The regions in the Minimal Supersymmetric Standard Model with the minimal amount of fine-tuning of electroweak symmetry breaking are presented for general messenger scale. No a priori relations among the soft supersymmetry breaking parameters are assumed and fine-tuning is minimized with respect to all the important parameters which affect electroweak symmetry breaking. The superpartner spectra in the minimally tuned region of parameter space are quite distinctive with large stop mixing at the low scale and negative squark soft masses at the high scale. The minimal amount of tuning increases enormously for a Higgs mass beyond roughly 120 GeV.
Curvaton is an effectively massless field whose energy density during inflation is negligible but which later becomes dominant. This is a novel mechanism to generate the scale invariant perturbations. I discuss the possibility that the curvaton could be found among the fields of the minimally supersymmetric standard model (MSSM), which contains a number of flat directions along which the renormalizable potential vanishes. The requirements of late domination and the absence of damping of the perturbations pick out essentially a unique candidate for the MSSM curvaton. One must also require that …
We analyse the electric dipole moment of the neutron in the MSSM, induced by the renormalisation of the soft-susy breaking terms. We run the RGEs using two-loop expressions for gauge and Yukawa couplings and retaining family dependence. The $μ$ and $B$ parameters were determined by minimising the full one-loop Higgs potential, and we find that the neutron EDM lies in the range $10^{-33}<|d_n| < 10^{-29} {\; e\;\mbox{cm}} $.
We consider an extension of the supersymmetric standard model which includes singlet Higgs superfield representations (in three generations) to generate neutrino masses via the see-saw mechanism. The resulting theory may then exhibit R-parity violation in the couplings of the singlets, inducing $R$-parity violating effective interactions among the standard model superfields, as well as inducing decay of the lightest neutralino, which otherwise would compose a stable LSP. We compute the rates for the resulting neutralino decays, depending on the particular superpotential couplings responsible f…
We construct supersymmetric theories in which the correct scale for electroweak symmetry breaking is obtained without significant fine-tuning. We calculate the fine-tuning parameter for these theories to be at the 20% level, which is significantly better than in conventional supersymmetry breaking scenarios. Supersymmetry breaking occurs at a low scale of order 100 TeV, and is transmitted to the supersymmetric standard-model sector through standard-model gauge interactions. The Higgs sector contains two Higgs doublets and a singlet field, with a superpotential that takes the most general form …
We construct realistic supersymmetric theories in which the correct scale for electroweak symmetry breaking is obtained without significant fine-tuning. We consider two classes of models. In one class supersymmetry breaking is transmitted to the supersymmetric standard model sector through Dirac gaugino mass terms generated by a D-term vacuum expectation value of a U(1) gauge field. In the other class the supersymmetry breaking sector is separated from the supersymmetric standard model sector in an extra dimension, and the transmission of supersymmetry breaking occurs through gauge mediation. …
The radiative seesaw mechanism proposed recently is minimally extended to include supersymmetry in a specific model. Relevant related issues such as leptogenesis and dark matter are discussed.
We construct and study the 5D realization of a composite Higgs model with minimal tuning. The Higgs is a (pseudo-)Goldstone boson from the spontaneous breaking of a global SO(5) symmetry to an SO(4) subgroup. The peculiarity of our construction lies in the specific choice of the SO(5) representations of the 5D fermions from which the Standard Model fields arise as chiral zero modes. This choice reduces the tuning of these models to the minimal model-independent value allowed by electroweak precision tests. We analyse the main differences between our 5D construction and other descriptions in te…
We address an issue what kind of tuning realizes a flat potential for inflaton in supergravity. We restrict ourselves to the case that inflationary dynamics is not affected by separate supersymmetry-breaking effects, and consider examples of a single chiral superfield as an inflaton with its vacuum of the vanishing cosmological constant. The examples potentially include the cases of Polonyi field or right-handed sneutrino as an inflaton.
