SUSY CP Research Articles

Muon g \u2212 2 in gauge mediation without SUSY CP problem

We discuss gauge mediated supersymmetry breaking models which explain the observed muon anomalous magnetic moment and the Higgs boson mass simultaneously. The successful explanation requires the messenger sector which violates the relation motivated by the grand unification theory (GUT). The naive violation of the GUT relation, however, ends up with the CP problem. We propose a model in which the phases of the gaugino masses are aligned despite the violation of the GUT relation. We also consider a model which generates the μ-term and the additional Higgs soft masses squared without causing CP violation. As a result, we find a successful model which explains the muon anomalous magnetic moment and the Higgs boson mass. The model is also free from the CP, flavor-changing neutral current and the lepton flavor violation problems caused by the subdominant gravity mediation effects. The lightest supersymmetric particles are gravitino/goldstini and the next-to-lightest ones are the Wino/Higgsinos in the typical parameter space. We also study the LHC constraints.

String landscape guide to soft SUSY breaking terms

We examine several issues pertaining to statistical predictivity of the string theory landscape for weak scale supersymmetry (SUSY). We work within a predictive landscape wherein super-renormalizable terms scan while renormalizable terms do not. We require stringy naturalness wherein the likelihood of values for observables is proportional to their frequency within a fertile patch of landscape including the MSSM as low energy effective theory with a pocket-universe value for the weak scale nearby to its measured value in our universe. In the string theory landscape, it is reasonable that the soft terms enjoy a statistical power-law draw to large values, subject to the existence of atoms as we know them (atomic principle). We argue that gaugino masses, scalar masses and trilinear soft terms should each scan independently. In addition, the various scalars should scan independently of each other unless protected by some symmetry. The expected non-universality of scalar masses-- once regarded as an undesirable feature-- emerges as an asset within the context of the string landscape picture. In models such as heterotic compactifications on Calabi-Yau manifolds, where the tree-level gauge kinetic function depends only on the dilaton, then gaugino masses may scale mildly, while scalar masses and A-terms, which depend on all the moduli, may scale much more strongly leading to a landscape solution to the SUSY flavor and CP problems in spite of non-diagonal K\"ahler metrics. We present numerical results for Higgs and sparticle mass predictions from the landscape within the generalized mirage mediation SUSY model and discuss resulting consequences for LHC SUSY and WIMP dark matter searches.

Landscape solution to the SUSY flavor and CP problems

In a fertile patch of the string landscape which includes the Minimal Supersymmetric Standard Model (MSSM) as the low energy effective theory, rather general arguments from Douglas suggest a power-law statistical selection of soft breaking terms (m(soft)^n where n=2n_F+n_D-1 with n_F the number of hidden sector F-SUSY breaking fields and n_D the number of D-term SUSY breaking fields). The statistical draw towards large soft terms must be tempered by requiring an appropriate breakdown of electroweak (EW) symmetry with no contributions to the weak scale larger than a factor 2-5 of its measured value, lest one violates the (anthropic) atomic principle. Such a simple picture of stringy naturalness generates a light Higgs boson with mass m_h~ 125 GeV with sparticles (other than higgsinos) typically beyond LHC reach. Then we expect first and second generation matter scalars to be drawn independently to the tens of TeV regime where the upper cutoff arises from two-loop RGE terms which drive third generation soft masses towards tachyonic values. Since the upper bounds on m_0(1,2) are the same for each generation, and flavor independent, then these will be drawn toward quasi-degenerate values. This mechanism leads to a natural mixed decoupling/quasi-degeneracy solution to the SUSY flavor problem and a decoupling solution to the SUSY CP problem.

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).

