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.     

Cold electroweak baryogenesis with Standard Model CP violation

We study a mechanism that generates the baryon asymmetry of the Universe during a tachyonic electroweak phase transition. We utilize as sole source of CP violation an operator that was recently obtained from the Standard Model by integrating out the quarks.     

Electroweak baryogenesis from late neutrino masses

Electroweak baryogenesis, given a first-order phase transition, does not work in the standard model because the quark Yukawa matrices are too hierarchical. On the other hand, the neutrino mass matrix is apparently not hierarchical. In models with neutrino mass generation at low scales, the neutrino Yukawa couplings lead to large CP violation in the reflection probability of heavy leptons by the expanding Higgs bubble wall, and can generate the observed baryon asymmetry of the universe. The mechanism predicts new vectorlike leptons below the TeV scale and sizable mu --> e processes.     

Models of neutrino masses and baryogenesis

Majorana masses of the neutrino implies lepton number violation and is intimately related to the lepton asymmetry of the universe, which gets related to the baryon asymmetry of the universe in the presence of the sphalerons during the electroweak phase transition. Assuming that the baryon asymmetry of the universe is generated before the electroweak phase transition, it is possible to discriminate different classes of models of neutrino masses. While see-saw mechanism and the triplet Higgs mechanism are preferred, the Zee-type radiative models and the R-parity breaking models requires additional inputs to generate baryon asymmetry of the universe during the electroweak phase transition.     

Where is the origin of CP violations?

If experimentally b → c is more suppressed than b → u, the Kobayashi-Maskawa mechanism of CP violation may not work. In the SU (2) × U(1) × S₃ model, which gives all elements of the KM matrix naturally by the quark masses, this is the case and CP violations originate mainly from the Yukawa sector.     

Baryogenesis and damping in nonminimal electroweak models

We calculate the baryon asymmetry of the Universe in the standard model of the electroweak theory with CP violation appropriate for simple extensions of the Higgs sector. The propagation of quarks of masses up to about 5 GeV are considered, taking into account the effect of damping rate. We find that the contribution of the b quark can still account for the observed baryon asymmetry to within the theoretical uncertainties of such models.

     

Postsphaleron baryogenesis

We present a new mechanism for generating the baryon asymmetry of the Universe directly in the decay of a singlet scalar field S(r) with a weak scale mass and a high dimensional baryon number-violating coupling. Unlike most currently popular models, this mechanism, which becomes effective after the electroweak phase transition, does not rely on the sphalerons for inducing a nonzero baryon number. CP asymmetry in S(r) decay arises through loop diagrams involving the exchange of W+/- gauge bosons and is suppressed by light quark masses, leading naturally to a value of eta(B) approximately 10(-10). The simplest realization of this idea which uses a six quark DeltaB=2 operator predicts colored scalars accessible to the CERN Large Hadron Collider and neutron-antineutron oscillation within reach of the next-generation experiments.     

CP violation with Higgs-dependent Yukawa couplings

The framework of Higgs-dependent Yukawa couplings allows one to eliminate small couplings from the Standard Model, which can be tested at the LHC. In this work, I study the conditions for CP violation to occur in such models. I identify a class of weak basis invariants controlling CP violation. The invariant measure of CP violation is found to be more than 10 orders of magnitude greater than that in the Standard Model, which can be sufficient for successful electroweak baryogenesis.     

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.     

Baryogenesis via density fluctuations with a second-order electroweak phase transition

We consider the presence of cosmic string-induced density fluctuations in the early universe at temperatures below the electroweak phase transition temperature. Resulting temperature fluctuations can restore the electroweak symmetry locally, depending on the amplitude of fluctuations and the background temperature. The symmetry will be spontaneously broken again in a given region as the temperature drops there (for fluctuations with length scales smaller than the horizon), resulting in the production of baryon asymmetry. The time-scale of the transition will be governed by the wavelength of fluctuation and, hence, can be much smaller than the Hubble time. This leads to strong enhancement in the production of baryon asymmetry for a second-order electroweak phase transition as compared to the case when transition happens due to the cooling of the universe via expansion. For a two-Higgs doublet model (with appropriate CP violation), we show that one can get the required baryon asymmetry if fluctuations propagate without getting significantly damped. If fluctuations are damped rapidly, then a volume factor suppresses the baryon production, though it is still 3–4 orders of magnitude larger than the conventional case of second-order transition.     

TADPOLE DIAGRAM,ΔI=1/2 ENHANCEMENT AND ε′/ε

The contributions of tadpole diagrams including t and c quark intermediate states to the amplitude of K⁰→2π and ε′/ε are analysed.The result shows it is quite possible that their contributions are the most important ones.They may give enough ΔI=1/2 enhancement for a reasonable quark relative momentum cutoff value which depends on K⁰ wave function.However,the calcualation value of │ε′/ε│ is too large if we suppose all CP violation effects come from the,Kobayashi-Maskawa phase δ. Perhaps,One approach to solve this difficulty is to assume the ε comes mainly from superweak CP violation.     

