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# The leading diagram that contributes to SUSY-breaking scalar masses in the models considered in this paper. The bulk line is a gaugino propagator with two mass insertions on the hidden brane.

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We consider supersymmetric theories where the standard-model quark and lepton fields are localized on a "3-brane" in extra dimensions, while the gauge and Higgs fields propagate in the bulk. If supersymmetry is broken on another 3-brane, supersymmetry breaking is communicated to gauge and Higgs fields by direct higher-dimension interactions, and to...

## Contexts in source publication

**Context 1**

... In par- ticular, the µ term can be generated by the Giudice-Masiero mechanism [10]. Other direct contact interactions between the hidden and visible sectors are suppressed be- cause of their spatial separation. The leading contribution to SUSY breaking for visible sector fields arises from loops of bulk gauge and Higgs fields, as illustrated in Fig. 1. These diagrams are ultraviolet convergent (and hence calculable) because the spatial separation of the hidden and visible branes acts as a physical point-splitting regulator. In effective field theory language, the contribution from loop momenta above the compactification scale is a (finite) matching contribution, while the con- ...

**Context 2**

... 5 compactified on a circle with circumference L ∼ 20/M, the exponential suppression is e −10 ∼ 5 × 10 −5 and Bµ/m 2 1/2 ∼ 4. As the number of extra dimensions increases, the strong coupling estimate is approached rapidly. See We now discuss the loop effects that communicate SUSY breaking to the visible sector fields, such as those illustrated in Fig. 1. These are ultraviolet convergent be- cause the separation of the hidden and visible branes acts as a physical point-splitting regulator for these diagrams. Another way to see this is that there is no local coun- terterm in the D-dimensional theory that can cancel a possible overall divergence. 5 Given a specific D-dimensional theory, ...

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## Citations

... It is capable of beautifully addressing the electroweak (EW) hierarchy problem, improving the fit to Grand Unification, and offering WIMP dark matter (DM) candidates, if SUSY breaking occurs close to the weak scale. In general, as in any rich weak-scale BSM scenario, it faces the challenge of understanding how excessive flavor-changing neutral currents (FCNCs) and CP violation are suppressed as well as internal challenges such as the µ problem, but there are now robust field theory mechanisms known, such as gauge-mediated SUSY breaking (GMSB) (for a review, see, for example, [2]) and the higher-dimensional sequestered structures of anomaly-mediated SUSY breaking AMSB [3] and gaugino-mediated SUSY breaking (gMSB) [4,5]. ...

... Along these lines, we consider ref. [55], building on ref. [50], to be the most attractive model in the literature so far. It is based ongMSB [4,5], which provides a flexible departure point for flavor-safe model-building to realize the Sleptonic SUSY hierarchy, rooted in a hierarchical UV gaugino mass parameters. The Sleptonic SUSY spectrum provides intriguing physics discovery opportunities at the LHC and future colliders. ...

... The central UV structure is depicted in figure 1. Gaugino-mediation requires an extradimensional interval [4,5], in which the SM fermions and sfermions ("matter" superfields) are localized on one (3 + 1-dimensional) boundary, while the hidden sector responsible for spontaneous SUSY-breaking is localized on the other boundary. The gauge and Higgs superfields propagate in the 5-dimensional bulk. ...

A bstract
We study an attractive scenario, “Sleptonic SUSY”, which reconciles the 125 GeV Higgs scalar and the non-observation of superpartners thus far with potentially pivotal roles for slepton phenomenology: providing viable ongoing targets for LHC discovery, incorporating a co-annihilation partner for detectable thermal relic dark matter, and capable of mediating the potential muon g − 2 anomaly. This is accomplished by a modestly hierarchical spectrum, with sub-TeV sleptons and electroweakinos and with multi-TeV masses for the other new states. We study new elements in the UV MSSM realization of Sleptonic SUSY based on higher-dimensional sequestering and the synergy between the resulting gaugino-mediation, hypercharge D -term mediation and Higgs-mediation of SUSY-breaking, so as to more fully capture the range of possibilities. This framework stands out by harmoniously solving the flavor, CP and μ − Bμ problems of the supersymmetric paradigm. We discuss its extension to orbifold GUTs, including gauge-coupling and b -tau unification. We also develop a non-minimal model with extra Higgs fields, in which the electroweak vacuum is more readily cosmologically stable against decay to a charge-breaking vacuum, allowing a broader range of sleptonic spectra than in the MSSM alone. We survey the rich set of signals possible at the LHC and future colliders, covering both R -parity conservation and violation, as well as for dark matter detection. While the multi-TeV squarks imply a Little Hierarchy Problem, intriguingly, small changes in parameter space to improve naturalness result in dramatic phase transitions to either electroweak-preservation or charge-breaking. In a Multiverse setting, the modest unnaturalness may then be explained by the “principle of living dangerously”.

