Spontaneous CP-violation in the strong interaction is analyzed at theta = pi within the framework of the two-flavor NJL model. It is found that the occurrence of spontaneous CP-violation at theta = pi depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chemical potential is examined in detail. When available a comparison to earlier results from chiral perturbation theory is made. From our results we conclude that spontaneous CP-violation in the strong interaction is an inherently low-energy phenomenon. In all cases we find agreement with the Vafa-Witten theorem, also at nonzero density and temperature. Meson masses and mixing in the CP-violating phase display some unusual features as a function of instanton interaction strength. A modification of the condition for charged pion condensation at nonzero isospin chemical potential and a novel phase of charged a_0 mesons are discussed.
As is well-known, spontaneous CP-violation in the strong interaction is possible at theta = pi, which is commonly referred to as Dashen's phenomenon. This phenomenon has been studied extensively using chiral Lagrangians. Here the two-flavor NJL model at theta = pi is discussed. It turns out that the occurrence of spontaneous CP-violation depends on the strength of the 't Hooft determinant interaction, which describes the effect of instanton interactions. The dependence of the phase structure, and in particular of the CP-violating phase, on the quark masses, temperature, baryon and isospin chem…
We present the Bayesian method for evaluating the evidence for a non-zero value of the leptonic mixing angle theta_13 and CP-violation in neutrino oscillation experiments. This is an application of the well-established method of Bayesian model selection, of which we give a concise and pedagogical overview. When comparing the hypothesis theta_13 = 0 with hypotheses where theta_13 > 0 using global data but excluding the recent reactor measurements, we obtain only a weak preference for a non-zero theta_13, even though the significance is over 3 sigma. We then add the reactor measurements one by o…
Assuming that the axion mechanism of solving the strong CP problem does not exist and the vanishing of theta at tree level is achieved by some model-building means, we study the naturalness of having large CP-violating sources in the leptonic sector. We consider the radiative mechanisms which transfer a possibly large CP-violating phase in the leptonic sector to the theta parameter. It is found that large theta cannot be induced in the models with one Higgs doublet as at least three loops are required in this case. In the models with two or more Higgs doublets the dominant source of theta is t…
We introduce a flavor ${\cal U}(1)$ symmetry à la Froggat-Nielsen to explain the magnitude of the CKM mixing angles as well bilarge mixing in the neutrino sector. In the framework of GUTs we also estimate the magnitude of the third leptonic mixing angle $θ_{13}$. Estimates for rare leptonic decays such as $μ\to e \ga $ are also provided. Finally, leptogenesis is exploited for estimating the magnitude of leptonic CP violation.
We suggest predictive scenarios for neutrino masses which provide a common origin for CP violation in early universe cosmology and in neutrino oscillations. Our setup is the seesaw mechanism in the context of MSSM with two quasi-degenerate right-handed neutrinos, with baryon asymmetry generated via resonant leptogenesis. Three different models are found with specific textures in the Yukawa coupling matrices, each with a single phase which controls leptogenesis and neutrino CP violation. One model leads to normal hierarchy of light neutrino masses and the prediction tan theta_13 = sin theta_12 …
We show a general form of neutrino mass matrix (M), whose matrix elements are denoted by M_{ij} (i.j=e, mu, tau) as flavor neutrino masses, that induces maximal CP violation as well as maximal atmospheric neutrino mixing. The masses of M_{mu mu}, M_{tau tau} and M_{mu tau}+sigma M_{ee} (sigma =\pm 1) turn out to be completely determined by M_{e mu} and M_{e tau} for given mixing angles. The appearance of CP violation is found to originate from the interference between the mu-tau symmetric part of M and its breaking part. If |M_{e mu}|=|M_{e tau}|, giving either M_{e mu}=-sigma e^{i theta} M_{e…
This work proposes a stringent concept of matter mass generation and Theta vacuum in the context of local gauge theory for the strong force under the constraint of the flat universe. The matter mass is generated as the consequence of dynamical spontaneous symmetry breaking (DSSB) of gauge symmetry and discrete symmetries, which is motivated by the parameter Theta representing the surface term. Matter mass generation introduces the typical features of constituent particle mass, dual Meissner effect, and hyperfine structure. The Theta term plays important roles on the DSSB of the gauge group and…