Fermion masses in a strong Yukawa coupling model

For strong enough Yukawa coupling the electroweak standard model fermion finds it energetically advantageous to transform itself into a bound state in the hedgehog background of the Higgs field in the semiclassical approximation. By considering that the bound states give the masses for the lepton and quark, it is found that all fermion masses can be described by the strongly Yukawa coupling constants which tend to a unitary constant.     

Scale of leptogenesis

We study the scale at which one can generate the lepton asymmetry of the universe which could then get converted to a baryon asymmetry during the electroweak phase transition. We consider the possibility that the Yukawa couplings could be arbitrarily small but sufficiently large to generate enough lepton asymmetry. This forbids the possibility of the breaking scale to be less than 10 TeV. Received: 14 April 1998 / Revised version: 8 August 1998 / Published online: 11 February 1999     

Flavor anarchy in a Randall-Sundrum model with 5D minimal flavor violation and a low Kaluza-Klein scale

A variant of a warped extra dimension model is presented. It is based on 5D minimal flavor violation, in which the only sources of flavor breaking are two 5D anarchic Yukawa matrices. These matrices also control the bulk masses, which are responsible for the resulting flavor hierarchy. The theory flows to a next to minimal flavor violation model where flavor violation is dominantly coming from the 3rd generation. Flavor violation is also suppressed by a parameter that dials the violation in the up or down sector. There is therefore a sharp limit in which there is no flavor violation in the down-type quark sector which, remarkably, is consistent with the observed flavor parameters. This is used to eliminate the current Randall-Sundrum flavor and CP problem. Our construction suggests that strong dynamic-based, flavor models may be built based on the same concepts.     

A soft origin for CKM-type CP violation

We present a two-Higgs-doublet model, with a Z₃ symmetry, in which CP violation originates solely in a soft (dimension-2) coupling in the scalar potential, and reveals itself solely in the CKM (quark mixing) matrix. In particular, in the mass basis the Yukawa interactions of the neutral scalars are all real. The model has only eleven parameters to fit the six quark masses and the four independent CKM-matrix observables. We find regions of parameter space in which the flavour-changing neutral couplings are so suppressed that they allow the scalars to be no heavier than a few hundred GeV.     

Strong CP in Heavy Quark Physics

We argue that strong CP phase should be shifted to b and t quark masses due to the requirement of vacuum stability. The strong CP problem in low energy sector thus disappears. We predict large CP violation in electric dipole moment of W and heavy quarks.     

CP violation in gauge theories and the electric dipole moment of the neutron

A nonvanishing contribution to the neutron electric dipole moment in CP-violating gauge theories of the weak interactions, arising from interaction of the photon with two-quark subsystems of the three-bound-quark neutron system, is calculated. In the Kobayashi-Maskawa model the resulting value of the moment is estimated as O(10^?32) e cm; however, strong interaction corrections (gluonic radiative corrections) give quark moment contributions which may be numerically larger (possibly 10^?30±1 e cm). Either case clearly distinguishes gauge-sector CP violation from Higgs-sector CP violation which typically gives a neutron moment of order 10^?24 e cm.     

CP violation in the neutrino sector: The new frontier

The discovery of neutrino masses has revealed a new flavour sector in the Standard Model. Just like the quark flavour sector, it contains a seed of CP violation, resulting in an asymmetric behaviour of matter and antimatter. It is argued that this new source of leptonic CP violation may be discovered in more precise neutrino oscillation experiments involving neutrino beams with energies in the GeV range that will be sent to distances of a few thousand kilometres.     

Baryogenesis at the electroweak scale

The generation of the baryon asymmetry of the universe is considered in the standard model of the electroweak theory with simple extensions of the Higgs sector. The propagation of quarks of masses up to about 5 GeV are considered, taking into account their markedly different dispersion relations due to propagation through the hot electroweak plasma. It is shown that the contribution of the b quark to the baryon asymmetry can be comparable to that for the t quark considered earlier.     

Spontaneous CP violation in the left-right model and the kaon system

A left-right model with spontaneous CP breakdown, consistent with the particle physics phenomenology, is presented. Constraints on free parameters of the model: mass of the new righthanded gauge boson M₂ and ratio r of the two vacuum expectation valuesof the bidoublet, are found from the measurement of ϵ in the kaon system. For most of the parameter space, M₂ is restricted to be below 10 TeV Higher masses can be achieved only by fine tuning of Kobayashi-Maskawa matrix elements, quark masses, r and the phase α which is the unique source of CP violation in the model. Large number of combinations of signs of quark masses, which are observables of the model, are found to be not allowed since they contradict with data. The range of ϵ'/ϵ the model predicts is around 10⁻⁴ in magnitude.