In this talk, we propose a model of mirage mediation, in which Peccei-Quinn symmetry is incorporated. In this \textit{axionic mirage mediation}, it is shown that the Peccei-Quinn symmetry breaking scale is dynamically determined around $10^{10}$ GeV to $10^{12}$ GeV due to the supersymmetry breaking effects. The problems in the original mirage mediation such as the $μ$-problem and the moduli problem can be solved simultaneouly. Furthermore, in our model the axino, which is the superpartner of the axion, is the lightest sparticle.
We compare the collider phenomenology of mirage mediation and deflected mirage mediation, which are two recently proposed "mixed" supersymmetry breaking scenarios motivated from string compactifications. The scenarios differ in that deflected mirage mediation includes contributions from gauge mediation in addition to the contributions from gravity mediation and anomaly mediation also present in mirage mediation. The threshold effects from gauge mediation can drastically alter the low energy spectrum from that of pure mirage mediation models, resulting in some cases in a squeezed gaugino spectr…
We derive explicitly the soft SUSY breaking parameters at arbitrary low energy scale in the (deflected) mirage type mediation scenarios with possible gauge or Yukawa mediation contributions. Based on the Wilsonian effective action after integrating out the messengers, we obtain analytically the boundary value (at the GUT scale) dependencies of the effective wavefunctions and gauge kinetic terms. Note that the messenger scale dependencies of the effective wavefunctions and gauge kinetic terms had already been discussed in GMSB. The RGE boundary value dependencies, which is a special feature in …
We study the next-to-minimal supersymmetric standard model with the TeV scale mirage mediation. The 125 GeV Higgs boson mass is realized with O(10)% tuning for 1.5 TeV gluino and 1TeV stop masses.
We complete the study of a class of string-motivated effective supergravity theories in which modulus-induced soft supersymmetry breaking is sufficiently suppressed in the observable sector so as to be competitive with anomaly-mediated supersymmetry breaking. Here we consider deflected mirage mediation (DMM), where contributions from gauge mediation are added to those arising from gravity mediation and anomaly mediation. We update previous work that surveyed the rich parameter space of such theories, in light of data from the CERN Large Hadron Collider (LHC) and recent dark matter detection ex…
Recent progress in string theory moduli stabilization has motivated a mixed modulus-anomaly mediated supersymmetry breaking scenario, also dubbed `mirage mediation'. This scenario has a number of phenomenologically attractive features, in particular with respect to the cosmological gravitino/moduli problem. In this note, we investigate the issues of fine-tuning associated with obtaining the correct electroweak symmetry breaking scale in the mirage mediation scenario. We find that, due to lighter gluinos, the fine-tuning is smaller than that in other mediation mechanisms.
In mirage-mediation models there exists a modulus field whose mass is O(1000) TeV and its late-decay may significantly change the standard thermal relic scenario of the dark matter. We study nonthermal production of the dark matter directly from the modulus decay, and find that for some parameter regions non-thermally produced neutralinos can become the dark matter.
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 periodi…
The recently introduced deflected mirage mediation (DMM) model is a string-motivated paradigm in which all three of the major supersymmetry-breaking transmission mechanisms are operative. We begin a systematic exploration of the parameter space of this rich model context, paying special attention to the pattern of gaugino masses which arise. In this work we focus on the dark matter phenomenology of the DMM model as such signals are the least influenced by the model-dependent scalar masses. We find that a large portion of the parameter space in which the three mediation mechanisms have a simila…
We present a general phenomenological framework for dialing between gravity mediation, gauge mediation, and anomaly mediation. The approach is motivated from recent developments in moduli stabilization, which suggest that gravity mediated terms can be effectively loop suppressed and thus comparable to gauge and anomaly mediated terms. The gauginos exhibit a mirage unification behavior at a "deflected" scale, and gluinos are often the lightest colored sparticles. The approach provides a rich setting in which to explore generalized supersymmetry breaking at the LHC.
We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which includes contributions from three mediation mechanisms, namely anomaly mediation, gravity mediation and gauge mediation, using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the soft supersymmetry breaking parameters in terms of the RGIs. We further discuss determining the supersymmetry breaking mechanism using a limited set of invariants, and derive sum rules valid for the DMMSB. In addition we examine…
We investigate the question of electroweak naturalness within the deflected mirage mediation (DMM) framework for supersymmetry breaking in the minimal supersymmetric standard model (MSSM). The class of DMM models considered are nine-parameter theories that fall within the general classification of the 19-parameter phenomenological MSSM (pMSSM). Our results show that these DMM models have regions of parameter space with very low electroweak fine-tuning, at levels comparable to the pMSSM. These parameter regions should be probed extensively in the current LHC run.