The recent measurements of the solar neutrino mixing angle theta_{sol} and the Cabibbo mixing angle theta_C reveal a surprising relation, theta_{sol}+theta_C ~ pi/4. Interpreting this empirical relation as a support of the quark-lepton unification, we find that the PMNS mixing matrix can be decomposed into a CKM-like matrix and maximal mixing matrices, which can give profound implications on the quark-lepton unification. We explore a possibility to probe the implication of quark-lepton unification by considering the relative sizes of branching ratios for the lepton flavor violating radiative d…
We propose the complex group theoretical Clebsch-Gordon coefficients as a novel origin of CP violation. This is manifest in our model based on SU(5) combined with the double tetrahedral group, T'. Due to the presence of the doublet representations in $T^{\prime}$, there exist complex CG coefficients, leading to explicit CP violation in the model, while the Yukawa couplings and the vacuum expectation of the scalar fields remain real. The tri-bimaximal neutrino mixing matrix arises from the CG coefficients of the T'. In addition to the prediction for theta_{13} ~ theta_{c}/(3 sqrt{2}), the model…
The logarithmic ultraviolet divergence in the theta-term induced by electroweak interactions in the Kobayashi-Maskawa model of CP-violation, found by Ellis and Gaillard, is discussed. We relate it to the Jarlskog CP-odd invariant of quark mass matrix. The divergence arises in 14th order in Higgs coupling as well as in 12th order plus 2nd order in U(1) gauge boson coupling.
We propose the complex group theoretical Clebsch-Gordon coefficients as a novel origin of CP violation. This is manifest in our model based on SUSY SU(5) combined with the double tetrahedral group, T', as a family symmetry. Due to the presence of the doublet representations in T', there exist complex CG coefficients, leading to explicit CP violation in the model, while the Yukawa couplings and the vacuum expectation values of the scalar fields remain real. The tri-bimaximal neutrino mixing matrix arises from the CG coefficients of T'. In addition to the prediction for theta_{13} ~ (1/ (3\sqrt{…
Using the PNJL model, we investigate C and P violations when theta =pi and Theta =mu/(iT)=π/3, where T, theta and mu are the temperature, the parameter of theta-vacuum and the quark number chemical potential, respectively. It is shown that the C violation and the P restoration happen almost simultaneously at theta=pi and Theta =pi/3, if the deconfinement and the chiral symmetry restoration happen almost simultaneously at theta =Theta =0.
We consider QCD at Theta ~ Pi with two, one and zero light flavours Nf, using the Di Vecchia-Veneziano-Witten effective lagrangian. For Nf=2, we show that CP is spontaneously broken at Theta = Pi for finite quark mass splittings, z= Md/Mu \not= 1. In the z-Theta plane, there is a line of first order transitions at Theta = Pi with two critical endpoints, z1* < z < z2*. We compute the tension of the domain walls relating the two CP violating vacua. For Mu=Md the tension of the family of equivalent domain walls agrees with the expression derived by Smilga from chiral perturbation theory at next-t…
Overview of spontaneous Lorentz and CPT breaking mechanism in the context of the standard model contributed to the proceedings for the Coral Gables meeting.
We propose octahedral group O_h as the family symmetry of neutrino-lepton sector. We find that O_h contains subgroups Z_2(mu-tau) x Z_2(solar) and Z_4^l for realizing the bimaximal (BM) mixings, theta_{23} = theta_{12} = 45^o and theta_{13}=0^o, where Z_2(mu-tau) x Z_2(solar) and Z_4^l serve as the residual symmetries of neutrinos and charged leptons, respectively. We present geometric interpretations of BM mixing in the octahedron, and construct natural geometrical breaking of Z_4^l, leading to nontrivial deviations from the BM mixings. Our theory makes truly simple predictions of a relativel…
Using a left-right symmetric model with Spontaneous CP Violation and the hypothesis of a weakly first order electroweak phase transition we derive a relation between the produced baryon asymmetry and the observed parameter $\varepsilon$, describing CP violation in the $K$ system.
In the flavor basis where the mass eigenstates of three charged leptons are identified with their flavor eigenstates, one may diagonalize a 3 X 3 Majorana neutrino mass matrix M_nu by means of the standard parametrization of the 3 X 3 neutrino mixing matrix V. In this treatment the unphysical phases of M_nu have to be carefully factored out, unless a special phase convention for neutrino fields is chosen so as to simplify M_nu to M'_nu without any unphysical phases. We choose this special flavor basis and establish some exact analytical relations between the matrix elements of M'_nu M'_nu^dag …
We show that in the context of large extra dimensions enough CP violation can be obtained from the spontaneous breaking in a simple non-SUSY model, which is usually considered not to cause the spontaneous CP violation. We estimate ε_{K} in our scenario to be of order 10^{-3} consistent with the experimental value. We also propose a modification to the see-saw mechanism and axion scenario to match with our model.
