Soft Supersymmetry Breaking Parameters Research Articles

Impact of physical principles at very high energy scales on the superparticle mass spectrum

We survey a variety of proposals for new physics at high scales that serve to relate the multitude of soft supersymmetry breaking parameters of the MSSM. We focus on models where the new physics results in non-universal soft parameters, in sharp contrast with the usually assumed mSUGRA framework. These include {\it i}) SU(5) and SO(10) grand unified (GUT) models, {\it ii}) the MSSM plus a right-handed neutrino, {\it iii}) models with effective supersymmetry, {\it iv}) models with anomaly-mediated SUSY breaking and gaugino mediated SUSY breaking, {\it v}) models with non-universal soft terms due to string dynamics, and {\it vi}) models based on $M$-theory. We outline the physics behind these models, point out some distinctive features of the weak scale sparticle spectrum, and allude to implications for collider experiments. To facilitate future studies, for each of these scenarios, we describe how collider events can be generated using the program ISAJET. Our hope is that detailed studies of a variety of alternatives will help point to the physics underlying SUSY breaking and how this is mediated to the observable sector, once sparticles are discovered and their properties measured.

Calculations of neutralino–stau coannihilation channels and the cosmologically relevant region of MSSM parameter space

Assuming that the lightest supersymmetric particle (LSP) is the lightest neutralino χ ̃ , we present a detailed exploration of neutralino–stau ( χ ̃ − τ ̃ ) coannihilation channels, including analytical expressions and numerical results. We also include χ ̃ coannihilations with the ẽ and μ ̃ . We evaluate the implications of coannihilations for the cosmological relic density of the LSP, which is assumed to be stable, in the constrained minimal supersymmetric extension of the Standard Model (CMSSM), in which the soft supersymmetry-breaking parameters are universal at the supergravity GUT scale. We evaluate the changes due to coannihilations in the region of the MSSM parameter space that is consistent with the cosmological upper limit on the relic LSP density. In particular, we find that the upper limit on m χ ̃ is increased from about 200 GeV to about 600 GeV in the CMSSM, and estimate a qualitatively similar increase for gauginos in the general MSSM.

Dynamical solution to the μ problem at the TeV scale

We introduce a new confining force (\ensuremath{\mu} color) at the TeV scale to dynamically generate a supersymmetry preserving mass scale which would replace the \ensuremath{\mu} parameter in the minimal supersymmetric standard model (MSSM). We discuss Higgs phenomenology and also the pattern of soft supersymmetry breaking parameters allowing correct electroweak symmetry breaking within the \ensuremath{\mu}-color model, which have quite distinctive features from the MSSM and also from other generalizations of the MSSM.

Naturally heavy scalars in supersymmetric grand unified theories

The supersymmetric flavor, CP and Polonyi problems are hints that the fundamental scale of the soft supersymmetry breaking parameters may be above a TeV, in apparent conflict with naturalness. We consider the possibility that multi-TeV scalar masses are generated by Planck- or unification-scale physics, and find the conditions under which the masses of scalars with large Yukawa couplings are driven, radiatively and asymptotically, to the weak scale through renormalization group evolution. Light third generation scalars then satisfy naturalness, while first and second generation scalars remain heavy to satisfy experimental constraints. We find that this mechanism is beautifully realized in the context of grand unified theories. In particular, the existence of right-handed neutrinos plays an important role in allowing remarkably simple scenarios. For example, for SO(10) boundary conditions with the squared masses of Higgs scalars double those of sleptons and squarks, we find that the entire scalar mass scale may be increased to 4 TeV at the unification scale without sacrificing naturalness.

Resolution to the SupersymmetricCPProblem with Large Soft Phases via D-Branes

We examine the soft supersymmetry breaking parameters that result from various ways of embedding the Standard Model (SM) on D-branes within the Type I string picture, allowing the gaugino masses and $\mu$ to have large CP- violating phases. One embedding naturally provides the relations among soft parameters to satisfy the electron and neutron electric dipole moment constraints even with large phases, while with other embeddings large phases are not allowed. The string models provide some motivation for large phases in the soft breaking parameters. The results generally suggest how low energy data might teach us about Planck scale physics.