We study LHC phenomenology of mirage mediation scenario in which anomaly and modulus contributions to soft SUSY breaking terms are comparable to each other. A Monte Carlo study of mirage mediation, with model parameters $α=1$,$ M_0=500$ GeV, $n_M=1/2$, $n_H=1$ and $\rm{tan}β=10$, is presented. It is shown that masses of supersymmetric particles can be measured in a model independent way, providing information on SUSY breaking sector. In particular, the mass ratio of gluino to the lightest neutralino for the benchmark scenario is determined to be $1.9 \lesssim m_{\tildeg}/m_{\tildeχ_1^0} \lesss…
We investigate the parameter space of a specific class of model within the deflected mirage mediation (DMM) scenario. We look at neutralino properties and compute the thermal relic density as well as interaction rates with xenon direct detection experiments. We find that there are portions of the parameter space which are in line with the current WMAP constraints. Further we find that none of the investigated parameter space is in conflict with current bounds from the Xenon10 experiment and that future large-scale liquid xenon experiments will probe a large portion of the model space.
With the aim of uncovering viable regions of parameter space in deflected mirage mediation (DMM) models of supersymmetry breaking, we study the landscape of particle mass hierarchies for the lightest four non-Standard Model states for DMM models and compare the results to that of minimal supergravity/constrained MSSM (mSUGRA/CMSSM) models, building on previous studies of Feldman, Liu, and Nath. Deflected mirage mediation is a string-motivated scenario in which the soft terms include comparable contributions from gravity mediation, gauge mediation, and anomaly mediation. DMM allows a wide varie…
We study the phenomenology of neutralino dark matter (DM) in mirage mediation scenario of supersymmetry breaking which results from the moduli stabilization in some string/brane models. Depending upon the model parameters, especially the anomaly to modulus mediation ratio determined by the moduli stabilization mechanism, the nature of the lightest supersymmetric particle (LSP) changes from Bino-like neutralino to Higgsino-like one via Bino-Higgsino mixing region. For the Bino-like LSP, the standard thermal production mechanism can give a right amount of relic DM density through the stop/stau-n…
In the supersymmetric scenario known as mirage mediation (MM), the soft SUSY breaking terms receive comparable anomaly-mediation and moduli-mediation contributions leading to the phenomenon of mirage unification. The simplest MM SUSY breaking models which are consistent with the measured Higgs mass and sparticle mass constraints are strongly disfavoured by fine-tuning considerations. However, while MM makes robust predictions for gaugino masses, the scalar sector is quite sensitive to specific mechanisms for moduli stabilization and potential uplifting. We suggest here a broader setup of gener…
Rather general considerations from the string theory landscape suggest a statistical preference within the multiverse for soft SUSY breaking terms as large as possible subject to a pocket universe value for the weak scale not greater than a factor of 2-5 from our measured value. Within the gravity/moduli-mediated SUSY breaking framework, the Higgs mass is pulled to m_h~ 125 GeV while first/second generation scalars are pulled to tens of TeV scale and gauginos and third generation scalars remain at the few TeV range. In this case, one then expects comparable moduli- and anomaly-mediated contrib…
We study the next-to-minimal supersymmetric standard model. We consider soft supersymmetry breaking parameters, which are induced by the mirage mediation mechanism of supersymmetry breaking. We concentrate on the mirage mediation, where the so-called mirage scale is the TeV scale. In this scenario, we can realize the up-type Higgs soft mass of O(200) GeV, while other masses such as gaugino masses and stop masses are heavy such as 1 TeV or more. Cancellation between the effective μ-term and the down-type Higgs soft mass ameliorates the fine-tuning in the electroweak symmetry breaking even for μ…
