SUSY CP Research Articles

CP violation versus flavour in supersymmetric theories

We show that the quark flavour structure and CP violating phenomena are strongly correlated in supersymmetric theories. For a generic pattern of supersymmetry breaking the two broad categories of Yukawa couplings, democratic and hierarchical textures, have entirely different phenomenological implications. With hierarchical Yukawas, the rephasing invariant phase, arg(VusVcbVcb∗Vcs∗), in the CKM mixing matrix has to be of order unity, while the SUSY CP violating phases are severely constrained by electric dipole moments, giving rise to the so-called SUSY CP problem. With democratic Yukawas, all experimental CP results can be accommodated with small values for the CKM and SUSY CP violating phases (i.e., CP can be considered as an approximate symmetry at the high energy scale). We also show that within this scenario, an entirely real CKM matrix in supersymmetric models is still allowed by the present experimental results.

Investigation of no-scale supersymmetry breaking models with a gaugedU(1)B−Lsymmetry

Noscale supersymmetry (SUSY) breaking model is investigated in the minimal extension of the minimal supersymmetric standard model (MSSM) with a gauged U(1)_{B-L} symmetry. We specifically consider a unification-inspired model with the gauge groups SU(3)_{C} \times SU(2)_{L} \times U(1)_Y \times U(1)_{B-L} \subset SU(5) \times U(1)_{5} for illustration. While the noscale boundary condition at the grand unification scale (M_{G}\simeq 2\times 10^{16} GeV) in the MSSM is not consistent with phenomenological constraints, we show that it is if the gaugino of the U(1)_{5} multiplet is several times heavier than the gauginos of the MSSM. However, if SU(5) \times U(1)_{5} is further embedded in a larger simple group, e.g. SO(10), the noscale boundary condition at M_{G} is inconsistent with phenomenological constraints. If we relax the noscale boundary condition and allow non-zero soft scalar masses for the Higgs fields which spontaneously break the U(1)_{5} symmetry, the resultant spectrum of SUSY particles becomes consistent with all the phenomenological constraints, even if we impose the GUT relation on the gauge coupling and the gaugino mass of the U(1)_{5}. In this case, the SUSY CP problem is also solved, since the condition B\mu =0 at the boundary can be imposed consistently with the electroweak symmetry breaking.

Supersymmetric CP violation: higgs and flavor

The phenomenolical implications of the flavor—blind and flavor—sensitive supersymmetric (SUSY) CP phases are analyzed by considering the SUSY Higgs sector and the neutral kaon system. It is shown that the production and decays of the Higgs bosons are significantly affected by their CP—violating mixings. On the other hand, the pure SUSY CP violation is shown to be insufficient for saturating the CP violation in the neutral kaon system given the existing experimental bounds on the branching fraction of the b → sγ decay.

Aspects of supersymmetric models with a radiatively driven inverted mass hierarchy

A promising way to reconcile naturalness with a decoupling solution to the SUSY flavor and CP problems is suggested by models with a radiatively driven inverted mass hierarchy (RIMH). The RIMH models arise naturally within the context of SUSY SO(10) grand unified theories. In their original form, RIMH models suffer from two problems: 1.) obtaining the radiative breakdown of electroweak symmetry, and 2.) generating the correct masses for third generation fermions. The first problem can be solved by the introduction of SO(10) D-term contributions to scalar masses. We show that correct fermion masses can indeed be obtained, but at the cost of limiting the magnitude of the hierarchy that can be generated. We go on to compute predictions for the neutralino relic density as well as for the rate for the decay $b\to s\gamma$, and show that these yield significant constraints on model parameter space. We show that only a tiny corner of model parameter space is accessible to Fermilab Tevatron searches, assuming an integrated luminosity of 25~$fb^{-1}$. We also quantify the reach of the CERN LHC collider for this class of models, and find values of $m_{\tg}\sim 1600$ GeV to be accessible assuming just 10 fb$^{-1}$ of integrated luminosity. In an Appendix, we list the two loop renormalization group equations for the MSSM plus right handed neutrino model that we have used in our analysis.

