Mu Term Research Articles

Anomaly-mediated SUSY breaking model retrofitted for naturalness

Anomaly-mediated supersymmetry breaking (AMSB) models seem to have become increasingly implausible due to 1. difficulty in generating a Higgs mass m(h)~125 GeV, 2. typically unnatural superparticle spectra characterized by a large superpotential mu term and 3. the possibility of a wino-like lightest SUSY particle (LSP) as dark matter now seems to be excluded. In the present paper we propose some minor modifications to the paradigm model which solve these three issues. Instead of adding a universal bulk scalar mass to avoid tachyonic sleptons, we add distinct Higgs and matter scalar soft masses which then allow for light higgsinos. To gain accord with the measured Higgs mass, we also include a bulk trilinear soft term. The ensuing natural generalized AMSB (nAMSB) model then has a set of light higgsinos with mass nearby the weak scale m(W,Z,h)~100 GeV as required by naturalness while the winos populate the several hundred GeV range and gluinos and squarks occupy the multi-TeV range. For LHC searches, the wino pair production followed by decay to same-sign diboson signature channel offers excellent prospects for discovery at high luminosity LHC along with higgsino pair production leading to soft dileptons plus jet(s)+MET. A linear e^+e^- collider operating above higgsino pair production threshold should be able to distinguish the AMSB gaugino spectra from unified or mirage unified scenarios. Dark matter is expected to occur as a higgsino-like WIMP plus axion admixture.

No-scale mu -term hybrid inflation

To solve the fine-tuning problem in mu -term hybrid inflation, we will realize the supersymmetry scenario with the TeV-scale supersymmetric particles and intermediate-scale gravitino from anomaly mediation, which can be consistent with the WMAP and Planck experiments. Moreover, we for the first time propose the mu -term hybrid inflation in no-scale supergravity. With four scenarios for the SU(3)_Ctimes SU(2)_Ltimes SU(2)_Rtimes U(1)_{B-L} model, we show that the correct scalar spectral index n_s can be obtained, while the tensor-to-scalar ratio r is predicted to be tiny, about 10^{-10}–10^{-8}. Also, the SU(2)_Rtimes U(1)_{B-L} symmetry breaking scale is around 10^{14} GeV, and all the supersymmetric particles except gravitino are around the TeV scale, while the gravitino mass is around 10^{9}–10^{10} GeV. Considering the complete potential terms linear in S, we for the first time show that the tadpole term, which is the key for such kind of inflationary models to be consistent with the observed scalar spectral index, vanishes after inflation. Thus, to obtain the mu term, we need to generate the supersymmetry breaking soft term A^{S Phi Phi '}_{kappa } kappa S Phi Phi ' due to A^{S Phi Phi '}_{kappa }=0 in no-scale supergravity, where Phi and Phi ' are vector-like Higgs fields at high energy. We show that the proper A^{S Phi Phi '}_{kappa } kappa S Phi Phi ' term can be obtained in the M-theory inspired no-scale supergravity. We also point out that A^{S Phi Phi '}_{kappa } around 700 GeV can be generated via the renormalization group equation running from string scale. We briefly comment on the supersymmetry phenomenological consequences as well.

MSSM without free parameters

It is often argued that the minimal supersymmetric standard model has O(100) free parameters and the generic parameter region is already excluded by the null observation of the flavor and CP violating processes as well as the constraints from the LHC experiments. This situation naturally leads us to consider the case where all the dangerous soft supersymmetry breaking terms such as the scalar masses and scalar couplings are absent, while only the unified gaugino mass term and the mu term are non-vanishing at the grand unification scale. We revisit this simple situation taking into account the observed Higgs boson mass, 125 GeV. Since the gaugino mass and the mu term are fixed in order to explain the Higgs boson and the Z boson masses, there is no free parameter left in this scenario. We find that there are three independent parameter sets exist including ones which have not been discussed in the literature. We also find that the abundance of the dark matter can be explained by relic gravitinos which are non-thermally produced as decay products of the SUSY particles while satisfying constraints from Big Bang Nucleosynthesis. We discuss the effects of the gravity mediation which generically give contribution to the soft terms of the order of the gravitino mass. It turns out that newly found parameter set is preferable to explain the Higgs boson mass as well as the gravitino dark matter while satisfying the constraints from the electric dipole moments of the electron and the nucleon.