Running of soft parameters in extra space-time dimensions

The evolution of the parameters including those in the soft supersymmetry-breaking (SSB) sector is studied in the minimal supersymmetric standard model (MSSM) with a certain set of Kaluza-Klein towers which has been recently considered by Dienes et al. We use the continuous Wilson renormalization group technique to derive the one-loop matching condition between the effective, renormalizable and original, unrenormalizable theories. We investigate whether the assumption of a large compactification radius in the model is consistent with the gauge coupling unification, the b− τ unification and the radiative breaking of the electroweak gauge symmetry with the universal SSB terms. We calculate the superpartner spectrum under the assumption of the universal SSB parameters to find differences between the model and the MSSM.

INFRARED QUASI FIXED POINTS AND MASS PREDICTIONS IN THE MSSM II: LARGE tan β SCENARIO

We consider the infrared quasi fixed point solutions of the renormalization group equations for the Yukawa couplings and soft supersymmetry breaking parameters in the MSSM in the large tan β regime. The existence of ir quasi fixed points together with the values of gauge couplings, third generation quarks, lepton and Z-boson masses allows one to predict masses of the Higgs bosons and SUSY particles as functions of the only free parameter, m1/2, or the gluino mass. The lightest Higgs boson mass for M SUSY ≈1 TeV is found to be mh=128.2-0.4-7.1± 5 GeV for μ>0 and mh= 120.6-0.1-3.8±5 GeV for μ<0.

Five-branes and supersymmetry breaking in M-Theory

Supersymmetry breaking via gaugino condensation is studied in vacua of heterotic M-theory with five-branes. We show that supersymmetry is still broken by a global mechanism and that the non-perturbative superpotential takes the standard form. When expressed in terms of low energy fields, a modification arises due to a threshold correction in the gauge kinetic function that depends on five-brane moduli. We also determine the form of the low energy matter field Kahler potential. These results are used to discuss the soft supersymmetry breaking parameters, in particular the question of universality.

Model of curvature-induced phase transitions in the inflationary universe

Chiral phase transitions driven by space-time curvature effects are investigated in de Sitter space in the supersymmetric Nambu-Jona-Lasinio model with soft supersymmetry breaking. The model is considered to be suitable for the analysis of possible phase transitions in inflationary universe. It is found that a restoration of the broken chiral symmetry takes place in two patterns for increasing curvature : the first order and second order phase transition respectively depending on initial settings of the four-body interaction parameter and the soft supersymmetry breaking parameter. The critical curves expressing the phase boundaries in these parameters are obtained. Cosmological implications of the result are discussed in connection with bubble formations and the creation of cosmic strings during the inflationary era.

Solving the supersymmetric flavor problem with radiatively generated mass hierarchies

The supersymmetric flavor problem may be solved if the first and second generation scalars are heavy (with multi-TeV masses) and scalars with large Higgs couplings are light (with sub-TeV masses). We show that such an inverted spectrum may be generated radiatively; that is, from initial conditions where all scalar masses are multi-TeV at some high scale, those with large Higgs couplings may be driven asymptotically to the weak scale in the infra-red. The lightness of third generation scalars is therefore a direct consequence of the heaviness of third generation fermions, and fine-tuning is avoided even though the fundamental scale of the soft supersymmetry breaking parameters is multi-TeV. We investigate this possibility in the framework of the usual Yukawa quasi-fixed point solutions. The required high scale boundary conditions are found to be simple and highly predictive. This scenario also alleviates the supersymmetric CP and Polonyi problems.

Cosmological fine tuning, supersymmetry and the gauge hierarchy problem

We study the extent to which the cosmological fine-tuning problem – why the relic density of neutralino cold dark matter particles χ is similar to that of baryons – is related to the fine-tuning aspect of the gauge hierarchy problem – how one arranges that M W ≪ M P without unnatural choices of MSSM parameters. Working in the minimal supergravity framework with universal soft supersymmetry-breaking parameters as inputs, we find that the hierarchical fine tuning is minimized for Ω χh 2∼0.1 . Conversely, imposing Ω χh 2<1 does not require small hierarchical fine tuning, but the exceptions to this rule are rather special, with parameters chosen such that m χ ∼ M Z /2 or M h /2, or else m χ ≳ m t . In the first two cases, neutralino annihilation receives a large contribution from a direct-channel pole, whereas in the third case it is enhanced by the large top Yukawa coupling.