We explore the possibility of spontaneous CP violation within the Next to Minimal Supersymmetric Standard Model. In the most general form of the model, without a discrete $Z_3$ symmetry, we find that even at tree level spontaneous CP violation can occur, while also permitting Higgs masses consistent with experiment.
A supersymmetric standard model with two Higgs doublets and two Higgs singlets is investigated if it can accommodate the possibility of spontaneous CP violation. Assuming the degeneracy of the scalar quark masses of the third generation, we find that spontaneous CP violation in the Higgs sector is viable in our model. In the case of spontaneous CP violation, the masses of the lightest two neutral Higgs bosons are estimated to be 80 and 125 GeV for some parameter values in our model, which, are consistent with LEP2 data.
In order to generate the baryon asymmetry of the Universe sufficiently strong CP violation is needed. It was therefore proposed that at finite temperature there might be spontaneous (transitional) CP violation within the bubble walls at the electroweak phase transition in supersymmetric models. We investigate this question in the MSSM.
I study many higgs doublet supersymmetric model with spontaneous CP violation. The damaging flavor changing interactions and large CP violation are brought under control simultaneously by an approximate PQ symmetry. I relate the smallness of the CP violating parameter in the kaon system to the small ${m_b \over m_t}$ ratio.
For the general Two-Higgs-Doublet model, we present conditions for having spontaneous CP violation, in terms of physical masses and couplings. These relations involve the charged-Higgs mass, its cubic couplings with neutral scalars and quartic coupling, and become particularly simple in the alignment limit. In the simplified model with softly broken $Z_2$ symmetry, some deviation from alignment is required for spontaneous CP violation to be present.
The most general Two Higgs Doublet Model (2HDM) allows both for the explicit and the spontaneous CP violation in the scalar sector. Here we discuss CP violation in terms of basis-independent quantities and show how using two different sets of known CP-odd weak-basis invariants one can distinguish between CP conservation, explicit CP violation and spontaneous CP violation. The special case of CP violation without CP mixing, in which the neutral Higgs gauge boson interaction respects CP while Higgs self-interaction violates CP symmetry, is also presented.
A scenario is suggested for spontaneous CP violation in non-SUSY and SUSY SU(10). The idea is to have a scalar potential which generates spontaneously a phase, at the high scale, in the VEV that gives a mass to the RH neutrinos. The case of the minimal renormalizable SUSY SO(10) is discussed in detail. The high scale CP breaking induces a phase in the CKM matrix as well. It is also pointed out that, in these models, the scales of Baryogenesis, Seesaw, Spontaneous CP violation and Spontaneous U(1)_QP breaking are all of the same order of magnitude.
The CP parameters $ε$ and $ε'/ε$ are calculated in the aspon model of spontaneous CP violation, a model which solves the strong CP problem. A new range for the scale of spontaneous breaking of CP is found. It is shown that $ε'/ε$ is suppressed by $\sim x^2 v^2/(κ^2 \sin^5 θ_C) \sim 5 \times 10^{-3}$ relative to the Standard Model. If experiment finds that $ε'/ε$ is $10^{-4}$ or greater in magnitude, it will mean that the present approach to spontaneous CP violation is excluded.
A scenario is suggested for spontaneous CP violation in non-SUSY and SUSY- SO(10). The idea is to have a scalar potential which generates spontaneously a phase, at the high scale, in the VEV that gives a mass to the RH neutrinos. As a possible realization the case of the minimal renormalizable SUSY SO(10) is discussed in detail and one finds that a phase is induced in the CKM matrix. It is also pointed out that, in these models, the scales of Baryogenesis, Seesaw, Spontaneous CP violation and Spontaneous U(1)PQ breaking are all at the same order of magnitude.