We propose to generate a realistic soft SUSY breaking spectrum for Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a generalized deflected mirage mediation scenario, in which additional Yukawa and gauge mediation contributions are included to deflect the renormalization group equation(RGE) trajectory. Based on the Wilsonian effective action obtained by integrating out the messengers, the NMSSM soft SUSY breaking spectrum can be given analytically at the messenger scale. We find that additional contributions to $m_S^2$ can possibly ameliorate the stringent constraints from the electr…
In this letter we analyze the consequences, for the LHC, of gauge and third family Yukawa coupling unification with a particular set of boundary conditions defined at the GUT scale, which we characterize as effective "mirage" mediation. We perform a global chi-squared analysis including the observables M_W, M_Z, G_F, alpha_em, alpha_s(M_Z), M_top, m_b(m_b), M_tau, BR(B -> X_s gamma), BR(B_s -> mu^+ mu^-) and M_{h}. The fit is performed in the MSSM in terms of 10 GUT scale parameters, while tanb and mu are fixed at the weak scale. We find good fits to the low energy data and a SUSY spectrum whi…
We consider the situation in which $m_{3/2}\sim O(100{\rm TeV})$ for solving the gravitino problem and the other supersymmetry(SUSY) breaking parameters are $O(1{\rm TeV})$ for the naturalness. We point out that the anomaly mediation cancels out the renormalization group contribution to the gaugino masses and the sfermion masses other than the stop masses at a scale which is called the mirage scale. The situation is similar to the mirage mediation, in which special boundary conditions for the SUSY breaking parameters are required, though for the stop masses and the up-type Higgs mass, such can…
We discuss the sparticle mass patterns that can be realized in deflected mirage mediation scenario of supersymmetry breaking, in which the moduli, anomaly, and gauge mediations all contribute to the MSSM soft parameters. Analytic expression of low energy soft parameters and also the sfermion mass sum rules are derived, which can be used to interpret the experimentally measured sparticle masses within the framework of the most general mixed moduli-gauge-anomaly mediation. Phenomenological aspects of some specific examples are also discussed.
Mirage mediation reduces the fine-tuning in the minimal supersymmetric standard model by dynamically arranging a cancellation between anomaly-mediated and modulus-mediated supersymmetry breaking. We explore the conditions under which a mirage "messenger scale" is generated near the weak scale and the little hierarchy problem is solved. We do this by explicitly including the dynamics of the SUSY-breaking sector needed to cancel the cosmological constant. The most plausible scenario for generating a low mirage scale does not readily admit an extra-dimensional interpretation. We also review the p…
Current results of LHC experiments exclude large area of light new particle region, namely natural parameter space, in supersymmetric extension models. One of the possibilities for achieving the correct electroweak symmetry breaking naturally is low scale messenger scenario. Actually, the next-to-minimal supersymmetric standard model with TeV scale mirage mediation realizes the natural electroweak symmetry breaking with various mass spectra. In this paper, we show the possible mass spectrum in the scenario, e.g. degenerate and/or hierarchical mass spectrum, and discuss these features.
Mirage mediation realized in the Kachru-Kallosh-Linde-Trivedi (KKLT) flux compactification can naturally suppress the up-type Higgs soft mass at low energy scales. As a result, compared to the conventional scenarios, the degree of electroweak fine-tuning can be reduced further up to by a loop factor if the Higgsinos are much lighter than the heavy Higgs doublet. Interestingly, this feature holds even in high-scale supersymmetry as long as the gauge coupling unification, which is required as a prerequisite for mirage mediation, accommodates such light Higgsinos. Under the experimental constrain…
We discuss some features of supersymmetry breaking induced by a brane-localized source which is stabilized at the IR end of warped throat, and also the resulting mirage mediation pattern of soft terms of the visible fields which are localized in the bulk space corresponding to the UV end of throat. Such supersymmetry breaking scheme can be naturally realized in KKLT-type string compactification, and predicts highly distinctive pattern of low energy superparticle masses which might be tested at the LHC.