Massive higher dimensional gauge fields as messengers of supersymmetry breaking

We consider theories with one or more compact dimensions with size r > 1/M, where M is the fundamental Planck scale, with the visible and hidden sectors localized on spatially separated "3-branes." We show that a bulk U(1) gauge field spontaneously broken on the hidden-sector 3-brane is an attractive candidate for the messenger of supersymmetry breaking. In this scenario scalar mass-squared terms are proportional to U(1) charges, and therefore naturally conserve flavor. Arbitrary flavor violation at the Planck scale gives rise to exponentially suppressed flavor violation at low energies. Gaugino masses can be generated if the standard gauge fields propagate in the bulk; \mu and B\mu terms can be generated by the Giudice-Masiero or by the VEV of a singlet in the visible sector. The latter case naturally solves the SUSY CP problem. Realistic phenomenology can be obtained either if all microscopic parameters are order one in units of M, or if the theory is strongly coupled at the scale M. (For the latter case, we estimate parameters by extending "naive dimensional analysis" to higher-dimension theories with branes.) In either case, the only unexplained hierarchy is the "large" size of the extra dimensions in fundamental units, which need only be an order of magnitude. All soft masses are naturally within an order of magnitude of m_{3/2}, and trilinear scalar couplings are negligible. Squark and slepton masses can naturally unify even in the absence of grand unification.

High scale parity invariance as a solution to the SUSY CP problem and an explanation of small ε′/ε

It is shown that if the supersymmetric Standard Model (MSSM) emerges as the low energy limit of a high scale left-right symmetric gauge structure, the number of uncontrollable CP violating phases of MSSM are drastically reduced. In particular it guarantees the vanishing of the dangerous phases that were at the root of the so called SUSY CP problem. Such a symmetric gauge structure is independently motivated by the smallness of neutrino masses that arise via seesaw mechanism automatic in the theory. The minimal version of this theory also provides an explanation of the smallness of e′/e as a consequence of the high scale parity invariance.

Seesaw-constrained minimal supersymmetric standard model, solution to the supersymmetricCPproblem, and a supersymmetric explanation ofε′/ε

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, $\epsilon'/\epsilon$ vanishes in this model above the seesaw scale; extrapolation to the weak scale then leads to a prediction in agreement with the NA31 and the recent KTeV observations. The electric dipole moment of the neutron is naturally suppressed, we estimate its magnitude to be about $4 \times 10^{-29}$ ecm. Additional predictions include a tightly constrained super particle spectrum and vanishingly small CP asymmetries in the $B$ meson system.

Electric dipole moments in gauge mediated models and a solution to the SUSY CP problem

The SUSY CP problem in the framework of gauge mediated SUSY breaking model is considered. We first discuss the electric dipole moments of the electron and neutron, which are likely to be larger than the experimental upper bound if all the phases in the Lagrangian are O(1). We derive a constraint on the phases in the so-called μ- and B μ -parameters and gaugino masses. Then, we discuss a model in which the CP violating phase can be adequately suppressed. If the μ- and B μ -parameters originate from the same superpotential interaction as the SUSY breaking field, the CP violating phase vanishes. However, in this class of models, the ratio B μ / μ becomes too large, and we discuss a possible scenario to fix this problem.

CP violation in SUSY left-right models

We analyze the minimal supersymmetric left-right model with non-renormalizable interactions induced by higher scale physics and study its CP violating properties. We show that it: (i) solves the strong CP problem; (ii) predicts the neutron electric dipole moment well within experimental limits (thus solving the usual SUSY CP problem). In addition, it automatically conserves R -parity. The key points are that the parity symmetry forces the Yukawa couplings to be hermitean, while supersymmetry ensures that the scalar potential has a minimum with real higgs doublet vacuum expectation values. Gluino and B-L gaugino masses are automatically real. The observed CP violation in the kaon system comes, as in the Standard Model, from the Kobayashi-Maskawa-type phases. These solutions are valid for any value of the right-handed breaking scale M R , as long as the effective theory below M R has only two Higgs doublets that couple fully to fermions. (i.e. the theory below M R is MSSMlike.) The potentially dangerous contributions from the SU (2) L gaugino one-loop diagram as well as from some higher dimensional terms to φ¯ below M R can be avoided if the left-right symmetry originates from a unified theory such as SO(10) and we discuss how this embedding is achieved for the SO(10) case.

On central charge dynamical generation in the d = 2 SUSY model

Dynamical mass transmutation is analyzed in the framework of the two-dimensional SUSY CP n−1 -model. The real symmetry of the quantum model is found to be different from the classical one and has to include central charges. This phenomenon can be viewed as a particular form of the reduction of 4 to 2 dimensions.