Conditions for spontaneous Charge-Parity (CP) violation in the scalar potential sector of general $S(3)$ Higgs-doublet model (3HDM) are analyzed. An analysis of the Higgs sector of the minimal $S(3)$-invariant extension of the Standard Model including CP violation arising from the spontaneous breaking of the electroweak symmetry is presented. This extended Higgs sector with three SU(2) doublets Higgs fields with complex vev's provides an interesting scenario to analyze the Higgs masses spectrum, trilinear self-couplings and CP violation. We present how the spontaneous electroweak symmetry brea…
The Standard Model for CP violation, the CKM model, works very well in explaining all laboratory experimental data. However, this model does not address the question that where it comes from. The origin of CP violation is still a mystery. In this talk I discuss a model\cite{model} addressing this problem in which the CP violating phase in the CKM matrix is identical to the phase in the Higgs potential resulting from spontaneous CP violation.
We study implications of spontaneous CP-violation in minimal susy models for CP-asymmetries in rare $B,\bar B$-decays. In particular, we estimate characteristic values of the angles of the unitarity triangle and show that sizeable CP-violating effects result from $B-\bar B$ mixing only. Significant deviations from the SM predictions are pointed out.
The Higgs boson mass problem is considered in the next-to-minimal supersymmetric standard model for the case of the spontaneous CP violation. The renormalization group equations for the gauge, Yukawa and scalar coupling constants, the effective Higgs potential and lower experimental bounds on Higgs boson and chargino masses are analyzed. The restrictions on the Higgs boson masses are found.
We investigate bounds from tree-level and one-loop processes in generic supersymmetric models with spontaneous R-parity breaking in the superpotential. We analyse the bounds from a general point of view. The bounds are applicable both for all models with spontaneous R-parity violation and for explicit bilinear R-parity violation based on general lepton-chargino and neutrino-neutralino mixings. We find constraints from semileptonic B, D and K decays, leptonic decays of the mu and tau, electric dipole moments, as well as bounds for the anomalous magnetic moment of the muon.
The large value of theta(13) recently measured by rector and accelerator experiments opens unprecedented opportunities for precision oscillation physics. In this paper, we reconsider the physics reach of medium baseline superbeams. For theta(13) ~ 9 degree we show that facilities at medium baselines -- i.e. L ~ O(1000 km) -- remain optimal for the study of CP violation in the leptonic sector, although their ultimate precision strongly depends on experimental systematics. This is demonstrated in particular for facilities of practical interest in Europe: a CERN to Gran Sasso and CERN to Phyasalm…
Based on the differential calculus and the gauge theory on discrete groups, we reconstruct two physics models with spontaneous CP violation: (1) The Georgi-Glashow-Lee model with two Higgs triplets; (2) The Weinberg-Salam-Branco model with three Higgs doublets and the natural flavor conservation (NFC). We focus on the Lagrangian terms containing the Higgs particles and show that with an appropriate choice of the discrete groups, we can obtain the physically meaningful Yukawa couplings and the Higgs potentials which lead to the spontaneous CP violation consequently.
In this talk I begin with some general discussion of the history of CP violation, then move on to aspects of the aspon model including the production of new particles at LHC, implications for B decay, generalized Cabibbo mixing and a reevaluation of kaon CP violation. Finally there is a summary.
We analyze the phenomenological consequences of assuming spontaneous CP violation in an SU(3) x U(1) model with three Higgs triplets and one sextuplet. After the identification of the relevant physical scalars, we estimate the contributions to the parameters $Δm_K$, $ε$ and $ε'$ coming from the Higgs-fermion couplings.
We implement the mechanism of spontaneous CP violation in the 3-3-1 model with right-handed neutrinos and recognize their sources of CP violation. Our main result is that the mechanism works already in the minimal version of the model and new sources of CP violation emerges as an effect of new physics at energies higher than the electroweak scale.
Scalar condensation, the well-established Higgs phenomenon, is the standard paradigm for building up renormalizable gauge-invariant theories of massive gauge bosons. In this short note, we demonstrate the uniqueness of the Higgs vacuum state under the possible presence of fermion condensates in a renormalizable U(1) model. In the same context, we explain why spontaneous spin-statistics violation is technically not admitted in conventional Quantum Field Theory.
We show that in the multi-Higgs extension of minimal supersymmetric standard model, which has N-pairs of Higgs doublets (called NHMSSM), it is impossible to break CP spontaneously, if we do not allow for fine-tuning relations between parameters. The result holds true even in the presence of spontaneous R-parity breaking.