Distinguishing LSP archetypes via gluino pair production at LHC13

The search for supersymmetry at Run 1 of LHC has resulted in gluino mass limits m(gluino)>~ 1.3 TeV for the case where m(gluino)<<m(squark) and in models with gaugino mass unification. The increased energy and ultimately luminosity of LHC13 will explore the range m(gluino)~ 1.3-2 TeV. We examine how the discovery of SUSY via gluino pair production would unfold via a comparative analysis of three LSP archetype scenarios: 1. mSUGRA/CMSSM model with a bino-like LSP, 2. charged SUSY breaking (CSB) with a wino-like LSP and 3. SUSY with radiatively-driven naturalness (RNS) and a higgsino-like LSP. In all three cases we expect heavy-to-very-heavy squarks as suggested by a decoupling solution to the SUSY flavor and CP problems and by the gravitino problem. For all cases, initial SUSY discovery would likely occur in the multi-b-jet + ETMISS channel. The CSB scenario would be revealed by the presence of highly-ionizing, terminating tracks from quasi-stable charginos. As further data accrue, the RNS scenario with 100-200 GeV higgsino-like LSPs would be revealed by the build-up of a mass edge/bump in the OS/SF dilepton invariant mass which is bounded by the neutralino mass difference. The mSUGRA/CMSSM archetype would contain neither of these features but would be revealed by a buildup of the usual multi-lepton cascade decay signatures.

CP-safe gravity mediation and muong − 2

We propose a CP-safe gravity mediation model, where the phases of the Higgs B parameter, scalar trilinear couplings and gaugino mass parameters are all aligned. Since all dangerous CP violating phases are suppressed, we are now safe to consider low-energy SUSY scenarios. As an application, we consider a gravity mediation model explaining the observed muon $g-2$ anomaly. The CP-safe property originates in two simple assumptions: SUSY breaking in the K\"ahler potential and a shift symmetry of a SUSY breaking field $Z$. As a result of the shift symmetry, the imaginary part of $Z$ behaves as a QCD axion, leading to an intriguing possibility: the strong CP problem in QCD and the SUSY CP problem are solved simultaneously.

Flavor symmetry based MSSM: Theoretical models and phenomenological analysis

We present a class of supersymmetric models in which symmetry considerations alone dictate the form of the soft SUSY breaking Lagrangian. We develop a class of minimal models, denoted as sMSSM -- for flavor symmetry-based minimal supersymmetric standard model, which respect a grand unified symmetry such as SO(10) and a non-Abelian flavor symmetry H which suppresses SUSY-induced flavor violation. Explicit examples are constructed with the flavor symmetry being gauged SU(2)_H and SO(3)_H with the three families transforming as 2 + 1 and 3 representations respectively. A simple solution is found in the case of SU(2)_H for suppressing the flavor violating D--terms based on an exchange symmetry. Explicit models based on SO(3)_H without the D--term problem are developed. In addition, models based on discrete non-Abelian flavor groups are presented which are automatically free from D--term issues. The permutation group S_3 with a 2 + 1 family assignment, as well as the tetrahedral group A_4 with a 3 assignment are studied. In all cases, a simple solution to the SUSY CP problem is found, based on spontaneous CP violation leading to a complex quark mixing matrix. We develop the phenomenology of the resulting sMSSM, which is controlled by seven soft SUSY breaking parameters for both the 2 + 1 assignment and the 3 assignment of fermion families. These models are special cases of the phenomenological MSSM (pMSSM), but with symmetry restrictions. We discuss the parameter space of sMSSM compatible with LHC searches, B physics constraints and dark matter relic abundance. Fine-tuning in these models is relatively mild, since all SUSY particles can have masses below about 3 TeV.

Naturalness implies intra-generational degeneracy for decoupled squarks and sleptons

The SUSY flavor, CP, gravitino and proton-decay problems are all solved to varying degrees by a decoupling solution wherein first/second generation matter scalars would exist in the multi-TeV regime. Recent models of natural SUSY presumably allow for a co-existence of naturalness with the decoupling solution. We show that: if sfermions are heavier than $\sim 10$ TeV, then a small first/second generation contribution to electroweak fine-tuning (EWFT) requires a rather high degree of intra-generational degeneracy of either 1. (separately) squarks and sleptons, 2. (separately) left- and right-type sfermions, 3. members of SU(5) multiplets, or 4. all members of a single generation as in SO(10). These (partial) degeneracy patterns required by naturalness hint at the necessity of an organizing principle, and highlight the limitations of models such as the pMSSM in the case of decoupled first/second generation scalars.