We present consistent supersymmetric theories invariant under the generalization of the Galilean shift symmetry to ${\cal{N}}=1$ superspace. These theories are constructed via the decoupling limit of certain non-minimally derivative coupled supergravities, thus they correspond to the supersymmetrization of the so-called covariant Galileon. Specifically, these theories are constructed in the linearized ${\cal{N}}=1$ new-minimal supergravity set-up where the chiral supermultiplet is minimally coupled to gravity via the standard R-current contact term, and, at the same time, non-minimally derivat…
We study the cosmology of the Supersymmetric Standard Model augmented by a gauge singlet to solve the $μ$-problem and describe the evolution of the domain walls which are created during electroweak symmetry breaking due to the discrete $Z_{3}$ symmetry in this model. The usual assumption, that non-renormalizable terms induced by gravity (which explicitly break this symmetry) may cause the walls to collapse on a cosmologically safe timescale, is reconsidered. Such terms are constrained by considerations of primordial nucleosynthesis, and also by the fact that by not respecting the $Z_{3}$ symme…
We explore dark matter in the Finely Tuned Minimal Supersymmetric Standard model recently proposed by Arkani-Hamed and Dimopoulos. Relative to the MSSM, there are fewer particles at freeze-out, so the calculation of the relic abundance simplifies. Similarly, the predictions for direct detection of the dark matter sharpen. There is a large region of mixed bino--higgsino dark matter where the lightest supersymmetric particle will be accessible at both the LHC and future direct detection experiments, allowing for a conclusive identification of the dark matter particle. Typical dark matter-nucleon…
We argue that given the experimental constraints on the Higgs mass the least fine tuned parameter space of minimal supersymmetric standard model is with negative stop masses squared at the grand unification scale. While stop mass squared is typically driven to positive values at the weak scale, the contribution to the Higgs mass squared parameter from the running can be arbitrarily small, which reduces fine tuning of electroweak symmetry breaking. At the same time the stop mixing is necessarily enhanced and the maximal mixing scenario for the Higgs mass can be generated radiatively even when s…
Discarding the prejudice about fine tuning, we propose a novel and efficient approach to identify relevant regions of fundamental parameter space in supersymmetric models with some amount of fine tuning. The essential idea is the mapping of experimental constraints at a low energy scale, rather than the parameter sets, to those of the fundamental parameter space. Applying this method to the non-universal Higgs masses model, we identify a new interesting superparticle mass pattern where some of the first two generation squarks are light whilst the stops are kept heavy as 6TeV. Furthermore, as a…
Can the Large Hadron Collider explain the masses and mixings of the known fermions? A promising possibility is that these masses and mixings are determined by flavor symmetries that also govern new particles that will appear at the LHC. We consider well-motivated examples in supersymmetry with both gravity- and gauge-mediation. Contrary to spreading belief, new physics need not be minimally flavor violating. We build non-minimally flavor violating models that successfully explain all known lepton masses and mixings, but span a wide range in their predictions for slepton flavor violation. In na…
We investigate couplings of squarks to gauge and Higgs-bosons within the framework of non-minimal flavour violation in the Minimal Supersymmetric Standard Model. Introducing non-diagonal elements in the mass matrices of squarks, we first study their impact on the self-energies and physical mass eigenvalues of squarks. We then present an extensive analysis of bosonic squark decays for variations of the flavour-violating parameters around the two benchmark scenarios SPS1a' and SPS1b. Signatures, that would be characteristic for a non-minimal flavour structure in the squark sector, can be found i…
We introduce a quantification of the question in the title: the logarithmic sensitivity of the relic neutralino density Omega-hsquared to variations in input parameters such as the supersymmetric mass scales m_0, m_1/2 and A_0, tan beta and the top and bottom quark masses. In generic domains of the CMSSM parameter space with a relic density in the preferred range 0.1 < Omega-hsquared < 0.3, the sensitivities to all these parameters are moderate, so an interesting amount of supersymetric dark matter is a natural and robust prediction. Within these domains, the accuracy in measuring the CMSSM an…
The $(B-L)$ Supersymmetric Standard Model (BLSSM) motivates several Dark Matter (DM) candidates beyond the Minimally Supersymmetric Standard Model (MSSM). We assess the comparative naturalness of the two models and discuss the potential detection properties of a particular candidate, the Right-Handed (RH) sneutrino.
