We extend the KKLT [1] approach to moduli stabilization by including the dilaton and the complex structure moduli into the effective supergravity theory. Decoupling of the dilaton is neither always possible nor necessary for the existence of stable minima with zero (or positive) cosmological constant. The pattern of supersymmetry breaking can be much richer than in the decoupling scenario of KKLT.

We examine the structure of soft supersymmetry breaking terms in KKLT models of flux compactification with low energy supersymmetry. Moduli are stabilized by fluxes and nonperturbative dynamics while a de Sitter vacuum is obtained by adding supersymmetry breaking anti-branes. We discuss the characteristic pattern of mass scales in such a set-up as well as some features of 4D N = 1 supergravity breakdown by anti-branes. Anomaly mediation is found to always give an important contribution and one can easily arrange for flavor-independent soft terms. In its most attractive realization, the modulus mediation is comparable to the anomaly mediation, yielding a quite distinctive sparticle spectrum. In addition, the axion component of the modulus/dilaton superfield dynamically cancels the relative CP phase between the contributions of anomaly and modulus mediation, thereby avoiding dangerous SUSY CP violation.

We discuss a scheme to implement the relaxion solution to the hierarchy problem with multiple axions, and present a UV-completed model realizing the scheme. All of the N axions in our model are periodic with a similar decay constant f well below the Planck scale. In the limit N ≫ 1, the relaxion φ corresponds to an exponentially long multi-helical flat direction which is shaped by a series of mass mixing between nearby axions in the compact field space of N axions. With the length of flat direction given by ∆φ = 2πf eff ∼ e ξN f for ξ = O(1), both the scalar potential driving the evolution of φ during the inflationary epoch and the φ-dependent Higgs boson mass vary with an exponentially large periodicity of O(f eff ), while the back reaction potential stabilizing the relaxion has a periodicity of O(f ). A natural UV completion of our scheme can be found in high scale or (mini) split supersymmetry (SUSY) scenario with the axion scales generated by SUSY breaking as f ∼ √ m SUSY M * , where the soft SUSY breaking scalar mass m SUSY can be well above the weak scale, and the fundamental scale M * can be identified as the Planck scale or the GUT scale.

We extend the Kim-Nilles-Peloso (KNP) alignment mechanism for natural inflation to models with $N>2$ axions, which obtains a super-Planckian effective axion decay constant $f_{\textrm{eff}}\gg M_{Pl}$ through an alignment of the anomaly coefficients of multiple axions having sub-Planckian fundamental decay constants $f_0\ll M_{Pl}$. The original version of the KNP mechanism realized with two axions requires that some of the anomaly coefficients should be of the order of $f_{\textrm{eff}}/f_0$, which would be uncomfortably large if $f_{\rm eff}/f_0 \gtrsim {\cal O}(100)$ as suggested by the recent BICEP2 results. We note that the KNP mechanism can be realized with the anomaly coefficients of $\mathcal{O}(1)$ if the number of axions $N$ is large as $N\ln N\gtrsim 2\ln (f_{\textrm{eff}}/f_0)$, in which case the effective decay constant can be enhanced as $f_{\rm eff}/f_0 \sim \sqrt{N !}\,n^{N-1}$ for $n$ denoting the typical size of the integer-valued anomaly coefficients. Comparing to the other multiple axion scenario, the N-flation scenario which requires $N \sim f_{\textrm{eff}}^2/f_0^2$, the KNP mechanism has a virtue of not invoking to a too large number of axions, although it requires a specific alignment of the anomaly coefficients, which can be achieved with a probability of ${\cal O}(f_0/f_{\rm eff})$ under a random choice of the anomaly coefficients. We also present a simple model realizing a multiple axion monodromy along the inflaton direction.Comment: 19 pages, 2 figures. v2: typos corrected, references added, some arguments improved. v3: references added, examples added. v4: references added, matches published versio

A slow-rolling scalar field (Q ≡ Quintessence) with potential energy V Q ∼ (3 × 10 −3 eV) 4 has been proposed as the origin of accelerating universe at present. We investigate the effective potential of Q in the framework of supergravity model including the quantum corrections induced by generic (nonrenormalizable) couplings of Q to the gauge and charged matter multiplets. It is argued that the Kähler potential, superpotential and gauge kinetic functions of the underlying supergravity model are required to be invariant under the variation of Q with an extremely fine accuracy in order to provide a working quintessence potential. Applying these results for string or M -theory, we point out that the heterotic M -theory or Type I string axion can be a plausible candidate for quintessence if (i) it does not couple to the instanton number of gauge interactions not weaker than those of the standard model and (ii) the modulus partner Re(Z) of the periodic quintessence axion Im(Z) ≡ Im(Z)+ 1 has a large VEV: Re(Z) ∼ 1 2π ln(m 2 3/2 M 2 P lanck /V Q ). It is stressed that such a large Re(Z) gives the gauge unification scale at around the phenomenologically favored value 3 × 10 16 GeV. To provide an accelerating universe, the quintessence axion should be at near the top of its effective potential at present, which requires a severe fine tuning of the initial condition of Q andQ in the early universe. We discuss a late time inflation scenario based on the modular and CP invariance of the moduli effective potential, yielding the required initial condition in a natural manner if the Kähler metric of the quintessence axion superfield receives a sizable nonperturbative contribution.

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

We present a detailed study of the collider observable m T 2 applied for pair-produced superparticles decaying to visible particles and a pair of invisible lightest supersymmetric particles (LSPs). Analytic expressions of the maximum of m T 2 over all events (m max T 2 ) are derived. It is noticed that if the decay product of each superparticle involves more than one visible particle, m max T 2 being a function of the trial LSP mass m χ has a kink structure at m χ = true LSP mass, which can be used to determine the mother superparticle mass and the LSP mass simultaneously. To see how well m max T 2 can be constructed from collider data, a Monte-Carlo analysis of the gluino m T 2 is performed for some superparticle spectra. * After [6], the kink structure of the endpoint values of transverse mass observable has been discussed also in [7,8]. For other approaches to measure superparticle masses at hadron collider, see [4,9,10,11].