Radiative natural supersymmetry: Reconciling electroweak fine-tuning and the Higgs boson mass

Models of natural supersymmetry seek to solve the little hierarchy problem by positing a spectrum of light higgsinos <~ 200-300 GeV and light top squarks <~ 600 GeV along with very heavy squarks and TeV-scale gluinos. Such models have low electroweak fine-tuning and satisfy the LHC constraints. However, in the context of the MSSM, they predict too low a value of m(h), are frequently in conflict with the measured b\to s\gamma branching fraction and the relic density of thermally produced higgsino-like WIMPs falls well below dark matter (DM) measurements. We propose "radiative natural SUSY" (RNS) which can be realized within the MSSM (avoiding the addition of extra exotic matter) and which maintains features such as gauge coupling unification and radiative electroweak symmetry breaking. The RNS model can be generated from SUSY GUT type models with non-universal Higgs masses (NUHM). Allowing for high scale soft SUSY breaking Higgs mass m_{H_u}> m_0 leads to automatic cancellations during renormalization group (RG) running, and to radiatively-induced low fine-tuning at the electroweak scale. Coupled with large mixing in the top squark sector, RNS allows for fine-tuning at the 3-10% level with TeV-scale top squarks and a 125 GeV light Higgs scalar h. The model allows for at least a partial solution to the SUSY flavor, CP and gravitino problems since first/second generation scalars (and the gravitino) may exist in the 10-30 TeV regime. We outline some possible signatures for RNS at the LHC and at a linear e^+e^- collider. If the strong CP problem is solved by the Peccei-Quinn mechanism, then RNS naturally accommodates mixed axion-higgsino cold dark matter, where the light higgsino-like WIMPS - which in this case make up only a fraction of the measured relic abundance - should be detectable at upcoming WIMP detectors.

Decays of H 0/A 0 in supersymmetric scenarios with heavy sfermions

The recent discovery of a new boson at the LHC, which resembles a SM-like Higgs boson with $m_h=125$ GeV, is starting to provide strong guidelines into SUSY model building. For instance, the identification of such a state with the lightest CP-even Higgs boson of the MSSM ($h^0$), requires large values of $\tan\beta$ and/or heavy sfermions. One outcome of this result is the possibility to solve the SUSY flavor and CP problems by decoupling, which points towards some realization of Split-inspired SUSY scenarios, in which scalars are much heavier than gauginos and higgsinos. However, we argue here that the remaining Higgs bosons of the MSSM ($H^0$, $A^0$, $H^{\pm}$) do not have to be as heavy as the sfermions, and having them with masses near the EW scale does not pose any conflict with current MSSM constraints. We discuss then some SUSY scenarios with heavy sfermions, from a bottom-up approach, which contain the full Higgs sector, as well as a possible dark matter candidate, with masses near the EW scale, and identify distinctive signals from these scenarios that could be searched at the LHC.

Fermiophobic Higgs boson and supersymmetry

If a light Higgs boson with mass 125 GeV is fermiophobic, or partially fermiophobic, then the MSSM is excluded. The minimal supersymmetric fermiophobic Higgs scenario can naturally be formulated in the context of the NMSSM that admits Z_3 discrete symmetries. In the fermiophobic NMSSM, the SUSY naturalness criteria are relaxed by a factor N_c y_t^4/g^4 \sim 25, removing the little hierarchy problem and allowing sparticle masses to be naturally of order 2--3 TeV. This scale motivates wino or higgsino dark matter. The SUSY flavour and CP problems as well as the constraints on sparticle and Higgs boson masses from b \to s\gamma, B_s \to \mu\mu\ and direct LHC searches are relaxed in fermiophobic NMSSM. The price to pay is that a new, yet unknown, mechanism must be introduced to generate fermion masses. We show that in the fermiophobic NMSSM the radiative Higgs boson branchings to \gamma\gamma, \gamma Z can be modified compared to the fermiophobic and ordinary standard model predictions, and fit present collider data better. Suppression of dark matter scattering off nuclei explains the absence of signal in XENON100.