We investigate how the Fine-Tuning (FT) in the B-L Supersymmetric Standard Model (BLSSM) compares to the Minimally Supersymmetric Standard Model (MSSM), where both models have universality. This is done for two scales: both low (i.e. collider) and high (i.e. Grand Unified Theory (GUT)) scales. We see this is similar for both models and the two scale regimes. We also study the possible Dark Matter (DM) candidates each model offers in a realistic scenario satisfying relic density constraints. Our findings are that whilst the parameter space for the single MSSM DM candidate is severely constraine…
We study constrained versions of the minimal supersymmetric model and investigate the hierarchy between the electroweak scale and the scale of superpartners that can be achieved without relying on specifying model parameters by more than one digit. This approach automatically avoids scenarios in which a large hierarchy is obtained by special choices of parameters and yet keeps scenarios that would be otherwise disfavored by various sensitivity measures. We consider models with universal gaugino and scalar masses, models with non-universal Higgs masses or non-universal gaugino masses and focus …
The solution of a fine tuning problem is one of the principal motivations of Supersymmetry. However experimental constraints indicate that many Supersymmetric models are also fine tuned (although to a much lesser extent). We review the traditional measure of this fine tuning used in the literature and propose an alternative. We apply this to the MSSM and show the implications.
We analyze CP violation in the supersymmetric standard model (MSSM) embedded minimally into a left-right symmetric gauge structure with the seesaw mechanism for neutrino masses. With the plausible assumption of universal scalar masses it is shown that CP violation in the hadron sector of the MSSM is described by a single phase residing in the supersymmetry breaking Lagrangian. This improves the CP properties of the MSSM by providing a natural solution to the SUSY CP problem. Furthermore, $ε'/ε$ vanishes in this model above the seesaw scale; extrapolation to the weak scale then leads to a predi…
A vast array of (metastable) vacuum solutions arise from string compactifications, each leading to different 4-d laws of physics. The space of these solutions, known as the string landscape, allows for an environmental solution to the cosmological constant problem. We examine the possibility of an environmental solution to the gauge hierarchy problem. We argue that the landscape favors softly broken supersymmetric models over particle physics models containing quadratic divergences, such as the Standard Model. We present a scheme for computing relative probabilities for supersymmetric models t…
We study a model with an exotic new sector strongly coupled to the Higgs boson, in which supersymmetry is introduced to protect the quartic coupling from a large running and avoid potential vacuum stability problem. The fermionic components present vector like mass terms, through which the Higgs diphoton decay branching ratio can be tuned. The bosonic components trigger a strongly first order electroweak phase transition. We find a large parameter region of effective Yukawa coupling $y\gtrsim2$ and mass parameters $m_f\sim m_s$ of a few hundred GeV, that can simultaneously accommodate the diph…
The lack of evidence for superparticles at the CERN LHC, along with the rather high value of the Higgs mass, has sharpened the perception that supersymmetric model parameter space is highly electroweak fine-tuned (EWFT). We compare three measures of fine-tuning in SUSY models. 1. \Del_HS measures a terms containing large log contributions to m_Z that are inevitable in models defined at scales much higher than the electroweak scale. 2. \Del_BG measures variation in m_Z against variation of model parameters and allows for correlations among high scale parameters which are not included in \Del_HS…
We present the dark matter (DM) extension (by N) of the minimal supersymmetric standard model to give the recent trend of the high energy positron spectrum of the PAMELA/HEAT experiments. If the trend survives by future experiments, the MSSM needs to be extended. Here, we minimally extend the MSSM with one more DM component N together with a heavy lepton E, and introduce the coupling e_R E_R^c N_R. This coupling naturally appears in the flipped SU(5) GUT models. This N_{DM}MSSM contains the discrete symmetry Z_6, and for some parameter ranges there result two DM components. For the MSSM fields…
We search for weakly interacting fixed points in extensions of the minimally supersymmetric standard model (MSSM). Necessary conditions lead to three distinct classes of anomaly-free extensions involving either new quark singlets, new quark doublets, or a fourth generation. While interacting fixed points arise prolifically in asymptotically free theories, their existence is significantly constrained as soon as some of the non-abelian gauge sectors are infrared free. Performing a scan over $\sim 200$k different MSSM extensions using matter field multiplicities and the number of superpotential c…
In this paper we analyze spectra in the phenomenological supersymmetric Standard Model that simultaneously result in the right dark-matter relic density $Ω_{\rm DM} h^2$, offer an explanation for the $(g-2)_μ$ discrepancy $Δa_μ$ and are minimally fine-tuned. We discuss the LHC phenomenology resulting from these spectra and the sensitivity of dark-matter direct detection experiments to these spectra. We find that the latter type of experiments with sensitivity to the spin-dependent dark-matter-nucleon scattering cross section $σ_{\rm SD,p}$ will probe all of our found solutions.
