scale is comparable to the axion scale and the resulting stronger QCD yields an axion mass heavier than the Hubble scale over a certain period. Combined with that the Hubble-induced axion scale during the primordial inflation is well above the intermediate axion scale at present, the stronger QCD in the early Universe suppresses the axion fluctuation to be small enough even when the inflationary Hubble scale saturates the current upper bound, while generating an axion misalignment angle of order unity.Comment: 5 pages, 1 figure; v2: discussion extended, references added, typos correcte

Higgs phenomenology in the Peccei-Quinn invariant NMSSM

We study the Higgs phenomenology in the Peccei-Quinn invariant NMSSM (PQ-NMSSM) where the low energy mass parameters of the singlet superfield are induced by a spontaneous breakdown of the Peccei-Quinn symmetry. In the generic NMSSM, scalar mixing among CP-even Higgs bosons is constrained by the observed properties of the SM-like Higgs boson, as well as by the LEP bound on the chargino mass and the perturbativity bound on the singlet Yukawa coupling. In the minimal PQ-NMSSM, scalar mixing is further constrained due to the presence of a light singlino-like neutralino. It is noticed that the $2\sigma$ excess of the LEP $Zb\bar b$ events at $m_{b\bar b}\simeq$ 98 GeV can be explained by a singlet-like 98 GeV Higgs boson in the minimal PQ-NMSSM with low $\tan\beta$, stops around or below 1 TeV, and light doublet-higgsinos around the weak scale.Comment: 31 pages, 4 figures; v2: references added, light stop effects discussed, bound on the Higgs invisible decay rate correcte

TeV Scale Mirage Mediation and Natural Little SUSY Hierarchy

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.Comment: 44 pages, 14 figures; added references, extended discussions in section