A solution to the μ/Bμ problem in gauge mediation with hidden gauge symmetry

We propose a solution to the mu/Bmu problem in gauge-mediated SUSY breaking, which does not suffer from the SUSY CP problem and is consistent with the solution to the strong CP problem. The model is based on Z_3-invariant NMSSM with additional vector-like matter charged under a hidden gauge group as well as the standard model gauge groups. The dynamical scale of the hidden gauge symmetry is set to be around 10 GeV. We show that this simple extension of the NMSSM resolves the domain wall problem and the mu/Bmu problem without a dangerous CP angle. The relative sign among gaugino masses and the mu parameter can be preferable in terms of the muon anomalous magnetic moment. We also discuss cosmological issues of this model, especially the effects of long-lived particles in the hidden gauge sector. The hidden glueball may cause a late-time entropy production, which opens up a possibility that the light gravitino can be a dominant component of dark matter while leptogenesis scenarios work successfully. There is a region where the electroweak symmetry is successfully broken with ~10 TeV stops, and the Higgs mass of ~125 GeV can be explained.

Neutrino properties inE6×SU(2)Fsupersymmetric GUT with spontaneousCPviolation

We examined the neutrino sector in E6 x SU(2)F SUSY GUT with spontaneous CP violation. At a glance, the discrete symmetry, which is introduced in order to solve the SUSY CP problem, constrains the allowed operators too strongly for the neutrino sector to be consistent with the experimental data, i.e., the mu neutrino becomes massless as commented in the previous paper. We showed that this issue can be solved if some operators are taken into account. And we saw that such operators do not play an important role in studying quark and charged lepton sectors. The predictions on the neutrino masses and mixings are the same as the E6 models, which are consistent with various experiments on the neutrino oscillations.

Natural supersymmetry: LHC, dark matter and ILC searches

Particle physics models with Natural Supersymmetry are characterized by a superpotential parameter μ ∼ m h ∼ 125 GeV, while third generation squarks have mass $ _\sim^< $ 0.5–1.5 TeV. Gluinos should be lighter than several TeV so as not to destabilize the lighter squarks. First and second generation sfermions can be at the tens-of-TeV level which yields a decoupling solution to the SUSY flavor and CP problems. Adopting a top- down approach, we delineate the range of GUT scale SUSY model parameters which leads to a Natural SUSY mass spectrum. We find natural SUSY models to be tightly constrained by the b → sγ branching fraction measurement while it is also difficult but not impossible to accommodate a light Higgs scalar of mass ≃ 125 GeV. We present several benchmark points which are expandable to slopes and planes. Natural SUSY is difficult to see at LHC unless some third generation squarks are very light. The top- and bottom- squarks cascade decay mainly to higgsino-like charginos and neutralinos via numerous possibilities, leading to a rather complex set of signatures. Meanwhile, a linear e + e − collider operating at $ \sqrt {s} $ ∼ 0.25–0.5 TeV would be a higgsino factory and is essentially guaranteed a SUSY discovery of the low-lying charged and neutral higgsino states. Since thermal neutralino cold dark matter is underproduced, we conjecture that the incorporation of a Peccei-Quinn sector or light moduli into the theory will augment higgsino dark matter production, possibly together with an admixture of axions. We present rates for direct and indirect higgsino dark matter detection for the case where light higgsinos dominate the dark matter abundance.

B-decay CP-asymmetries in SUSY with a U(2)3 flavour symmetry

We study CP asymmetries in rare B decays within supersymmetry with a U(2)^3 flavour symmetry, motivated by the SUSY flavour and CP problems, the hierarchies in the Yukawa couplings and the absence so far of any direct evidence for SUSY. Even in the absence of flavour-blind phases, we find potentially sizable CP violating contributions to b -> s decay amplitudes. The effects in the mixing-induced CP asymmetries in B ->phi K(S) and B -> eta' K(S), angular CP asymmetries in B -> K* mu+ mu- and the direct CP asymmetry in B -> X(s) gamma can be in the region to be probed by LHCb and next generation B factories. At the same time, these effects in B decays are compatible with CP violating contributions to meson mixing, including a non-standard B(s) mixing phase hinted by current tensions in the CKM fit mostly between S(psi K(S)), epsilon(K) and Delta M(B(s))/Delta M(B(d)).