... There is another breaking mechanism in literature such as the Anomaly mediated SUSY breaking [167,168], Gaugino mediated SUSY breaking [169,170], Gravity-Gauge mediated SUSY breaking [171] and SUSY-breaking using extra dimensions. These both have a fine-tuning problem. ...

The discovery of the Higgs boson raises the question of its "lightness" in mass when the Standard Model is considered as an effective quantum field theory. Supersymmetry is the only currently known symmetry which can protect the Higgs mass while still treating the Higgs as an elementary quantum field. However in the view of null experimental confirmation from both direct (LHC) and indirect searches (flavour, dark matter) of the supersymmetric particles and the constraints from the Higgs mass, several possible heavy spectra for supersymmetric partners have been proposed. In the present thesis, we study the possible origins of these heavy spectra by considering a considering many sequestered spurion fields as carriers of supersymmetry breaking. We show that "natural" supersymmetric spectrum is possible in these models and in particular a "coherent" scenario leads to low fine tuning, light Higgsino mixed dark matter ( a la focus point region) even with heavy supersymmetric spectrum. We then consider this model within the context of string landscape, where we use the Bousso-Polchinski framework of four form fluxes to model the spurions. We show that the flavour violating parameters of supersymmetric spectrum can be "diluted" away in the presence of large number of fluxes. One of the possible supersymmetric spectra which emerges by considering all the data is the generation split (Gensplit) spectrum which allows for flavour violation to be present for the first two generations, which are heavy. We study this spectrum within the context of supersymmetric SU(5) and proton decay. The results are quite interesting and dependent on the proton decay mode considered. The strongest bound p to k \nu is now modified depending on the flavour of the neutrino and brings the parameter space within the realms of upcoming experiments of JUNO, DUNE and Hyper K. These results will be discussed.

... Elaborate mechanisms of SUSY breaking such as gauge mediation (see refs. [27, 28] for reviews) and gaugino mediation [29,30] are able to address the issue. ...

A bstract
Hierarchical masses of quarks and leptons are addressed by imposing horizontal symmetries. In supersymmetric Standard Models, the same symmetries play a role in suppressing flavor violating processes induced by supersymmetric particles. Combining the idea of spontaneous CP violation to control contributions to electric dipole moments (EDMs), the mass scale of supersymmetric particles can be lowered. We present supersymmetric models with U(1) horizontal symmetries and discuss CP and flavor constraints. Models with two U(1) symmetries are found to give a viable solution to the muon g − 2 anomaly. Interestingly, the parameter space to explain the anomaly will be probed by future electron EDM experiments.

... These flavor violating processes originate from soft SUSY breaking mass parameters which mixes different generations of sfermions. The dangerous flavor violating sfermion masses are avoided when the SUSY breaking masses are generated through gauge interactions and SM Yukawa interactions, leading us to gaugino mediation [10][11][12] or Higgs mediation [13,14]. 1 In these mediation mechanisms, the slepton and squark masses vanish at the tree-level and they are generated radiatively via gaugino loops or Higgs loops. Therefore, the flavor problem is absent within MSSM even if some SUSY particles are as light as O(0.1-1 TeV) [17]. ...

A bstract
We consider supersymmetric (SUSY) models for the muon g − 2 anomaly without flavor violating masses at the tree-level. The models can avoid LHC constraints and the vacuum stability constraint in the stau-Higgs potential. Although large flavor violating processes are not induced within the framework of minimal SUSY standard model, once we adopt a seesaw model, sizable lepton flavor violating (LFV) processes such as μ → eγ and μ → e conversion are induced. These LFV processes will be observed at future experiments such as MEG-II, COMET and Mu2e if right-handed neutrinos are heavier than 10 ⁹ GeV motivated by the successful leptogenesis. This conclusion is somewhat model independent since Higgs doublets are required to have large soft SUSY breaking masses, leading to flavor violations in a slepton sector via neutrino Yukawa interactions.

