We study the contributions of supersymmetric models with a $U(1)$ horizontal symmetry and only spontaneous CP breaking to various lepton flavor observables, such as $μ\to eγ$ and the electron electric dipole moment. We show that both a horizontal symmetry and a lack of explicit CP violation can alleviate the existing bounds from such observables. The undetermined $\mathcal{O}(1)$ coefficients in such mass matrix models muddle the interpretation of the bounds from various flavor observables. To overcome this, we define a new fine-tuning measure for different observables in such setups. This allows us to study how naturally the observed IR flavor observables can emerge from a given mass matrix model. We use our flavor-naturalness measure in study of our supersymmetric models and quantify the degree of fine tuning required by the bounds from various lepton flavor observables at each mass scale of sleptons, neutralinos, and charginos.
The experiments at the Large Hadron Collider (LHC) have pushed the limits on masses of supersymmetric particles beyond the $\sim$TeV scale. This compromises naturalness of the simplest supersymmetric extension of the Standard Model, the minimal supersymmetric Standard Model (MSSM). In this paper we advocate that perhaps the current experimental data are actually hinting towards the physics beyond MSSM. To illustrate this, we treat MSSM as a low energy limit of a more fundamental yet unspecified theory at a scale $Λ$, and compute the fine-tuning measure $Δ$ for generic boundary conditions on so…
Recent years have seen increased use of Bayesian model comparison to quantify notions such as naturalness, simplicity, and testability, especially in the area of supersymmetric model building. After demonstrating that Bayesian model comparison can resolve a paradox that has been raised in the literature concerning the naturalness of the proton mass, we apply Bayesian model comparison to GUTs, an area to which it has not been applied before. We find that the GUTs are substantially favored over the non-unifying puzzle model. Of the GUTs we consider, the $B-L$ MSSM GUT is the most favored, but th…
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.
In this report, we compare the naturalness and Dark Matter (DM) properties of the Minimal Supersymmetric Standard Model (MSSM) and the $B-L$ Supersymmetric Standard Model (BLSSM), with universality in both cases. We do this by adopting standard measures for the quantitative analysis of the Fine-Tuning (FT), at both low (i.e. supersymmetric (SUSY)) and high (i.e. unification) scales. We will see a similar level of FT for both models in these scenarios, with a slightly better FT for the BLSSM at SUSY scales and MSSM at Grand Unification Theory (GUT) scales. When including DM relic constraints, w…
In the Minimal Supersymmetric Extension of the Standard Model (MSSM) the higgsino mass parameter $μ$ appears both in the masses of the Higgs bosons and in the neutralino mass matrix. Electroweak finetuning therefore prefers small values of $|μ|$. On the other hand, bino--like neutralinos make a good dark matter candidate. We show that current direct search limits then impose a strong lower bound on $|μ|$, in particular for $μ> 0$ or if the masses of the heavy Higgs bosons of the MSSM are near their current limit from LHC searches. There is therefore some tension between finetuning and neutrali…
There exists a vast literature examining the electroweak (EW) fine-tuning problem in supersymmetric scenarios, but little concerned with the dark matter (DM) one, which should be combined with the former. In this paper, we study this problem in an, as much as possible, exhaustive and rigorous way. We have considered the MSSM framework, assuming that the LSP is the lightest neutralino, $χ_1^0$, and exploring the various possibilities for the mass and composition of $χ_1^0$, as well as different mechanisms for annihilation of the DM particles in the early Universe (well-tempered neutralinos, fun…
The absence of any signal of supersymmetry (SUSY) at the LHC has raised the SUSY particle mass scale compared to $Z$ boson mass $M_Z$. We investigate the naturalness of the electroweak symmetry breaking after considering radiative symmetry breaking along with 125 GeV Higgs mass. We find that the important quantity to measure the naturalness of the hierarchy between the SUSY scale and $M_Z$ is the separation between the radiative symmetry breaking scale, i.e., where $m_{H_u}^2+μ^2$ turns negative for large $\tanβ$ case ($μ$ is the Higgsino mass and $m_{H_u}$ is the SUSY breaking up-type Higgs b…
It is pointed out that in supersymmetric models with a new gauge symmetry under which the Higgs is charged, the fine-tuning of the electroweak symmetry breaking is relaxed due to suppression of the top Yukawa coupling at higher scales by a new large gauge coupling. We calculate the fine-tuning in an explicit model and find that the lower bounds on stops and gluino masses from the naturalness criterion are increased by several hundred GeV in comparison to the Minimal Supersymmetric Standard Model (MSSM). The fine-tuning is improved by one to two orders of magnitude as compared to the MSSM, as a…
