Electric Dipole Moment Constraints Research Articles

A geometric approach to CP violation: applications to the MCPMFV SUSY model

We analyze the constraints imposed by experimental upper limits on electric dipole moments (EDMs) within the Maximally CP- and Minimally Flavour-Violating (MCPMFV) version of the MSSM. Since the MCPMFV scenario has 6 non-standard CP-violating phases, in addition to the CP-odd QCD vacuum phase \theta_QCD, cancellations may occur among the CP-violating contributions to the three measured EDMs, those of the Thallium, neutron and Mercury, leaving open the possibility of relatively large values of the other CP-violating observables. We develop a novel geometric method that uses the small-phase approximation as a starting point, takes the existing EDM constraints into account, and enables us to find maximal values of other CP-violating observables, such as the EDMs of the Deuteron and muon, the CP-violating asymmetry in b --> s \gamma decay, and the B_s mixing phase. We apply this geometric method to provide upper limits on these observables within specific benchmark supersymmetric scenarios, including extensions that allow for a non-zero \theta_QCD.

A comprehensive analysis of electric dipole moment constraints on CP-violating phases in the MSSM

We analyze the constraints placed on individual, flavor diagonal CP-violating phases in the minimal supersymmetric extension of the Standard Model (MSSM) by current experimental bounds on the electric dipole moments (EDMs) of the neutron, Thallium, and Mercury atoms. We identify the four CP-violating phases that are individually highly constrained by current EDM bounds, and we explore how these phases and correlations among them are constrained by current EDM limits. We also analyze the prospective implications of the next generation of EDM experiments. We point out that all other CP-violating phases in the MSSM are not nearly as tightly constrained by limits on the size of EDMs. We emphasize that a rich set of phenomenological consequences is potentially associated with these generically large EDM-allowed phases, ranging from B physics, electroweak baryogenesis, and signals of CP-violation at the CERN Large Hadron Collider and at future linear colliders. Our numerical study takes into account the complete set of contributions from one- and two-loop EDMs of the electron and quarks, one- and two-loop Chromo-EDMs of quarks, the Weinberg 3-gluon operator, and dominant 4-fermion CP-odd operator contributions, including contributions which are both included and not included yet in the CPsuperH2.0 package. We also introduce an open-source numerical package, 2LEDM, which provides the complete set of two-loop electroweak diagrams contributing to the electric dipole moments of leptons and quarks.

CEDM Constraints on Modified Sfermion Universality and Spontaneous CP Violation

We discuss the supersymmetric CP problem that arises when the sfermion soft mass universality is modified. We place the 3rd generation SU(5) ten-plet sfermion masses in the weak scale in view of the naturalness. The other sfermion masses are assumed to be universal and a TeV scale in order to weaken the flavor changing neutral current processes and electric dipole moment (EDM) constraints. However this modification generically induces too large up quark chromo-EDM (CEDM) via the weak scale stop loop. In order to suppress this CEDM, we propose certain type of flavor structure where the parameters of the up-(s)quark sector are real whereas those of the down-(s)quark and the charged (s)lepton sectors are complex at the GUT scale. It is shown that, in this set up, up quark CEDM can be suppressed within the range where the current and future experiments have their sensitivity. We briefly illustrate the simple realization of these particular forms of the modified sfermion universality with real up-(s)quark sector by spontaneous CP violation in E$_6$ SUSY GUT with SU(2) flavor symmetry.

EDM constraints on flavored CP-violating phases

The CP-violating phenomenology of the MSSM with Minimal Flavor Violation (MFV) in the lepton sector is revisited. To this end, the most general parametrizations of the slepton soft-breaking terms are constructed assuming a seesaw mechanism of type I. After a critical reassessment of how the CP-symmetry is broken within the MFV framework, all possible CP-violating phases are introduced. From the strong hierarchy of their contributions to the Electric Dipole Moments (EDMs), these phases are split into three classes: flavor-blind, flavor-diagonal and flavor off-diagonal. In particular, the phases from the neutrino sector belong to the last class; they start to contribute only at the second order in the mass-insertion approximation and have thus a negligible effect. It is then shown that to each class of phases corresponds a unique largely dominant term in the MFV expansion. Numerically, for a realistic range of MSSM and neutrino parameters, such that B ( μ → e γ ) does not exceed its experimental bound, the three types of phases are found to be allowed by the current bound on the electron EDM, though the next generation of experiments should constrain tightly the flavor-blind phase. Finally, we relax the MFV hypothesis and show how in the general MSSM, the MFV operator basis can be used to judge of the naturality of the slepton soft-breaking terms.