INFRARED QUASI-FIXED POINTS AND MASS PREDICTIONS IN THE MSSM

We consider the infrared quasi-fixed point solutions of the renormalization group equations for the top-quark Yukawa coupling and soft supersymmetry breaking parameters in the MSSM. The ir quasi-fixed points together with the values of the gauge couplings, the top-quark and Z-boson masses allow one to predict masses of the Higgs bosons, the stop squarks and the lightest chargino as functions of the only free parameter m1/2 or the gluino mass. The mass of the lightest Higgs boson for μ&gt;0 and M SUSY ≈ 1 TeV is found to be mh = (94.3+1.6+0.6±5±0.4) GeV. The case with μ&lt;0 is excluded by experimental data.

Small instanton contribution to the axion potential in supersymmetric models

Small size QCD instantons may spoil the axion solution to the strong $\mathrm{CP}$ problem if QCD is not asymptotically free at high-energy scales. We examine this issue in supersymmetric models using a manifestly supersymmetric scheme to compute the axion potential induced by small size instantons. Applying this scheme for a class of illustrative models, it is found that the resulting high-energy axion potential is highly model dependent, but suppressed by more powers of the soft supersymmetry breaking parameters and/or of the other small mass scales than what is expected based on a naive instanton graph analysis. Our analysis suggests that the axion solution is stable against the small QCD instanton effects in a wide class of supersymmetric models even when QCD is not asymtotically free at high-energy scales.

Systematics of single superpartners production at leptonic colliders

We examine the effects of the lepton number violating R parity odd interactions, $\lambda_{ijk} $, on single production of fermion (charginos and neutralinos) and scalar (sleptons and sneutrinos) superpartners at leptonic colliders for center of mass energies up to $500GeV - 1TeV$. The probability amplitudes for all the five relevant $2 \to 2$ body processes and the decays branching ratios for the produced superpartners are calculated at tree level. A semi-quantitative discussion is developed within a supergravity model assuming grand unification of gauge interactions and universal (flavor independent) soft supersymmetry breaking parameters at the unification scale. The predictions obtained for the total and partial rates show that the single production reactions have a good potential of observability at NLC (Next Linear Colliders) energies. For values of the R parity violating coupling constant, $\lambda _{ijk}= 0.05$, close to the current bounds, the $\tilde \chi^{\pm, 0}$ reactions could probe all the relevant intervals for $\tan \beta$ and $m_0$ and broad regions of the parameter space for $\mu$ and $M_2$, while the $\tilde \nu $ and $\tilde l $ productions could probe sneutrinos and sleptons masses up to the kinematical limits. Using the hypothesis of a single dominant R parity violating coupling constant, a Monte Carlo events simulation for the $ \tilde \chi^{\pm, 0} $ reactions is employed to deduce some characteristic final states dynamical distributions.

U(1)′symmetry breaking in supersymmetricE6models

We study the electroweak and $U(1)^{'}$ symmetry breaking patterns in models with the particle content of supersymmetric $E_{6}$, including standard model singlets $S$ and exotic quarks $D,~\bar{D}$. Motivated by free fermionic string models, we do not require $E_{6}$-type relations between Yukawa couplings. In particular, we assume that baryon and lepton numbers are conserved, so that the exotic quarks can be light. Gauge invariance allows Yukawa interactions between $S$ and Higgs doublets, and between $S$ and the exotic quarks, allowing radiative $U(1)^{'}$ symmetry breaking and the generation of an effective $\mu$ parameter at the electroweak scale. For both the $E_{6}$ $\psi$ and $\eta$ models, universal soft supersymmetry breaking parameters and Yukawa universality at the high (string) scale do not yield acceptable low energy phenomenology. Relaxing universality, we find solutions with phenomenologically acceptable values of $M_{Z^{'}}$ and the $Z-Z^{'}$ mixing angle. In addition, by varying the $U(1)^{'}$ charge assignments due to the mixing of $U(1)_{\chi}$ and $U(1)_{\psi}$ of $E_{6}$, it is possible to have acceptable low energy phenomenology with universal boundary conditions.

Infrared behaviour of softly broken SQCD and its dual

Applying the recently obtained results on the renormalization of soft supersymmetry-breaking parameters, we investigate the infrared behaviour of the softly broken supersymmetric QCD as well as its dual theory in the conformal window. Under general assumptions on β-functions, it is shown that the soft supersymmetry-breaking parameters asymptotically vanish in the infrared limit so that superconformal symmetry in softly broken supersymmetric QCD and in its dual theory revives at the infrared fixed point, provided the soft scalar masses satisfy certain renormalization group invariant relations. If these relations are not satisfied, there exist marginal operators in both theories that lead to the breaking of supersymmetry and also colour symmetry.