The Higgs mass and natural supersymmetric spectrum from the landscape

In supersymmetric models where the superpotential mu term is generated with mu<< m_{soft} (e.g. from radiative Peccei-Quinn symmetry breaking or compactified string models with sequestration and stabilized moduli), and where the string landscape 1. favors soft supersymmetry (SUSY) breaking terms as large as possible and 2. where the anthropic condition that electroweak symmetry is properly broken with a weak scale m_{W,Z,h}~100 GeV ({\it i.e.} not too weak of weak interactions), then these combined landscape/anthropic requirements act as an attractor pulling the soft SUSY breaking terms towards values required by models with radiatively-driven naturalness: near the line of criticality where electroweak symmetry is barely broken and the Higgs mass is ~125 GeV. The pull on the soft terms serves to ameliorate the SUSY flavor and CP problems. The resulting sparticle mass spectrum may barely be accessible at high-luminosity LHC while the required light higgsinos should be visible at a linear e^+e^- collider with \sqrt{s}>2m(higgsino).

Natural Higgs-Flavor-Democracy Solution of theμProblem of Supersymmetry and the QCD Axion

We show that the hierarchically small μ term in supersymmetric theories is a consequence of two identical pairs of Higgs doublets taking a democratic form for their mass matrix. We briefly discuss the discrete symmetry S(2)×S(2) toward the democratic mass matrix. Then, we show that there results an approximate Peccei-Quinn symmetry and hence the value μ is related to the axion decay constant.

Higgs bosons in supersymmetricU(1)′models withCPviolation

We study the Higgs sector of the U(1)'-extended MSSM with CP violation. This is an extension of the MSSM Higgs sector by one singlet field, introduced to generate the \mu term dynamically. We are particularly interested in non-standard decays of Higgs particles, especially of the lightest one, in the presence of CP violating phases for \mu_{eff} and the soft parameters. We present analytical expressions for neutral and charged Higgs bosons masses at tree and one-loop levels, including contributions from top and bottom scalar quark sectors. We then study the production and decay channels of the neutral Higgs for a set of benchmark points consistent with low energy data and relic density constraints. Numerical simulations show that a Higgs boson lighter than 2m_W can decay in a quite distinctive manner, including invisible modes into two neutralinos (h->\chi^0\chi^0) up to 50% of the time, when kinematically allowed. The branching ratio into h->bb, the dominant decay in the SM, is reduced in some U(1)' models and enhanced in others, while the branching ratios for the decays h -> \tau+ \tau-, h -> WW^* and h -> Z Z^*-> 4l are always reduced with respect to their SM expectations. This possibility has important implications for testing the U(1)' model both at the LHC and later at the ILC.

Vacuum stability bound on extended GMSB models

Extensions of GMSB models were explored to explain the recent reports of the Higgs boson mass around 124-126 GeV. Some models predict a large mu term, which can spoil the vacuum stability of the universe. We study two GMSB extensions: i) the model with a large trilinear coupling of the top squark, and ii) that with extra vector-like matters. In both models, the vacuum stability condition provides upper bounds on the gluino mass if combined with the muon g-2. The whole parameter region is expected to be covered by LHC at sqrt{s} = 14 TeV. The analysis is also applied to the mSUGRA models with the vector-like matters.

Peccei-Quinn invariant extension of the NMSSM

We study a Peccei-Quinn invariant extension of the next-to-minimal supersymmetric Standard Model (NMSSM), which turns out to be free from the tadpole and domain wall problems. Having a non-renormalizable coupling to the axion superfield, the SM singlet added to the Higgs sector can naturally generate an effective Higgs mu term around the weak scale. In the model, the lightest neutralino is dominated by the singlino, which gets a mass only through mixing with the neutral Higgsinos. We explore the phenomenological consequences resulting from the existence of such a relatively light neutralino. The coupling of the SM singlet to the Higgs doublets is constrained by the experimental bound on the invisible Z-boson decay width. Under this constraint, we examine the properties of the SM-like Higgs boson paying attention to its mass and decays. We also demonstrate a UV completion of the model in SU(5) grand unified theory with a missing-partner mechanism.