Electric dipole moments in the MSSM reloaded

We present a detailed study of the Thallium, neutron, Mercury and deuteron electric dipole moments (EDMs) in the CP-violating Minimal Supersymmetric extension of the Standard Model (MSSM). We take into account the complete set of one-loop graphs, the dominant Higgs-mediated two-loop diagrams, the complete CP-odd dimension-six Weinberg operator and the Higgs-mediated four-fermion operators. We improve upon earlier calculations by including the resummation effects due to CP-violating Higgs-boson mixing and to threshold corrections to the Yukawa couplings of all up- and down-type quarks and charged leptons. As an application of our study, we analyse the EDM constraints on the CPX, trimixing and Maximally CP- and Minimally Flavour-Violating (MCPMFV) scenarios. Cancellations may occur among the CP-violating contributions to the three measured EDMs arising from the 6 CP-violating phases in the MCPMFV scenario, leaving open the possibility of relatively large contributions to other CP-violating observables. The analytic expressions for the EDMs are implemented in an updated version of the code CPsuperH2.0.

Probing new CP-odd thresholds with electric dipole moments

We dicuss the utility of precision probes for flavour-diagonal CP-violation, namely, searches for electric dipole moments of nucleons, atoms, and molecules, in looking for new physics thresholds that manifest themselves primarily through higher dimensional operators. After reviewing the status of the electric dipole moment (EDM) constraints, we consider first the sensitivity to a generic class of dimension-five operators generated at a supersymmetric threshold, through their contribution to CP- and flavour-violating observables. Such thresholds can be probed by EDMs up to a scale of order 108 GeV depending on the flavour structure. We then turn to consider the possibility that electroweak baryogenesis is made feasible by the introduction of dimension-six operators at a TeV-scale threshold. The EDM costraints on dimension-six couplings of the Higgs to the fermions currently still allow a reasonable window in parameter space for these models, but the next generation of experiments should provide a conclusive test. PACS Nos.: 11.30.Er, 12.60.Fr, 12.60.Jv

Collider searches and cosmology in the MSSM with heavy scalars

In a variety of supersymmetric extensions of the standard model, the scalar partners of the quarks and leptons are predicted to be very heavy and beyond the reach of next-generation colliders. For instance, the realization of electroweak baryogenesis in supersymmetry requires new sources of $CP$ violation, which can only be naturally accommodated with electric dipole moment constraints if the first- and second-generation scalar fermions are beyond the TeV scale. Also, in focus-point supersymmetry and split supersymmetry the scalar fermions are very heavy. In this work, the phenomenology of scenarios with electroweak baryogenesis and in the focus-point region at the CERN LHC and ILC is studied, which becomes challenging due to the presence of heavy scalar fermions. Implications for the analysis of baryogenesis and dark matter are deduced. It is found that precision measurements of superpartner properties allow an accurate determination of the dark matter relic density in both scenarios, while important but only incomplete information about the baryogenesis mechanism can be obtained.

WMAP dark matter constraints and Yukawa unification in supergravity models withCPphases

The compatibility of producing the observed amount of dark matter, as indicated by the Wilkinson Microwave Anisotropy Probe (WMAP) data, through the relic abundance of neutralinos with Yukawa unification and with the measured rate of $b\ensuremath{\rightarrow}s\ensuremath{\gamma}$ is analyzed in mSUGRA and extended SUGRA unified models with the inclusion of $CP$ phases. The $CP$ phases affect the analysis in several ways, e.g., through the threshold corrections to the $b$-quark mass, via their effects on the neutralino relic density and through the supersymmetry (SUSY) contribution to the $\mathrm{BR}(b\ensuremath{\rightarrow}s\ensuremath{\gamma})$ which is sensitive to the $CP$ phases. We present some specific models with large SUSY phases, which can accommodate the fermion electric dipole moment constraints and give a neutralino relic density in agreement with observations as well as with the $b\mathrm{\text{\ensuremath{-}}}\ensuremath{\tau}$ unification constraint. The possibility of achieving WMAP relic density constraints with full Yukawa unification is also explored.

CP-odd phase correlations and electric dipole moments

We revisit the constraints imposed by electric dipole moments (EDMs) of nucleons and heavy atoms on new CP-violating sources within supersymmetric theories. We point out that certain two-loop renormalization group corrections induce significant mixing between the basis-invariant CP-odd phases. In the framework of the constrained minimal supersymmetric standard model (CMSSM), the CP-odd invariant related to the soft trilinear A-phase at the GUT scale, theta_A, induces non-trivial and distinct CP-odd phases for the three gaugino masses at the weak scale. The latter give one-loop contributions to EDMs enhanced by tan beta, and can provide the dominant contribution to the electron EDM induced by theta_A. We perform a detailed analysis of the EDM constraints within the CMSSM, exhibiting the reach, in terms of sparticle spectra, which may be obtained assuming generic phases, as well as the limits on the CP-odd phases for some specific parameter points where detailed phenomenological studies are available. We also illustrate how this reach will expand with results from the next generation of experiments which are currently in development.