We consider the minimal supersymmetric SO(10) model, where only one {\bf 10} and one $\bar{\bf 126}$ Higgs multiplets have Yukawa couplings with matter multiplets. This model has the high predictive power for the Yukawa coupling matrices consistent with the experimental data of the charged fermion mass matrices, and all the Yukawa coupling matrices are completely determined once a few parameters in the model are fixed. This feature is essential for definite predictions to the proton decay rate through the dimension five operators. We analyze the proton decay rate for the dominant decay modes $…
We quantify and examine the uncertainties in predictions of the lightest $CP$ even Higgs boson pole mass $M_h$ in the Minimal Supersymmetric Standard Model (MSSM), utilising current spectrum generators and including some three-loop corrections. There are two broadly different approximations being used: effective field theory (EFT) where an effective Standard Model (SM) is used below a supersymmetric mass scale, and a fixed order calculation, where the MSSM is matched to QCD$\times$QED at the electroweak scale. The uncertainties on the $M_h$ prediction in each approach are broken down into loga…
In order for neutralino dark matter to avoid being overproduced in the early universe, these particles must annihilate (or coannihilate) rather efficiently. Neutralinos with sufficiently large couplings to annihilate at such high a rate (such as those resulting from gaugino-higgsino mixing, as in "well-tempered" or "focus point" scenarios), however, have become increasingly disfavored by the null results of XENON100 and other direct detection experiments. One of the few remaining ways that neutralinos could potentially evade such constraints is if they annihilate through a resonance, as can oc…
Many models for dynamical supersymmetry breaking have the domain wall solution of the Kovner-Shifman type and therefore contain the potential cosmological domain wall problem.We show that the degeneracy of the vacua is lifted in any model in which the cosmological constant is fine-tuned to zero through an explicit $Z_{n}^{R}$ symmetry breaking constant in the superpotential. In this respect, we do not have to add unnatural non-renormalizable terms which explicitly break the symmetry. We also discuss the conditions for the safe decay of the walls for several concrete examples.
Gluon mediated exclusive hadronic decays of b quarks are studied within the standard model (SM) and the constrained minimally supersymmetric standard model (MSSM). For all allowed regions of the MSSM parameter space (A, tan beta, m_0, m_{1/2}) the penguin magnetic dipole form factor F^R_2 is dominant over the electric dipole and can be larger than the magnetic dipole form factor of the SM. However, overall the SM electric dipole decay amplitude F^L_1 dominates the decay rate. The MSSM penguin contributions to the free quark decay rate approach the 10% level for those regions of parameter space…
We study the complementarity between dark matter experiments (direct detection and indirect detections) and accelerator facilities (the CERN LHC and a $\sqrt{s}= 1$ TeV $e^+e^-$ Linear Collider) in the framework of the constrained Minimal Supersymmetric Standard Model (MSSM). We show how non--universality in the scalar and gaugino sectors can affect the experimental prospects to discover the supersymmetric particles. The future experiments will cover a large part of the parameter space of the MSSM favored by WMAP constraint on the relic density, but there still exist some regions beyond reach …
We explore the dark matter sector in extensions of the Minimal Supersymmetric Standard Model (MSSM) that can provide a good fit to the PAMELA cosmic ray positron excess, while at the same time addressing the little hierarchy problem of the MSSM. Adding a singlet Higgs superfield, S, can account for the observed positron excess, as recently discussed in the literature, but we point out that it requires a fine-tuned choice for the parameters of the model. We find that including an additional singlet allows both a reduction of the weak-scale fine-tuning, and an interpretation of the cosmic ray ob…
The PQ mechanism resolving the strong CP problem and the seesaw mechanism explaining the smallness of neutrino masses may be related in a way that the PQ symmetry breaking scale and the seesaw scale arise from a common origin. Depending on how the PQ symmetry and the seesaw mechanism are realized, one has different predictions on the color and electromagnetic anomalies which could be tested in the future axion dark matter search experiments. Motivated by this, we construct various PQ seesaw models which are minimally extended from the (non-) supersymmetric Standard Model and thus set up differ…