The μ problem and sneutrino inflation

We consider sneutrino inflation and post-inflation cosmology in the singlet extension of the MSSM with approximate Peccei-Quinn(PQ) symmetry, assuming that supersymmetry breaking is mediated by gauge interaction. The PQ symmetry is broken by the intermediate-scale VEVs of two flaton fields, which are determined by the interplay between radiative flaton soft masses and higher order terms. Then, from the flaton VEVs, we obtain the correct mu term and the right-handed(RH) neutrino masses for see-saw mechanism. We show that the RH sneutrino with non-minimal gravity coupling drives inflation, thanks to the same flaton coupling giving rise to the RH neutrino mass. After inflation, extra vector-like states, that are responsible for the radiative breaking of the PQ symmetry, results in thermal inflation with the flaton field, solving the gravitino problem caused by high reheating temperature. Our model predicts the spectral index to be n_s\simeq 0.96 due to the additional efoldings from thermal inflation. We show that a right dark matter abundance comes from the gravitino of 100 keV mass and a successful baryogenesis is possible via Affleck-Dine leptogenesis.

Axion model in gauge-mediated supersymmetry breaking and a solution to the μ/Bμ problem

We present a simple supersymmetric axion model that can naturally explain the origin of the Higgs mu and Bmu terms in gauge mediation while solving the strong CP problem. To stabilize the Peccei-Quinn scale, we consider mixing between the messenger fields that communicate the supersymmetry and Peccei-Quinn symmetry breaking to the visible sector. Such mixing leads to the radiative stabilization of the Peccei-Quinn scale. In the model, a Higgs coupling to the axion superfield generates the B parameter at the soft mass scale while a small mu term is induced after the Peccei-Quinn symmetry breaking. We also explore the phenomenological and cosmological aspects of the model, which crucially depend on the saxion and axino interactions with the ordinary particles induced by the Higgs coupling to the axion superfield.

Scalar neutrinos at the LHC

We study a softly-broken supersymmetric model whose gauge symmetry is that of the standard model (SM) gauge group times an extra Abelian symmetry U(1)'. We call this gauge-extended model U(1)' model, and we study a U(1)' model with a secluded sector such that neutrinos acquire Dirac masses via higher-dimensional terms allowed by the U(1)' invariance. In this model the mu term of the minimal supersymmetric model (MSSM) is dynamically induced by the vacuum expectation value of a singlet scalar. In addition, the model contains exotic particles necessary for anomaly cancellation, and extra singlet bosons for achieving correct Z'/Z mass hierarchy. The neutrinos are charged under U(1)', and thus, their production and decay channels differ from those in the MSSM in strength and topology. We implement the model into standard packages and perform a detailed analysis of sneutrino production and decay at the Large Hadron Collider, for various mass scenarios, concentrating on three types of signals: (1) 0lep+ MET,(2) 2lep+MET, and (3) 4lep + MET. We compare the results with those of the MSSM whenever possible, and analyze the SM background for each signal. The sneutrino production and decays provide clear signatures enabling distinction of the U(1)' model from the MSSM at the LHC.

Low scale nonuniversal, nonanomalousU(1)F′in a minimal supersymmetric standard model

We propose a non-universal U(1)'_F symmetry combined with the Minimal Supersymmetric Standard Model. All anomaly cancellation conditions are satisfied without exotic fields other than three right-handed neutrinos. Because our model allows all three generations of chiral superfields to have different U(1)'_F charges, upon the breaking of the U(1)'_F symmetry at a low scale, realistic masses and mixing angles in both the quark and lepton sectors are obtained. In our model, neutrinos are predicted to be Dirac fermions and their mass ordering is of the inverted hierarchy type. The U(1)'_F charges of the chiral super-fields also naturally suppress the mu term and automatically forbid baryon number and lepton number violating operators. While all flavor-changing neutral current constraints in the down quark and charged lepton sectors can be satisfied, we find that constraint from D0-D0bar turns out to be much more stringent than the constraints from the precision electroweak data.

Constraining proton lifetime in SO(10) with stabilized doublet-triplet splitting

We present a class of realistic unified models based on supersymmetric SO(10) wherein issues related to natural doublet-triplet (DT) splitting are fully resolved. Using a minimal set of low dimensional Higgs fields which includes a single adjoint, we show that the Dimopoulos--Wilzcek mechanism for DT splitting can be made stable in the presence of all higher order operators without having pseudo-Goldstone bosons and flat directions. The \mu term of order TeV is found to be naturally induced. A Z_2-assisted anomalous U(1)_A gauge symmetry plays a crucial role in achieving these results. The threshold corrections to alpha_3(M_Z), somewhat surprisingly, are found to be controlled by only a few effective parameters. This leads to a very predictive scenario for proton decay. As a novel feature, we find an interesting correlation between the d=6 (p\to e^+\pi^0) and d=5 (p\to \nu-bar K+) decay amplitudes which allows us to derive a constrained upper limit on the inverse rate of the e^+\pi^0 mode. Our results show that both modes should be observed with an improvement in the current sensitivity by about a factor of five to ten.