Erratum: Electroweak breaking and the μ problem in supergravity models with an additional U(1) [Phys. Rev. D56, 2861 (1997)

We consider electroweak symmetry breaking in supersymmetric models with an extra non-anomalous U(1)' gauge symmetry and an extra standard-model singlet scalar S. For appropriate charges the U(1)' forbids an elementary mu term, but an effective mu is generated by the VEV of S, leading to a natural solution to the mu problem. There are a variety of scenarios leading to acceptably small Z-Z' mixing and other phenomenological consequences, all of which involve some but not excessive fine tuning. One class, driven by a large trilinear soft supersymmetry breaking term, implies small mixing, a light Z' (e.g., 200 GeV), and an electroweak phase transition that may be first order at tree level. In another class, with m_S^2 < 0 (radiative breaking), the typical scale of dimensional parameters, including M_{Z'} and the effective mu, is O(1 TeV), but the electroweak scale is smaller due to cancellations. We relate the soft supersymmetry breaking parameters at the electroweak scale to those at the string scale, choosing Yukawa couplings as determined within a class of string models. We find that one does not obtain either scenario for universal soft supersymmetry breaking mass parameters at the string scale and no exotic multiplets contributing to the renormalization group equations. However, either scenario is possible when the assumption of universal soft breaking is relaxed. Radiative breaking can also be generated by exotics, which are expected in most string models.

On the soft supersymmetry-breaking parameters in gauge-mediated models

Gauge mediation of supersymmetry breaking in the observable sector is an attractive idea, which naturally alleviates the flavor changing neutral current problem of supersymmetric theories. Quite generally, however, the number and quantum number of the messengers are not known; nor is their characteristic mass scale determined by the theory. Using the recently proposed method to extract supersymmetry-breaking parameters from wave-function renormalization, we derived general formulae for the soft supersymmetry-breaking parameters in the observable sector, valid in the small and moderate tan β regimes, for the case of split messengers. The full leading-order effects of top Yukawa and gauge couplings on the soft supersymmetry-breaking parameters are included. We give a simple interpretation of the general formulae in terms of the renormalization group evolution of the soft supersymmetry-breaking parameters. As a by-product of this analysis, the one-loop renormalization group evolution of the soft supersymmetry-breaking parameters is obtained for arbitrary boundary conditions of the scalar and gaugino mass parameters at high energies.

Spontaneous R-parity violation and electroweak baryogenesis

The possibility of baryogenesis at the electroweak phase transition is considered within the context of a minimal supersymmetric standard model with spontaneous R-parity violation. Provided that at least one of the sneutrino fields acquires a large enough vacuum expectation value, a sufficient baryon asymmetry can be created. Compared to R-parity conserving models the choice of soft supersymmetry breaking parameters is less restricted. The observed baryon asymmetry, n B s ∼10 −10 , can be explained by this scenario and the produced baryon-to-entropy ratio may easily be as high as n B s ∼10 −9 .

Solution to the strongCPproblem with gauge-mediated supersymmetry breaking

We demonstrate that a certain class of low scale supersymmetric ``Nelson-Barr'' type models can solve the strong and supersymmetric CP problems while at the same time generating sufficient weak CP violation in the $K^{0}-\bar{K}^{0}$ system. In order to prevent one-loop corrections to $\bar{\theta}$ which violate bounds coming from the neutron electric dipole moment (EDM), one needs a scheme for the soft supersymmetry breaking parameters which can naturally give sufficient squark degeneracies and proportionality of trilinear soft supersymmetry-breaking parameters to Yukawa couplings. We show that a gauge-mediated supersymmetry breaking sector can provide the needed degeneracy and proportionality, though that proves to be a problem for generic Nelson-Barr models. The workable model we consider here has the Nelson-Barr mass texture enforced by a gauge symmetry; one also expects a new U(1) gauge superfield with mass in the TeV range. The resulting model is predictive. We predict a measureable neutron EDM and the existence of extra vector-like quark superfields which can be discovered at the LHC. Because the $3\times 3$ Cabbibo-Kobayashi-Maskawa matrix is approximately real, the model also predicts a flat unitarity triangle and the absence of substantial CP violation in the $B$ system at future $B$ factories. We discuss the general issues pertaining to the construction of such a workable model and how they lead to the successful strategy. A detailed renormalization group study is then used to establish the feasibility of the model considered.