Hidden SUSY at the LHC: the light higgsino-world scenario and the role of a lepton collider

While the SUSY flavor, CP and gravitino problems seem to favor a very heavy spectrum of matter scalars, fine-tuning in the electroweak sector prefers low values of superpotential mass \mu. In the limit of low \mu, the two lightest neutralinos and light chargino are higgsino-like. The light charginos and neutralinos may have large production cross sections at LHC, but since they are nearly mass degenerate, there is only small energy release in three-body sparticle decays. Possible dilepton and trilepton signatures are difficult to observe after mild cuts due to the very soft p_T spectrum of the final state isolated leptons. Thus, the higgsino-world scenario can easily elude standard SUSY searches at the LHC. It should motivate experimental searches to focus on dimuon and trimuon production at the very lowest p_T(\mu) values possible. If the neutralino relic abundance is enhanced via non-standard cosmological dark matter production, then there exist excellent prospects for direct or indirect detection of higgsino-like WIMPs. While the higgsino-world scenario may easily hide from LHC SUSY searches, a linear e^+e^- collider or a muon collider operating in the \sqrt{s}\sim 0.5-1 TeV range would be able to easily access the chargino and neutralino pair production reactions.

Electroweak baryogenesis and dark matter with an approximate R-symmetry

It is well known that R-symmetric models dramatically alleviate the SUSY flavor and CP problems. We study particular modifications of existing R-symmetric models which share the solution to the above problems, and have interesting consequences for electroweak baryogenesis and the Dark Matter (DM) content of the universe. In particular, we find that it is naturally possible to have a strongly first-order electroweak phase transition while simultaneously relaxing the tension with EDM experiments. The R-symmetry (and its small breaking) implies that the gauginos (and the neutralino LSP) are pseudo-Dirac fermions, which is relevant for both baryogenesis and DM. The singlet superpartner of the U(1)_Y pseudo-Dirac gaugino plays a prominent role in making the electroweak phase transition strongly first-order. The pseudo-Dirac nature of the LSP allows it to behave similarly to a Dirac particle during freeze-out, but like a Majorana particle for annihilation today and in scattering against nuclei, thus being consistent with current constraints. Assuming a standard cosmology, it is possible to simultaneously have a strongly first-order phase transition conducive to baryogenesis and have the LSP provide the full DM relic abundance, in part of the allowed parameter space. However, other possibilities for DM also exist, which are discussed. It is expected that upcoming direct DM searches as well as neutrino signals from DM annihilation in the Sun will be sensitive to this class of models. Interesting collider and Gravity-wave signals are also briefly discussed.

SUSY CP problem in gauge mediation model

SUSY CP problem in the gauge mediation supersymmetry breaking model is reconsidered. We pay particular attention to two sources of CP violating phases whose effects were not seriously studied before; one is the effect of the breaking of the GUT relation among the gaugino masses due to the field responsible for the GUT symmetry breaking, and the other is the supergravity effect on the supersymmetry breaking parameters, in particular, on the bi-linear supersymmetry breaking Higgs mass term. We show that both of them can induce too large electric dipole moments of electron, neutron, and so on, to be consistent with the experimental bounds.

Variations on the supersymmetricQ6model of flavor

We observe that a recently proposed supersymmetric model with Q6 flavor symmetry admits a new CP violating ground state. A new sum rule for the quark mixing parameters emerges, which is found to be consistent with data. Simple extensions of the model to the neutrino sector suggest an inverted hierarchical mass spectrum with nearly maximal CP violation (|delta_{MNS}| simeq pi/2). Besides reducing the number of parameters in the fermion sector, these models also provide solutions to the SUSY flavor problem and the SUSY CP problem. We construct a renormalizable scalar potential that leads to the spontaneous breaking of CP symmetry and the family symmetry.

CP violation in supersymmetry with Effective Minimal Flavour Violation

We analyze CP violation in supersymmetry with Effective Minimal Flavour Violation, as recently proposed in arXiv:1011.0730. Unlike the case of standard Minimal Flavour Violation, we show that all the phases allowed by the flavour symmetry can be sizable without violating existing Electric Dipole Moment constraints, thus solving the SUSY CP problem. The EDMs at one and two loops are precisely analyzed as well as their correlations with the expected CP asymmetries in B physics.