Hadronic EDM constraints on orbifold GUTs

We point out that the null results of the hadronic electric dipole moment (EDM) searches constrain orbifold grand unified theories (GUTs), where the GUT symmetry and supersymmetry (SUSY) are both broken by boundary conditions in extra dimensions and it leads to rich fermion and sfermion flavor structures. A marginal chromoelectric dipole moment (CEDM) of the up quark is induced by the misalignment between the CP violating left- and right-handed up-type squark mixings, in contrast to the conventional four-dimensional SUSY GUTs. The up quark CEDM constraint is found to be as strong as those from charged lepton flavor violation (LFV) searches. The interplay between future EDM and LFV experiments will probe the structures of the GUTs and the SUSY breaking mediation mechanism.

EDM constraints and CP asymmetries of B processes in supersymmetric models

We demonstrate that electric dipole moments (EDMs) strongly constrain possible SUSY contributions to the CP asymmetries of B processes; LL and/or RR flavour mixings between second and third generations are severely restricted by the experimental limit on the mercury EDM, and so therefore are their possible contributions to the CP asymmetries of B→ϕK and B→η′K. We find that SUSY models with dominant LR and RL mixing through non-universal A-terms is the only way to accommodate the apparent deviation of CP asymmetries from those expected in the Standard Model without conflicting with the EDM bounds or with any other experimental results.

Electric dipole moments as probes of new physics

We review several aspects of flavour-diagonal CP-violation, focussing on the role played by the electric dipole moments (EDMs) of leptons, nucleons, atoms, and molecules, which constitute the source of several stringent constraints on new CP-violating physics. We dwell specifically on the calculational aspects of applying the hadronic EDM constraints, reviewing in detail the application of QCD sum-rules to the calculation of nucleon EDMs and CP-odd pion–nucleon couplings. We also consider the current status of EDMs in the Standard Model, and on the ensuing constraints on the underlying sources of CP-violation in physics beyond the Standard Model, focussing on weak-scale supersymmetry.

THE CONSTRAINTS ON CP VIOLATING PHASES IN MODELS WITH A DYNAMICAL GLUINO PHASE

We analyze the electric dipole moment and the Higgs mass constraints on the supersymmetric model which offers dynamical solutions to the μ and strong CP problems. The trilinear coupling phases, and tan β-|μ| are strongly correlated, particularly in the low-tan β regime. Certain values of the phases of the trilinear couplings are forbidden, whereas the CP violating phase from the chargino sector is imprisoned to lie near a CP conserving point, by the Higgs mass and electric dipole moment constraints.

CP-violating chargino contributions to the Higgs coupling to photon pairs in the decoupling regime of the Higgs sector

In most supersymmetric theories, charginos $\tilde{\chi}^\pm_{1,2}$ belong to the class of the lightest supersymmetric particles and the couplings of Higgs bosons to charginos are in general complex so that the CP--violating chargino contributions to the loop--induced coupling of the lightest Higgs boson to photon pairs can be sizable even in the decoupling limit of large pseudoscalar mass $m_A$ with only the lightest Higgs boson kinematically accessible at future high energy colliders. We introduce a specific benchmark scenario of CP violation consistent with the electric dipole moment constraints and with a commonly accepted baryogenesis mechanism in the minimal supersymmetric Standard Model. Based on the benchmark scenario of CP violation, we demonstrate that the fusion of the lightest Higgs boson in linearly polarized photon--photon collisions can allow us to confirm the existence of the CP--violating chargino contributions {\it even in the decoupling regime of the Higgs sector} for nearly degenerate SU(2) gaugino and higgsino mass parameters of about the electroweak scale.

B→Xsγin supersymmetry with explicitCPviolation

We discuss B -> X_s gamma decay in both constrained and unconstrained supersymmetric models with explicit CP violation within the minimal flavor violation scheme by including tan(beta) -enhanced large contributions beyond the leading order. In this analysis, we take into account the relevant cosmological and collider bounds, as well as electric dipole moment constraints. In the unconstrained model, there are portions of the parameter space yielding a large CP asymmetry at leading order (LO). In these regions, we find that the CP phases satisfy certain sum rules, e.g., the sum of the phases of the \mu parameter and the stop trilinear coupling centralize around \pi with a width determined by the experimental bounds. In addition, at large values of tan(beta), the sign of the CP asymmetry tracks the sign of the gluino mass, and the CP asymmetry is significantly larger than the LO prediction. In the constrained minimal supersymmetric standard model based on minimal supergravity, we find that the decay rate is sensitive to the phase of the universal trilinear coupling. This sensitivity decreases at large values of the universal gauino mass. We also show that for a given set of the mass parameters, there exists a threshold value of the phase of the universal trilinear coupling which grows with tan(beta) and beyond which the experimental bounds are satisfied. In both supersymmetric scenarios, the allowed ranges of the CP phases are wide enough to have phenomenological consequences.