... The origins of supersymmetry-breaking being a separate sector does force us to expand our model of particle physics, but on the upshot this sequestering means we can explore interesting phenomenology in sectors which are unconstrained. One can write down models where supersymmetry breaking is mediated by supergravity effects [123,124,125,126,127,128,129], communicated to the SM fields by our gauge bosons from a sector with new, massive SM-charged particles [130,131,132,133,134,135], or takes place at a physically separate location in an extra dimension [136,137,138,139,140,141,142,143,144,145], for a few examples. A full discussion of the mechanisms and strategies for models of supersymmetry-breaking is beyond our scope, but we highly recommend ...

We begin this thesis with an extensive pedagogical introduction aimed at clarifying the foundations of the hierarchy problem. After introducing effective field theory, we discuss renormalization at length from a variety of perspectives. We focus on conceptual understanding and connections between approaches, while providing a plethora of examples for clarity. With that background we can then clearly understand the hierarchy problem, which is reviewed primarily by introducing and refuting common misconceptions thereof. We next discuss some of the beautiful classic frameworks to approach the issue. However, we argue that the LHC data have qualitatively modified the issue into `The Loerarchy Problem'---how to generate an IR scale without accompanying visible structure---and we discuss recent work on this approach. In the second half, we present some of our own work in these directions, beginning with explorations of how the Neutral Naturalness approach motivates novel signatures of electroweak naturalness at a variety of physics frontiers. Finally, we propose a New Trail for Naturalness and suggest that the physical breakdown of EFT, which gravity demands, may be responsible for the violation of our EFT expectations at the LHC.

... These flavor violating processes originate from soft SUSY breaking mass parameters which mixes different generations of sfermions. The dangerous flavor violating sfermion masses are avoided when the SUSY breaking masses are generated through gauge interactions and SM Yukawa interactions, leading us to gaugino mediation [9][10][11] or Higgs mediation [12,13]. 1 In these mediation mechanisms, the slepton and squark masses vanish at the tree-level and they are generated radiatively via gaugino loops or Higgs loops. Therefore, the flavor problem is absent within MSSM even if some SUSY particles are as light as O(0.1-1 TeV) [16]. ...

We consider supersymmetric (SUSY) models for the muon $g-2$ anomaly without flavor violating masses at the tree-level. The models can avoid LHC constraints and the vacuum stability constraint in the stau-Higgs potential. Although large flavor violating processes are not induced within the framework of minimal SUSY standard model, once we adopt a seesaw model, sizable lepton flavor violating (LFV) processes such as $\mu \to e \gamma$ and $\mu \to e$ conversion are induced. These LFV processes will be observed at future experiments such as MEG-II, COMET and Mu2e if right-handed neutrinos are heavier than $10^9$ GeV motivated by the successful leptogenesis. This conclusion is somewhat model independent since Higgs doublets are required to have large soft SUSY breaking masses, leading to flavor violations in a slepton sector via neutrino Yukawa interactions.

... One can also consider other flavor-safe mediation mechanisms e.g. refs.[14][15][16][17][18]. ...

A simple model for the explanation of the muon anomalous magnetic moment was proposed by the present authors within the context of the minimal supersymmetric standard model [1, 2]: Higgs-anomaly mediation. In the setup, squarks, sleptons, and gauginos are massless at tree-level, but the Higgs doublets get large negative soft supersymmetry (SUSY) breaking masses squared mHu2≃mHd2<0 at a certain energy scale, Minp. The sfermion masses are radiatively generated by anomaly mediation and Higgs-loop effects, and gaugino masses are solely determined by anomaly mediation. Consequently, the smuons and bino are light enough to explain the muon g − 2 anomaly while the third generation sfermions are heavy enough to explain the observed Higgs boson mass. The scenario avoids the SUSY flavor problem as well as various cosmological problems, and is consistent with the radiative electroweak symmetry breaking. In this paper, we show that, although the muon g − 2 explanation in originally proposed Higgs-anomaly mediation with Minp∼ 1016 GeV is slightly disfavored by the latest LHC data, the muon g − 2 can still be explained at 1σ level when Higgs mediation becomes important at the intermediate scale, Minp∼ 1012 GeV. The scenario predicts light SUSY particles that can be fully covered by the LHC and future collider experiments. We also provide a simple realization of mHu2≃mHd2<0 at the intermediate scale.

... A detail collider simulation is important but beyond the scope of the present paper. A smaller M inp would effectively lead to larger |µ|-term and thus larger muon g−2 (see (18)). To see this, let us fix the gravitino mass. ...

... One can also consider other flavor-safe mediation mechanisms e.g. Refs.[14][15][16][17][18].2 This kind of cosmological safety with alleviation of the gravitino problem with m 3/2 O(10) TeV can be found in the pure-gravity mediation scenario[19,20], minimal-split SUSY[21] or the split-SUSY[22,23].3 ...