We analyse the general constraints on unified gauge models with spontaneous CP breaking that satisfy the conditions that (i) CP violation in the quark sector is described by a realistic complex CKM matrix, and (ii) there is no significant flavor changing neutral current effects in the quark sector. We show that the crucial requirement in order to conform to the above conditions is that spontaneous CP breaking occurs at a very high scale by complex vevs of standard model singlet Higgs fields. Two classes of models are found, one consisting of pure Higgs extensions and the other one involving fe…
Models of spontaneous CP violation can solve the Strong CP problem without the need of an anomalous Peccei-Quinn symmetry. In this work we review the Nelson-Barr approach, quantifying a peculiar coincidence between unrelated mass scales that these models must satisfy in order to correctly reproduce the Standard Model quark masses and CP violation. We investigate the compatibility between this requirement and the induced radiative corrections to the neutron electric dipole moment, and with bounds coming from collider, electroweak and flavor observables.
We find that, at the one-loop level, the spontaneous CP violation is possible in a supersymmetric standard model that has an extra chiral Higgs triplet with hypercharge Y=0. At the tree level, this triplet-extended supersymmetric standard model (TESSM) cannot have any reasonable parameter spaces for the spontaneous CP violation, because the experimental constraints on the coupling coefficient of the neutral Higgs boson to a pair of $Z$ bosons exclude them. By contrast, at the one-loop level, we find that there are experimentally allowed parameter regions, where the spontaneous CP violation may…
We study the possibilities of spontaneous CP violation in the Next-to-Minimal Supersymmetric Standard Model with an extra singlet tadpole term in the scalar potential. We calculate the Higgs boson masses and couplings with radiative corrections including dominant two loop terms. We show that it is possible to satisfy the LEP constraints on the Higgs boson spectrum with non-trivial spontaneous CP violating phases. We also show that these phases could account for the observed value of epsilonK.
We construct the minimal SUSY model that causes spontaneous CP violation with an abelian flavor symmetry in the context of the large extra dimensions and show that various phenomenological problems can be solved by introducing only scales below the low fundamental scale. We also realize the realistic size of the CP violation and the small masses of the neutrinos. The strong CP problem can be solved by the axion scenario and the axion can be made invisible by introducing an additional large extra dimension.
We briefly review the question of spontaneous CP violation in some models of weak interactions. The next-to-minimal supersymmetric standard model, with two Higgs doublets and one gauge singlet, is one of the minimal extensions of the standard model where SCPV is viable. We analyse the possibility of spontaneous CP violation in the next-to-minimal supersymmetric standard model with an extra singlet tadpole term in the scalar potential, and confirm the existence of phenomenologically consistent minima with non-trivial CP violating phases.
This study proposes that the longstanding problems of quantum chromodynamics (QCD) as an SU(3)_C gauge theory, the confinement mechanism and Θvacuum, can be resolved by dynamical spontaneous symmetry breaking (DSSB) through the condensation of singlet gluons and quantum nucleardynamics (QND) as an SU(2)_N x U(1)_Z gauge theory is produced. The confinement mechanism is the result of massive gluons and the Yukawa potential provides hadron formation. The evidences for the breaking of discrete symmetries (C, P, T, CP) during DSSB appear explicitly: baryons and mesons without their parity partners,…
We derive sufficient conditions that guarantee a robust solution of the strong CP problem in theories with spontaneous CP violation, and introduce a class of models satisfying these requirements. In the simplest scenarios the dominant contribution to the topological angle arises at 3-loop order in the Yukawa couplings. A variety of realizations are possible on a warped extra dimension, which can simultaneously address the Planck-TeV hierarchy. Experimental signatures of this approach to the strong CP problem include flavor violation and vector-like partners of the top or bottom quarks.
We calculate the neutron electric dipole form factor induced by the CP violating theta-term of QCD, within a perturbative chiral quark model which includes pion and kaon clouds. On this basis we derive the neutron electric dipole moment and the electron-neutron Schiff moment. From the existing experimental upper limits on the neutron electric dipole moment we extract constraints on the theta-parameter and compare our results with other approaches.
We propose a possibility of spontaneous CP-violation (SCPV) at high scale in a SUSY SO(10) theory. The model is L-R symmetric SUSY SO(10) with \textbf{\noun{10}} and \textbf{126} dimensional Higgs generating fermion masses, and the CP phase is generated through complex VEV of B-L breaking \textbf{126} Higgs . The model can have potential application in explaining $ν$ masses and leptogenesis as well.