Compact F-theory GUTs with U(1)PQ

We construct semi-local and global realizations of SU(5) GUTs in F-theory that utilize a U(1)_PQ symmetry to protect against dimension four proton decay. Symmetries of this type, which assign charges to H_u and H_d that forbid a tree level \mu term, play an important role in scenarios for neutrino physics and gauge mediation that have been proposed in local F-theory model building. As demonstrated in arXiv:0906.4672, the presence of such a symmetry implies the existence of non-GUT exotics in the spectrum, when hypercharge flux is used to break the GUT group and to give rise to doublet-triplet splitting. These exotics are of precisely the right type to solve the unification problem in such F-theory models and might also comprise a non-standard messenger sector for gauge mediation. We present a detailed description of models with U(1)_PQ in the semi-local regime, which does not depend on details of any specific Calabi-Yau four-fold, and then specialize to the geometry of arXiv:0904.3932 to construct three-generation examples with the minimal allowed number of non-GUT exotics. Among these, we find a handful of models in which the D3-tadpole constraint can be satisfied without requiring the introduction of anti-D3-branes. Finally, because SU(5) singlets that carry U(1)_PQ charge may serve as candidate right-handed neutrinos or can be used to lift the exotics, we study their origin in compact models and motivate a conjecture for how to count their zero modes in a semi-local setting.

An instanton toolbox for F-theory model building

Several dimensionful parameters needed for model building can be engineered in a certain class of SU(5) F-theory GUTs by adding extra singlet fields which are localized along pairwise intersections of D7-branes. The values of these parameters, however, depend on dynamics external to the GUT which causes the singlets to acquire suitable masses or expectation values. In this note, we demonstrate that D3-instantons which wrap the same 4-cycle as one of the intersecting D7's can provide precisely the needed dynamics to generate several important scales, including the supersymmetry-breaking scale and the right-handed neutrino mass. Furthermore, these instantons seem unable to directly generate the \mu term suggesting that, at least in this class of models, it should perhaps be tied to one of the other scales in the problem. More specifically, we study the simple system consisting of a pair of D7-branes wrapping del Pezzo surfaces which intersect along a curve $\Sigma$ of genus 0 or 1 and classify all instanton configurations which can potentially contribute to the superpotential. This allows one to formulate topological conditions which must be imposed on \Sigma for various model-building applications. Along the way, we also observe that the construction of arXiv:0808.1286 which engineers a linear superpotential in fact realizes an O'Raifeartaigh model at the KK scale whose 1-loop Coleman-Weinberg potential generically leads to a metastable, long-lived SUSY-breaking vacuum.

Combining anomaly and Z′ mediation of supersymmetry breaking

We propose a scenario in which the supersymmetry breaking effect mediated by an additional U(1)' is comparable with that of anomaly mediation. We argue that such a scenario can be naturally realized in a large class of models. Combining anomaly with Z' mediation allows us to solve the tachyonic slepton problem of the former and avoid significant fine tuning in the latter. We focus on an NMSSM-like scenario where U(1)' gauge invariance is used to forbid a tree-level mu term, and present concrete models, which admit successful dynamical electroweak symmetry breaking. Gaugino masses are somewhat lighter than the scalar masses, and the third generation squarks are lighter than the first two. In the specific class of models under consideration, the gluino is light since it only receives a contribution from 2-loop anomaly mediation, and it decays dominantly into third generation quarks. Gluino production leads to distinct LHC signals and prospects of early discovery. In addition, there is a relatively light Z', with mass in the range of several TeV. Discovering and studying its properties can reveal important clues about the underlying model.