Although the mirage mediation is one of the most plausible mediation mechanisms of supersymmetry breaking, it suffers from two crucial problems. One is the μ-/B μ-problem and the second is the cosmological one. The former stems from the fact that the B parameter tends to be comparable with the gravitino mass, which is two order of magnitude larger than the other soft masses. The latter problem is caused by the decay of the modulus whose branching ratio into the gravitino pair is sizable. In this paper, we propose a model of mirage mediation, in which Peccei-Quinn symmetry is incorporated. In t…
We present a model of supersymmetry breaking in which the contributions from gravity/modulus, anomaly, and gauge mediation are all comparable. We term this scenario "deflected mirage mediation," which is a generalization of the KKLT-motivated mirage mediation scenario to include gauge mediated contributions. These contributions deflect the gaugino mass unification scale and alter the pattern of soft parameters at low energies. In some cases, this results in a gluino LSP and light stops; in other regions of parameter space, the LSP can be a well-tempered neutralino. We demonstrate explicitly th…
We propose that the TeV scale mirage mediation in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) is a novel solution for the little hierarchy problem in supersymmetry. The 125 GeV Higgs boson can be accommodated with the new quartic coupling or the mixing with the singlet. The fine-tuning measures are estimated numerically and found as low as 10\% or below for $1.5$ TeV gluino and $1$ TeV stop. The higgsino can be as heavy as 500 GeV without deteriorating the fine-tuning. An undesirable singlet-doublet mixing in the Higgs sector is suppressed due to approximate scale symmetries. We …
We study the mass of the lightest CP-even Higgs boson in the deflected mirage mediation that is a quite general framework of the mediation of supersymmetry breaking, incorporating the case where all of the modulus-, the anomaly- and the gauge-mediated contributions to the soft supersymmetry breaking parameters become sizable. We evaluate the degree of tuning the so-called mu parameter required for realizing a correct electroweak symmetry breaking and study how to accomplish both the observed Higgs boson mass and the relaxed fine-tuning. We identify the parameter space favored from such a persp…
We discuss effective models derived from a supersymmetric model whose mediation mechanism of supersymmetry (SUSY) breaking is namely mirage mediation. In this model, light higgsino mass, that is required by the natural realization of the electroweak scale, is achieved by the unification of the soft SUSY breaking parameters at the low scale. Besides, we find that extra Higgs fields are also possibly light in some cases. Then, the effective model is a two Higgs doublet model (2HDM) with higgsinos, and it is distinguishable with namely type-II 2HDM which is widely discussed. In this paper, we stu…
We consider a class of $b-τ$ Yukawa unified Supersymmetric (SUSY) $SU(5)$ GUTs, in which the asymptotic gaugino $M_{1,2,3}$ masses are generated through a combination of gravity and mirage mediated supersymmetry breaking. Due to the contributions from mirage mediation, $M_{3}$ is always lighter than M_{1} and M_{2}, and consequently for the range of asymptotic masses considered, the gluino mass at low scale is bounded from above at about 4 TeV. We realize two different regions, one in which the MSSM $μ-$term is less than about 3 TeV. This region yields a stop mass up to 5 TeV, and the stop mas…
We study the next-to-minimal supersymmetric standard model (NMSSM) with the TeV scale mirage mediation, which is known as a solution for the little hierarchy problem in supersymmetry. Our previous study showed that 125 GeV Higgs boson is realized with O(10) % fine-tuning for 1.5 TeV gluino (1 TeV stop) mass. The $μ$ term could be as large as 500 GeV without sacrificing the fine-tuning thanks to a cancellation mechanism. The singlet-doublet mixing is suppressed by $\tanβ$. In this paper, we further extend this analysis. We argue that approximate scale symmetries play a role behind the suppressi…
We study a new class of scenarios with the gaugino mass unification at the weak scale. The general condition is first derived for the unification to occur. Among the general cases, a particular attention is drawn to the mirage gauge mediation where the low-energy mass spectrum is governed by the mirage of unified gauge coupling which is seen by low-energy observers. The gaugino masses have natural and stable low-scale unification. The mass parameters of scalar quarks and leptons are given by gauge couplings but exhibit no large mass hierarchy. They are non-universal even when mediated at the g…
We examine supersymmetric models with mixed modulus-anomaly mediated SUSY breaking (MM-AMSB) soft terms which get comparable contributions to SUSY breaking from moduli-mediation and anomaly-mediation. The apparent (mirage) unification of soft SUSY breaking terms at Q=mu_mir not associated with any physical threshold is the hallmark of this scenario. The MM-AMSB structure of soft terms arises in models of string compactification with fluxes, where the addition of an anti-brane leads to an uplifting potential and a de Sitter universe, as first constructed by Kachru {\it et al.}. The phenomenolog…
We realize high scale supersymmetry in the mirage mediation. The Higgs sector is extended with the Peccei-Quinn symmetry, and the higgsino mass term is generated by the Kim-Nilles mechanism. In particular, the Peccei-Quinn symmetry breaking scale naturally lies on the mirage messenger scale due to the mixed modulus-anomaly mediation with the gauge coupling unification. Consequently, the higgsino mass term is of order the weak scale while the gravitino mass is of PeV order. This hierarchy naturally leads to the correct electroweak symmetry breaking. The higgsinos are thus in the range accessibl…
