Mixing-induced CP violating sources for electroweak baryogenesis from a semiclassical approach

The effects of flavor mixing in electroweak baryogenesis is investigated in a generalized semiclassical WKB approach. Through calculating the non-adiabatic corrections to the particle currents, it is shown that extra CP violation sources arise from the off-diagonal part of the equation of motion of particles moving inside the bubble wall. This type of mixing-induced source is of first order in a derivative expansion of the Higgs condensate, but it is oscillation suppressed. The numerical importance of the mixing-induced source is discussed in the minimal supersymmetric standard model and compared with the source term induced by a semiclassical force. It is found that in a large parameter space where oscillation suppression is not strong enough, the mixing-induced source can dominate over that from the semiclassical force.     

CP violating asymmetries in the neutral kaon decays

We study the time dependence of the integrated asymmetries in strangeness of kaons in the decays in two and three pions and in two photons with the purpose of disentangling theCP violating effects in the decay amplitudes from the ones related to the mass matrix. We find two cases where they are not reduced by the I=1/2 rule or hidden byCP violation in the mass matrix, namely the strangeness-energy correlation of the charged pions in the prompt decay ( _S ) in ^+-0, and the decays in two photons. The semileptonic decays are also briefly studied.     

CP violating rate asymmetries in B decays

We briefly discuss measurements of angles β and α of the unitarity triangle. We then review rate asymmetries usingSU(3) relationships in the standard model (SM). Some methods to measure angle y usingSU(3) are then discussed. We note that rate forb → sγ can be used to set limits on extra dimensions in which standard model particles propagate.     

Spontaneous CP violating phase as the CKM matrix phase

We propose that the CP violating phase in the CKM mixing matrix is identical to the CP phases responsible for the spontaneous CP violation in the Higgs potential. A multi-Higgs model with Peccei–Quinn (PQ) symmetry is constructed to realize this idea. The CP violating phase does not vanish when all Higgs masses become large. In general, here are flavor changing neutral current (FCNC) interactions mediated by neutral Higgs bosons at the tree level. However, unlike general multi-Higgs models, the FCNC Yukawa couplings are fixed in terms of the quark masses and CKM mixing angles. Implications for meson–anti-meson mixing, including recent data on D–D̄ mixing, and the electric dipole moment (EDM) of the neutron are studied. We find that the neutral Higgs boson masses can be at the order of one hundred GeV. The neutron EDM can be close to the present experimental upper bound.     

Spontaneous CP violating phase as the phase in PMNS matrix

We study the possibility of identifying the CP violating phases in the PMNS mixing matrix in the lepton sector and also that in the CKM mixing matrix in the quark sector with the phase responsible for the spontaneous CP violation in the Higgs potential, and some implications. Since the phase in the CKM mixing matrix is determined by experimental data, the phase in the lepton sector is also fixed. The mass matrix for neutrinos is constrained, leading to constraints on the Jarlskog CP violating parameter J, and the effective mass 〈m _ββ 〉 for neutrinoless double beta decay. The Yukawa couplings are also constrained. Different ways of identifying the phases have different predictions for \(\mu\to e e\bar{e}\) and \(\tau\to l_{1} l_{2} \bar{l}_{3}\). Future experimental data can be used to distinguish different models.     

Temperature dependence of standard model CP violation

We analyze the temperature dependence of CP violation effects in the standard model by determining the effective action of its bosonic fields, obtained after integrating out the fermions from the theory and performing a covariant gradient expansion. We find nonvanishing CP violating terms starting at the sixth order of the expansion, albeit only in the C-odd-P-even sector, with coefficients that depend on quark masses, Cabibbo-Kobayashi-Maskawa matrix elements, temperature and the magnitude of the Higgs field. The CP violating effects are observed to decrease rapidly with temperature, which has important implications for the generation of a matter-antimatter asymmetry in the early Universe. Our results suggest that the cold electroweak baryogenesis scenario may be viable within the standard model, provided the electroweak transition temperature is at most of order 1 GeV.     

A simple model for the dynamics towards metastable states

Circumstances under which a quenched system will freeze in a metastable state are studied in simple systems with long-range order. The model used is the time-dependent pair approximation, based on the most probable path (MPP) method. The time dependence of the solution is shown by means of flow diagrams. The fixed points and other features of the differential equations in time are independent of the choice of the rate constants. It is explained qualitatively how the system behaves under varying descending temperatures: the role of the initial conditions, the dependence on the quenching rate, and the response to precooling.     

CP violating asymmetry in stop decay into bottom and chargino

In the MSSM with complex parameters, loop corrections to the decay of a stop into a bottom quark and a chargino can lead to a CP violating decay rate asymmetry. We calculate this asymmetry at full one-loop level and perform a detailed numerical study, analyzing the dependence on the parameters and complex phases involved. If the stop can decay into a gluino, the self-energy and the vertex correction dominate due to the strong coupling. It is shown that the vertex contribution is always suppressed. We therefore give a simple approximate formula for the asymmetry. We account for the constraints on the parameters coming from several experimental limits. Asymmetries up to 25 percent are obtained. We also comment on the feasibility of measuring this asymmetry at the LHC.     

The Higgs mass in the CP violating MSSM,NMSSM and beyond

We discuss the automatised calculation of the Higgs mass in renormalisable supersymmetric models with complex parameters at the two-loop level. Our setup is based on the public codes SARAH and SPheno, which can now compute the two-loop corrections to masses of all neutral scalars in such theories. The generic ansatz for these calculations and the handling of the ‘Goldstone Boson catastrophe’ is described. It is shown that we find perfect agreement with other existing two-loop calculations performed in the \(\overline{\mathrm {DR}}\) scheme. We also use the functionality to derive results for the MSSM and NMSSM not available before: the Higgs mass in the constrained version of the complex MSSM and the impact of CP phases in the two-loop corrections beyond \(O(\alpha _s \alpha _t)\) for the scale-invariant NMSSM are briefly analysed.     

A CP violating mixing matrix compatible with neutral flavour conservation and spontaneous CP violation

A specific ansatz for the Yukawa couplings of a four-generation SU(2)_L×U(1) model with two Higgs doublets is discussed which leads to neutral flavour conservation, spontaneous CP violation and to a genuinely complex mixing matrix. W exchange conserves CP in the limit m_t′ = m_t only. The decay rate for t→b is reduced by factor two compared to the standard model wit three generations. The phenomenological implications for K⁰−K̄⁰ and B⁰−B̄⁰ are investigated.     

Unitarity polygons and CP violation areas and phases in the standard electroweak model

A geometrical interpretation of CP violation in terms of areas of unitarity triangles is presented, in the standard electroweak model with three families of quarks. The extension of the results to the case of four families is investigated. A special case is worked out in detail where it is shown how one determines the CP violating invariant phases and the areas of the CP violation triangles as functions of the moduli of the elements of the quark mixing matrix. For the most general four-family case, which is found to be rather involved, the necessary formulae, for determining the invariant phases and the CP violation areas, are given.