We explore in detail the consequences of the CP-violating phases residing in the supersymmetric and soft SUSY breaking parameters in the approximation that family flavour mixings are ignored. We allow for non-universal boundary conditions and in such a consideration the model is described by twelve independent CP-violating phases and one angle which misaligns the vacuum expectation values (VEVs) of the Higgs scalars. We run two-loop renormalization group equations (RGEs), for all parameters involved, including phases, and we properly treat the minimization conditions using the one-loop effecti…
We propose a novel mechanism of electroweak symmetry breaking in supersymmetric models, as the one recently discussed by Birkedal, Chacko and Gaillard, in which the Standard Model Higgs doublet is a pseudo-Goldstone boson of some global symmetry. The Higgs mass parameter is generated at one loop level by two different, moderately fine-tuned sources of the global symmetry breaking. The mechanism works for scalar superpartner masses of order 10 TeV, but gauginos can be light. The scale at which supersymmetry breaking is mediated to the visible sector has to be low, of order 100 TeV. Fine-tuning …
We study the phenomenology of a new Minimally-extended Supersymmetric Standard Model (nMSSM) where a gauge singlet superfield is added to the MSSM spectrum. The superpotential of this model contains no dimensionful parameters, thus solving the mu-problem of the MSSM. A global discrete R-symmetry, forbidding the cubic singlet self-interaction, imposed on the complete theory, guarantees its stability with respect to generated higher-order tadpoles of the singlet and solves both the domain wall and Peccei-Quinn axion problems. We give the free parameters of the model and display some general cons…
In some supersymmetric extensions of the Standard Model fairly light superpartner of t-quark is predicted, which may form bound states ({\it stoponiums}) under certain conditions. We study prospects of search for stoponium at the future Photon Linear Collider. It is found that this machine could be the best machine for discovery and study of these resonances at some scenarios of supersymmetric extension of the Standard Model. In particular, if the $hh$ decay channel is dominant stoponium could be observed at the beginning of PLC run with collision energy tuned at the stoponium mass. If this ch…
Supersymmetric GUTs based on SO(10) gauge group are leading contenders to describe particle physics beyond the Standard Model. Among these the "New minimal supersymmetric SO(10) grand unified theory" (NMSGUT) based on Higgs system 10+120+210+126+$\overline{126}$ has been developing since 1982. It now successfully fits the whole standard Model gauge coupling, symmetry breaking and fermion mass-mixing data as well as the neutrino mass and mixing data in terms of NMSGUT parameters and just 6 soft supersymmetry breaking parameters defined at the GUT scale. In this thesis we study the phenomenology…
We find that minimizing the number of fine tuning relations in non-supersymmetric models can determine the scales at which some gauge symmetries beyond the standard model must break. We show that $SU(2)_R$ and $B-L$ gauge symmetries of the minimal left-right symmetric model must break at a scale $10^{15} GeV$ or higher, determined by the hierarchy problem and small ratios of quark masses, if parameters that break chiral or $μ$-symmetries (and therefore can be naturally small), are not fine-tuned. This provides the $raison \ d'\hat{e}tre$ for the seesaw scale $\sim 10^{15}GeV$ indicated by neut…
The Next-to-Minimal Supersymmetric Standard Model (NMSSM) can incorporate inflation, where a combination of the Higgs-doublet fields plays the role of the inflaton. At the high scale, the Higgs doublets are non-minimally coupled to supergravity; this coupling appears as an additional contribution to the $μ$ term in the low-energy effective superpotential and potentially changes physics at the electroweak scale. In a recent publication, we investigate the extended parameter space of this model with respect to collider phenomenology at the electroweak scale, and discuss scenarios which are poten…
The solution to fine tuning is one of the principal motivations for Beyond the Standard Model (BSM) Studies. However constraints on new physics indicate that many of these BSM models are also fine tuned (although to a much lesser extent). To compare these BSM models it is essential that we have a reliable, quantitative measure of tuning. We review the measures of tuning used in the literature and propose an alternative measure. We apply this measure to several toy models and the Minimal Supersymmetric Standard Model.