We discuss the pattern of low energy sparticle spectra which appears in some class of moduli stabilization scenario. In case that light moduli are stabilized by non-perturbative effects encoded in the superpotential and a phenomenologically viable de Sitter vacuum is obtained by a sequestered supersymmetry breaking sector, the anomaly-mediated soft terms become comparable to the moduli-mediated ones, leading to a quite distinctive pattern of low energy spacticle masses dubbed the mirage mediation pattern. We also discuss low energy sparticle masses in more general mixed-mediation scenario whic…
String compactification with fluxes yields MSSM soft SUSY breaking terms that receive comparable contributions from modulus and anomaly mediation whose relative strength is governed by a phenomenological parameter $α$. Gaugino and first/second generation (and sometimes also Higgs and third generation) scalar mass parameters unify at a mirage unification scale $Q \not= M_{\rm GUT}$, determined by the value of $α$. The ratio of scalar to gaugino masses at this mirage unification scale depends directly on the scalar field modular weights, which are fixed in turn by the brane or brane intersection…
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 modulus-anomaly 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 consequence…
We study the moduli-induced gravitino problem within the framework of the phenomenologically attractive mirage mediations. The huge amount of gravitino generated by the moduli decay can be successfully diluted by introducing an extra light modulus field which does not induce the supersymmetry breaking. Since the lifetime of extra modulus field becomes longer than usually considered modulus field, our proposed mechanism is applied to both the low- and high-scale supersymmetry breaking scenarios. We also point out that such an extra modulus field appears in the flux compactification of type II s…
We examine the effects of anomalous U(1)_A gauge symmetry on soft supersymmetry breaking terms while incorporating the stabilization of the modulus-axion multiplet responsible for the Green-Schwarz (GS) anomaly cancellation mechanism. In case of the KKLT stabilization of the GS modulus, soft terms are determined by the GS modulus mediation, the anomaly mediation and the U(1)_A mediation which are generically comparable to each other, thereby yielding the mirage mediation pattern of superparticle masses at low energy scale. Independently of the mechanism of moduli stabilization and supersymmetr…
Recent anomalies in cosmic rays could be due to dark matter annihilation in our galaxy. In order to get the required large cross-section to explain the data while still obtaining the right relic density, we rely on a non standard thermal history between dark matter freeze-out and Big-Bang Nucleosynthesis (BBN). We show that through a reheating phase from the decay of a heavy moduli or even the gravitino, we can produce the right relic density of dark matter if its self-annihilation cross-section is large enough. In addition to fitting the recent data, this scenario solves the cosmological modu…
We argue that the axion arising in the solution of the strong CP problem can be identified with the Majoron, the (pseudo-)Goldstone boson of spontaneously broken lepton number symmetry. At low energies, the associated $U(1)_L$ becomes, via electroweak parity violation and neutrino mediation, indistinguishable from an axial Peccei-Quinn symmetry in relation to the strong interactions. The axionic couplings are then fully computable in terms of known SM parameters and the Majorana mass scale, as we illustrate by computing the effective couplings to photons and quarks at two loops.
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 Kähler 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 Kähler potential and sparticle spectra …
We study gauge theories where quasi-hidden sectors are added to the MSSM for the sake of string consistency conditions which would otherwise not be satisfied. We focus on quiver gauge theories motivated by weakly coupled type II orientifold compactifications. Model independent features in this class include an anomalous U(1)_V symmetry which protects messenger masses and has strong consequences for superpotential couplings, a rich phenomenology of heavy and light Z' bosons, and axionic couplings required for anomaly cancellation via the Green-Schwarz mechanism. We discuss possibilities for dar…
String theoretic axion is a prime candidate for the QCD axion solving the strong CP problem. For a successful realization of the QCD axion in string theory, one needs to stabilize moduli including the scalar partner (saxion) of the QCD axion, while keeping the QCD axion unfixed until the low energy QCD instanton effects are turned on. We note that a simple generalization of KKLT moduli stabilization provides such set-up realizing the axion solution to the strong CP problem. Although some details of moduli stabilization are different from the original KKLT scenario, this set-up leads to the mir…
We present detailed arguments and calculations in support of our recent proposal to identify the axion arising in the solution of the strong CP problem with the Majoron, the (pseudo-)Goldstone boson of spontaneously broken lepton number symmetry. At low energies, the associated $U(1)_L$ becomes, via electroweak parity violation and neutrino mediation, indistinguishable from an axial Peccei-Quinn symmetry in relation to the strong interactions. The axionic couplings are then fully computable in terms of known SM parameters and the Majorana mass scales. The determination of these couplings invol…