Fully supersymmetricCPviolation in the kaon system

We show that, contrary to the usual claims, fully supersymmetric CP violation in the kaon system is possible through gluino mediated flavor changing interactions. Both ${\ensuremath{\epsilon}}_{K}$ and $\mathrm{Re}({\ensuremath{\epsilon}}^{\ensuremath{'}}/{\ensuremath{\epsilon}}_{K})$ can be accommodated for relatively large $\mathrm{tan}\ensuremath{\beta}$ without any fine-tuning or contradictions to the flavor changing neutral current and electric dipole moment constraints.

EDM-free supersymmetric CP violation with non-universal soft terms

Non-universality in the soft breaking terms is a common feature in most superstring inspired SUSY models. This property is required to obtain sizeable CP violation effects from SUSY and, on the other hand, can be used to avoid the Electric Dipole Moment constraints. We take advantage of these qualities and explore a class of SUSY models based on type I string theory where scalar masses, gaugino masses and trilinear couplings are non-universal. In this framework, we show that, in the presence of large SUSY phases, the bounds on the Electric Dipole Moments can be controled without fine-tuning. At the same time, we find that these phases, free from EDM constraints, lead to large contributions to the observed CP phenomena in Kaon system and, in particular, to direct CP violation in epsilon'/epsilon.

Can flavor-independent supersymmetric soft phases Be the source of all CP violation?

Recently it has been demonstrated that large phases in softly broken supersymmetric (SUSY) theories are consistent with electric dipole moment constraints, and are motivated in some (type I) string models. Here we consider whether large flavor-independent soft phases may be the dominant (or only) source of all CP violation. In this framework, epsilon and epsilon(')/epsilon can be accommodated, and the SUSY contribution to the B system mixing can be large and dominant. An unconventional flavor structure of the squark mass matrices (with enhanced super-Cabibbo-Kobayashi-Maskawa mixing) is required for consistency with B and K system observables.

CPviolating phases, nonuniversal soft breaking, and D-brane models

The question of $\mathrm{CP}$ violating phases and electric dipole moments (EDMs) for the electron ${(d}_{e})$ and the neutron ${(d}_{n})$ for supergravity models with nonuniversal soft breaking is considered for models with a light $(\ensuremath{\lesssim}1\mathrm{TeV})$ mass spectrum and R-parity invariance. As with models with universal soft breaking (MSUGRA) one finds that a serious fine-tuning problem generally arises for ${\ensuremath{\theta}}_{0B}$ (the phase of the B soft breaking parameter at the GUT scale), if the experimental EDM constraints are obeyed and radiative breaking of ${\mathrm{SU}(2)}_{L}\ifmmode\times\else\texttimes\fi{}{U(1)}_{Y}$ occurs. A D-brane model where ${\mathrm{SU}(3)}_{C}\ifmmode\times\else\texttimes\fi{}{U(1)}_{Y}$ is associated with one set of 5-branes and ${\mathrm{SU}(2)}_{L}$ with another intersecting set of 5-branes is examined, and the cancellation phenomena is studied over the parameter space of the model. Large values of ${\ensuremath{\theta}}_{B}$ (the phase of B at the electroweak scale) can be accommodated, though again ${\ensuremath{\theta}}_{0B}$ must be fine-tuned. Using the conventional prescription for calculating ${d}_{n},$ one finds the region in parameter space where the experimental EDM constraints on both ${d}_{e}$ and ${d}_{n}$ hold is significantly reduced, and generally requires $\mathrm{tan}\ensuremath{\beta}\ensuremath{\lesssim}5$ for most of the parameter space, though there are small allowed regions even for $\mathrm{tan}\ensuremath{\beta}\ensuremath{\gtrsim}10.$ We find that the Weinberg three gluon term generally makes significant contributions, and the results are sensitive to the values of the quark masses.

Constraints on phases of supersymmetric flavour conserving couplings

In the unconstrained MSSM, we reanalyze the constraints on the phases of supersymmetric flavour conserving couplings that follow from the electron and neutron electric dipole moments (EDM). We find that the constraints become weak if at least one exchanged superpartner mass is > O(1 TeV) or if we accept large cancellations among different contributions. However, such cancellations have no evident underlying symmetry principle. For light superpartners, models with small phases look like the easiest solution to the experimental EDM constraints. This conclusion becomes stronger the larger is the value of tan β. We discuss also the dependence of ϵ K , Δm B and b→ sγ decay on those phases.