Utilizing results on the cosmology of anomalous discrete symmetries we show that models of spontaneous CP violation can in principle avoid the domain wall problem first pointed out by Zel'dovich, Kobzarev and Okun. A small but nonzero $θ_{QCD}$ explicitly breaks CP and can lift the degeneracy of the two CP conjugate vacua through nonperturbative effects so that the domain walls become unstable, but survive to cosmologically interesting epochs. We explore the viability of spontaneous CP violation in the context of two Higgs models, and find that the invisible axion solution of the strong CP pro…
Spontaneous CP violation motivates the introduction of two Higgs doublets in the electroweak theory, such a simple extension of the standard model has five physical Higgs bosons and rich CP-violating sources. Exploration on more than one Higgs boson is a direct evidence for new physics beyond the standard model. The neutral Higgs production at LHC is investigated in such a general two Higgs doublet model with spontaneous CP violation, it is shown that the production cross section and decays of the neutral Higgs boson can significantly be different from the predictions from the standard model.
We consider a particular two-Higgs-doublet model with spontaneous CP violation, where two neutral Higgses have no definite CP properties and the third one is CP-even. In this model, as the parameter $θ$ of CP violation increases, the masses of the neutral Higgs bosons are drawn towards the mass of the lightest one and the chance of detection of neutral Higgses at an $e^+e^-$ collider in Z+Higgs, $b\bar{b}$+Higgs and $t\bar{t}$+Higgs production increases with respect to the CP conserving case.
We perform a global analysis of neutrino oscillation data, including high-precision measurements of the neutrino mixing angle theta_13 at reactor experiments, which have confirmed previous indications in favor of theta_13>0. Recent data presented at the Neutrino 2012 Conference are also included. We focus on the correlations between theta_13 and the mixing angle theta_23, as well as between theta_13 and the neutrino CP-violation phase delta. We find interesting indications for theta_23< pi/4 and possible hints for delta ~ pi, with no significant difference between normal and inverted mass hier…
We study the effect of spontaneous Lorentz violation on neutrinos. We consider two kinds of effects: static effects, where the neutrino acquires a Lorentz-violating dispersion relation, and dynamic effects, which arise from the interactions of the neutrino with the Goldstone boson of spontaneous Lorentz violation. Static effects are well detailed in the literature. Here, special emphasis is given to the novel dynamic effect of Goldstone-Cerenkov radiation, where neutrinos moving with respect to a preferred rest frame can spontaneously emit Goldstone bosons. We calculate the observable conseque…
We study CP-violating effects in $B\to ψK_{s}$ decay within minimal supersymmetric models with spontaneous CP-violation. We find that the CP-asymmetry predicted by the Standard Model in this decay, $\sin 2β\geq 0.4$, cannot be accommodated in these models without violating the bound on the neutron electric dipole moment. This result holds for NMSSM-like models with an arbitrary number of sterile superfields. Further implications of the scenario are discussed.
Charge conjugation (C) and Parity (P) are exact symmetries at theta =pi and Theta = mu/(iT)=pi, where theta is the parameter of the so-called theta-vacuum, mu is the imaginary quark-number chemical potential and T is the temperature. Spontaneous breakings of these discrete symmetries are investigated by the the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. At zero T, P symmetry is spontaneously broken while C symmetry is conserved. As T increases, P symmetry is restored just after C symmetry is spontaneously broken, so that either P or C symmetry or both the symmetries are spontaneo…
We study the possibility of spontaneous CP violation in the next-to-minimal supersymmetric standard model (NMSSM). It is shown that the spontaneous CP violation is induced by the radiative effects of top, stop, bottom and sbottom superfields. The available regions of parameters, which are obtained by imposing the constraints from experiments, are rather narrow. We also obtain strong constraints for light Higgs masses such as m_H \le 36 GeV numerically. Sum of masses of two light neutral Higgs should set around 93 GeV and charged Higgs boson has a rather higher mass larger than 700 GeV.
We consider phenomenological implications of susy models with spontaneously broken CP-symmetry. In particular, we analyze CP-asymmetries in B decays and find that the predictions of these models are vastly different from those of the SM. These features are common to NMSSM-like models with an arbitrary number of sterile superfields and the MSSM with broken R-parity.
We show that in two Higgs doublet models at tree-level the potential minimum preserving electric charge and CP symmetries, when it exists, is the global one. Furthermore, we derived a very simple condition, involving only the coefficients of the quartic terms of the potential, that guarantees spontaneous CP breaking.