We study the naturalness properties of the $B-L$ Supersymmetric Standard Model (BLSSM) and compare them to those of the Minimal Supersymmetric Standard Model (MSSM) at both low (i.e., Large Hadron Collider) energies and high (i.e., unification) scales. By adopting standard measures of naturalness, we assess that, in presence of full unification of the additional gauge couplings and scalar/fermionic masses of the BLSSM, such a scenario reveals a somewhat higher degree of Fine-Tuning (FT) than the MSSM, when the latter is computed at the unification scale and all available theoretical and experi…
Naturalness, Supersymmetry and Light Higgsinos: A Snowmass Whitepaper
我们证明了由弱标度参数表示的电弱对称性破缺条件导出的电弱微调参数Δ_{ \rm EW}导致{ \it a bound on fine-tuning in MSSM}，并解释了它在唯象分析中的实用性.我们认为，μ参数的小幅度和轻希格斯玻色子的伴随存在是超对称模型中自然性的最基本结果，并列出了这对LHC和未来e^+e^-对撞机实验的影响。
The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a $\mathbb{Z}_3$ conserving semi-constrained Next-to-Minimal Supersymmetric Standard Model (NMSSM) to the constrained MSSM (CMSSM). We contrast popular fine-tuning measures with naturalness priors, which automatically appear in statistical measures of the plausibility that a given model reproduces the weak scale. Our comparison shows that naturalness priors provide valuable ins…
Models with a light, additional gauge boson are attractive extensions of the standard model. Often these models are only considered as effective low energy theory without any assumption about an UV completion. This leaves not only the hierarchy problem of the SM unsolved, but introduces a copy of it because of the new fundamental scalars responsible for breaking the new gauge group. A possible solution is to embed these models into a supersymmetric framework. However, this gives rise to an additional source of fine-tuning compared to the MSSM and poses the question how natural such a setup is.…
Non-minimal supersymmetric models that predict a tree-level Higgs mass above the Minimal Supersymmetric Standard Model (MSSM) bound are well motivated by naturalness considerations. Indirect constraints on the stop sector parameters of such models are significantly relaxed compared to the MSSM; in particular, both stops can have weak-scale masses. We revisit the stop-catalyzed electroweak baryogenesis (EWB) scenario in this context. We find that the LHC measurements of the Higgs boson production and decay rates already rule out the possibility of stop-catalyzed EWB. We also introduce a gauge-i…
In order to interpret the Higgs mass and its decays more naturally, we hope to intrude the BLMSSM and B-LSSM. In the both models, the right-handed neutrino superfields are introduced to better explain the neutrino mass problems. In addition, there are other superfields considered to make these models more natural than MSSM. In this paper, the method of $χ^2$ analyses will be adopted in the BLMSSM and B-LSSM to calculate the Higgs mass, Higgs decays and muon $g-2$. With the fine-tuning in the region $0.67\%-2.5\%$ and $0.67\%-5\%$, we can obtain the reasonable theoretical values that are in acc…
The latest experimental results from the LHC and dark matter (DM) searches suggest that the parameter space allowed in supersymmetric theories is subject to strong reductions. These bounds are especially constraining for scenarios entailing light DM particles. Previous studies have shown that light neutralino DM in the Minimal Supersymmetric Standard Model (MSSM), with parameters defined at the electroweak scale, is still viable when the low energy spectrum of the model features light sleptons, in which case, the relic density constraint can be fulfilled. In view of this, we have investigated …
We present a solution to the strong CP problem, which relies on the horizontal gauge symmetry and CP invariance in a full theory. Similar to other Nelson-Barr type solutions, CP violation in both the strong and weak sectors in the Standard model (SM) is attributed to the condensation of complex scalars $Φ$ in the model. The model is differentiated by others in that it explains the hierarchy in quark-Higgs Yukawa coupling in the SM based on a series of sequential breaking of the horizontal $SU(3)_{f}$ gauge symmetry. The experimental constraint $\overlineθ\lesssim10^{-10}$ requires $<\!\!Φ\!\!>…
MSSM4G models, in which the minimal supersymmetric standard model is extended to include vector-like copies of standard model particles, are promising possibilities for weak-scale supersymmetry. In particular, two models, called QUE and QDEE, realize the major virtues of supersymmetry (naturalness consistent with the 125 GeV Higgs boson, gauge coupling unification, and thermal relic neutralino dark matter) without the need for fine-tuned relations between particle masses. We determine the implications of these models for dark matter and collider searches. The QUE and QDEE models revive the pos…
Top squark (stop) is a crucial part of supersymmetric models (SUSY) to understand the naturalness problem. Other than the traditional stop pair production, the single production via electroweak interaction provides signals with distinctive features which could help confirm the existence of the top squark. In this paper, we investigate the observability of stop through the mono-top channel of the single stop production at the future proton-proton colliders, FCC-hh and SPPC, in a simplified Minimal Supersymmetric Standard Model (MSSM). With the integrated luminosity of 3000 $\text{fb}^{-1}$, we …