The phases in a generic low-energy supersymmetric model are severely constrained by the experimental upper bounds on the electric dipole moments of the electron and the neutron. Coupled with the requirement of radiative electroweak symmetry breaking, this results in a large degree of fine tuning of the phase parameters at the unification scale. In supergravity type models, this corresponds to very highly tuned values for the phases of the bilinear Higgs coupling parameter $B$ and the universal trilinear coupling $A_0$. We identify a cancellation/enhancement mechanism associated with the renorm…
A general electroweak scale $Z'$ is applied in a supersymmetric SU(6)$\timesSU(2)_h$ grand unification model, to have a $\Z_6$ for the hexality. We briefly show that there cannot exist any baryonic U(1)$'_B$ in any subgroup of E$_6$. Any effect that requires sizable $Z'$ couplings to quarks like the reported Wjj anomaly of CDF, if observed, implies a substantial $Z'$ coupling to leptons or Higgs doublets. The kinetic mixing considered in a supersymmetric model from E$_6$ is restricted by the gauge coupling unification and neutrino mixing. The mass of $Z'$ is strongly constrained by the electro…
Flavour and CP violations that the neutrino-seesaw couplings of types I, II, and III induce radiatively in the soft massive parameters of the minimal supersymmetric SU(5) model, made realistic by nonrenormalizable operators, are analyzed. Effective couplings are used to parametrize the couplings of renormalizable operators and of the corrections that nonrenormalizable ones provide at the tree level. It is found that for a limited, but sufficient accuracy in the calculations of such violations, it is possible to extend the picture of effective couplings to the quantum level, all the way to the …
We study the implications of the absence of a direct discovery of a Higgs boson at LEP. First we exhibit 15 physically different ways in which one or more Higgs bosons lighter than the LEP limit could still exist. In the minimal supersymmetric standard model (MSSM) all of these, as well as the cases where the Higgs mass equals or exceeds 115 GeV, seem fine-tuned. We examine some interpretations of the fine tuning in high scale theories. The least fine-tuned MSSM outcome will have a Higgs mass at 115 GeV, while approaches that extend the MSSM at the weak scale can naturally have larger Higgs ma…
The cosmological constant problem is a failure of naturalness and suggests that a fine-tuning mechanism is at work, which may also address the hierarchy problem. An example -- supported by Weinberg's successful prediction of the cosmological constant -- is the potentially vast landscape of vacua in string theory, where the existence of galaxies and atoms is promoted to a vacuum selection criterion. Then, low energy SUSY becomes unnecessary, and supersymmetry -- if present in the fundamental theory -- can be broken near the unification scale. All the scalars of the supersymmetric standard model…
We suggest a criterion to minimize the amount of fine-tuning in a composite Higgs model. The paradigm of this type of model is the top-condensate model of Bardeen, Hill and Lindner (BHL). Although "minimally fine-tuned", this model failed to account correctly for the masses of the top quark and the 125~GeV Higgs boson. We propose a generalization of the BHL model that employs finely-tuned extended technicolor (ETC) plus technicolor (TC) interactions. The additional freedom of this model may accommodate both m_t(173) and M_H(125). This paper studies the large-N_{TC} and N_C limit of this model …
In this paper, we give a systematic procedure for building locally stable dS vacua in $\mathcal{N}=1$ supergravity models motivated by string theory. We assume that one of the superfields has a Kahler potential of no-scale type and impose a hierarchy of supersymmetry breaking conditions. In the no-scale modulus direction the supersymmetry breaking is not small, in all other directions it is of order $ε$. We establish the existence of an abundance of vacua for large regions in the parameter space spanned by $ε$ and the cosmological constant. These regions exist regardless of the details of the …