A simple model for the explanation of the muon anomalous magnetic moment was proposed by the present authors within the context of the minimal supersymmetric standard model [1607.05705, 1608.06618]: "Higgs-anomaly mediation". In the setup, squarks, sleptons, and gauginos are massless at tree-level, but the Higgs doublets get large negative soft supersymmetry (SUSY) breaking masses squared $m_{H_u}^2 \simeq m_{H_d}^2 < 0$ at a certain energy scale, $M_{\rm inp}$. The sfermion masses are radiatively generated by anomaly mediation and Higgs-loop effects, and gaugino masses are solely determined by anomaly mediation. Consequently, the smuons and bino are light enough to explain the muon $g-2$ anomaly while the third generation sfermions are heavy enough to explain the observed Higgs boson mass. The scenario avoids the SUSY flavor problem as well as various cosmological problems, and is consistent with the radiative electroweak symmetry breaking. In this paper, we show that, although the muon $g-2$ explanation in originally proposed Higgs-anomaly mediation with $M_{\rm inp}\sim 10^{16}\,$GeV is slightly disfavored by the latest LHC data, the muon $g-2$ can still be explained at $1\sigma$ level when Higgs mediation becomes important at the intermediate scale, $M_{\rm inp} \sim 10^{12}\,$GeV. The scenario predicts light SUSY particles that can be fully covered by the LHC and future collider experiments. We also provide a simple realization of $m_{H_u}^2 \simeq m_{H_d}^2 < 0$ at the intermediate scale.

... Probably nowhere is this stress more visible than in models characterized by zero scalar masses at a high scale. Often using "locality" in setups with extra dimensions [1,2], or lattices of gauge groups connected by link fields [3,4], or even strong and nearly conformal dynamics of the hidden sector [5][6][7], these models sequester scalar masses at the input scale (say Λ int ), thereby ensuring that flavor universal gaugino mediation remains the sole source of scaler masses at infrared (IR). These elegant solutions to the flavor problem in supersymmetry [8] can also solve the μ-B μ problem [5], and provide a unique perspective to the fine-tuning problem [7], where dynamics brings in large cancellations in the Higgs mass matrix, while at the same time, accommodating gaugino mass unification. ...

We report that models of electroweak supersymmetry with gaugino mass unification and sequestered scalar masses can still produce viable spectra, as long as we include a set of nonstandard supersymmetry breaking terms, which are trilinear in scalars like the A-terms, but are nonholomorphic in visible sector fields unlike the A- terms. These terms impart a subtle feature to one loop renormalization group equations of soft supersymmetry breaking terms, indirectly sourcing flavor universal contributions to all scalar masses. These new contributions can even dominate over radiative corrections from bino, and help raise right handed sleptons above bino, while leaving a tell-tale signature in the spectrum.

... A significant consideration in any ultraviolet (UV) framework must be the SUSY flavour problem, since the presence of weak-scale sleptons (and squarks) will generically have disastrous consequences in flavour observables, such as µ → eγ. With this in mind, we work within the framework of gaugino mediation [24][25][26], which provides an elegant solution to the SUSY flavour problem: the soft masses of the squarks and sleptons are initially negligible at the grand unified theory (GUT) scale and are then radiatively generated via flavour-blind gaugino loops. ...

... Next, the strong constraint from stau instability motivates us to consider, in section 3, a model with gaugino+Higgs mediation, where there is a direct coupling of the Higgs doublets to the SUSY breaking field. Such a coupling is expected if the sequestered Kähler potential originates from an extra dimension and the Higgs doublets live in the bulk [26]. In this setup, the soft SUSY breaking masses for the Higgs doublets are assumed to be tachyonic, allowing hierarchical sfermion masses to be generated from Higgs loops without inducing too large FCNC [28][29][30]. ...

A bstract
We explore the possibility that the muon g − 2 anomaly and the nature of dark matter can be simultaneously explained within the framework of gaugino mediation, focusing on bino-like dark matter where the observed abundance is obtained via co-annihilations. The minimal model with non-universal gaugino masses is excluded by stau vacuum instability, although this constraint can be somewhat relaxed via the addition of a universal soft scalar mass (or B − L gaugino mediation). A more promising alternative is gaugino+Higgs mediation, which significantly raises the soft masses of the third generation sfermions leading to a split spectrum. In this framework, the muon g − 2 can be easily explained and the dark matter abundance obtained through either bino-wino or bino-slepton co-annihilations.