F-theory, GUTs, and the weak scale

In this paper we study a deformation of gauge mediated supersymmetry breaking in a class of local F-theory GUT models where the scale of supersymmetry breaking determines the value of the mu term. Geometrically correlating these two scales constrains the soft SUSY breaking parameters of the MSSM. In this scenario, the hidden SUSY breaking sector involves an anomalous U(1) Peccei-Quinn symmetry which forbids bare mu and B mu terms. This sector typically breaks supersymmetry at the desired range of energy scales through a simple stringy hybrid of a Fayet and Polonyi model. A variant of the Giudice-Masiero mechanism generates the value mu ~ 10^2 - 10^3 GeV when the hidden sector scale of supersymmetry breaking is F^(1/2) ~ 10^(8.5) GeV. Further, the B mu problem is solved due to the mild hierarchy between the GUT scale and Planck scale. These models relate SUSY breaking with the QCD axion, and solve the strong CP problem through an axion with decay constant f_a ~ M_(GUT) * mu / L, where L ~ 10^5 GeV is the characteristic scale of gaugino mass unification in gauge mediated models, and the ratio \mu / L ~ M_(GUT)/M_(pl) ~ 10^(-3). We find f_a ~ 10^12 GeV, which is near the high end of the phenomenologically viable window. Here, the axino is the goldstino mode which is eaten by the gravitino. The gravitino is the LSP with a mass of about 10^1 - 10^2 MeV, and a bino-like neutralino is (typically) the NLSP with mass of about 10^2 - 10^3 GeV. Compatibility with electroweak symmetry breaking also determines the value of tan(beta) ~ 30 +/- 7.

Gauge mediation with a smallμterm and light squarks

We consider a solution to the mu problem in the context of Non-Minimal Gauge Mediation with two Singlets and Low-Scale Messengers. This solution reduces tuning associated with the "Little Hierarchy" problem by permitting a naturally small mu term (100-300 GeV) due to small mixing between the Singlets. The smallness of mu also relies crucially on compressing the Gauge Mediated sparticle spectrum resulting in 330-400 GeV squarks. In addition to a small mu term, the theory achieves a Higgs mass > 114.4 GeV through a large Higgs quartic coupling when tanbeta ~ 1.5. The vacua studied are globally stable with all couplings perturbative to the GUT scale. The amount of tuning required to get the correct Electroweak scale is of order 10%, with a similar residual tuning associated with the region of parameter space where the lightest CP-even Higgs mass is above the LEP bound.

Electroweak symmetry breaking and singlino dark matter with deflected anomaly mediation

We investigate the phenomenology of the Nearly Minimal Supersymmetric Standard Model (nMSSM) in the deflected anomaly mediation scenario. We also include the Fayet-Iliopoulos D-term of the standard model gauge group. In the nMSSM, the mu term is replaced by the vacuum expectation value of the gauge singlet; therefore, there is no difficulty in generating the B-term of the SUSY breaking scale. Although the messenger sector is introduced, direct couplings between nMSSM fields and messenger sector fields are forbidden by the discrete symmetry. Therefore, the phenomenology at the weak scale does not depend on the detail of the messenger sector. We show that there are regions of parameter space in which electroweak symmetry breaking occurs successfully and the lightest Higgs is heavier than the LEP bound. We show that the gluino is light in this scenario. The lightest neutralino, which is mainly composed of a singlino, is a candidate for dark matter. The relic density explains the observed abundance of dark matter. The dark matter-nucleon scattering cross section satisfies the current limit from CDMS and XENON10 with a small value for the strange quark content of a nucleon.

GUTs and exceptional branes in F-theory — II. Experimental predictions

We consider realizations of GUT models in F-theory. Adopting a bottom up approach, the assumption that the dynamics of the GUT model can in principle decouple from Planck scale physics leads to a surprisingly predictive framework. An internal U(1) hypercharge flux Higgses the GUT group directly to the MSSM or to a flipped GUT model, a mechanism unavailable in heterotic models. This new ingredient automatically addresses a number of puzzles present in traditional GUT models. The internal U(1) hyperflux allows us to solve the doublet-triplet splitting problem, and explains the qualitative features of the distorted GUT mass relations for lighter generations due to the Aharanov-Bohm effect. These models typically come with nearly exact global symmetries which prevent bare mu terms and also forbid dangerous baryon number violating operators. Strong curvature around our brane leads to a repulsion mechanism for Landau wave functions for neutral fields. This leads to large hierarchies of the form exp(-c/B^(2*g)) where c and g are order one parameters and B ~ M_(GUT)/(M_(pl)*alpha_(GUT)). This effect can simultaneously generate a viably small mu term as well as an acceptable Dirac neutrino mass on the order of 0.5 * 10^(-2 +/- 0.5) eV. In another scenario, we find a modified seesaw mechanism which predicts that the light neutrinos have masses in the expected range while the Majorana mass term for the heavy neutrinos is ~ 3 * 10^(12 +/- 1.5) GeV. Communicating supersymmetry breaking to the MSSM can be elegantly realized through gauge mediation. In one scenario, the same repulsion mechanism also leads to messenger masses which are naturally much lighter than the GUT scale.