Real CP violation in a simple extension of the standard model
I present a simple three-Higgs-doublet extension of the standard model in which real CP violation takes place. The strong CP problem is attenuated by this model.
arXiv subjects
Publications and source records attributed to L. Lavoura.
I present a simple three-Higgs-doublet extension of the standard model in which real CP violation takes place. The strong CP problem is attenuated by this model.
I present a new model for the quark mass matrices, which uses four scalar doublets together with a horizontal symmetry S3 x Z3. The model is inspired on a suggestion made a few years ago by Ma, but it is different. The predictions |Vts| \approx ms/mb and |Vub/Vcb| > 0.085 are obtained. Flavour-changing neutral Yukawa interactions do not exist in the down-type-quark sector.
We analyze the prospects for observing CPT violation using neutral-meson P0-P0bar systems. Before one can claim a measurement of CPT violation, one must be able to rule out the possibility that its result is due to simpler new-physics effects. In particular, one must be able to separate the CPT-violating quantities from parameters violating the Delta P = ΔQ rule of semileptonic decays, and from new-physics contributions to the production mechanism of the neutral mesons. One can isolate CPT violation using the semileptonic decays of single, tagged neutral mesons; unfortunately, this situation cannot be implemented at the Upsilon(4S). For P0-P0bar pairs produced in a correlated parity-odd state we show that, by combining the di-lepton with the single-lepton decays, it is in principle possible to extract unambiguously one CPT-violating parameter. Finally, we develop the formalism necessary for describing new-physics effects in the production mechanism; this includes both cascade decays and violations of the rule of associated production.
In a recent paper, Banuls and Bernabeu have claimed the existence of a new form of indirect CP violation which would have its most prominent manifestation in the $B_d$-$\bar B_d$ system. I analyse this claim in detail. I emphasize the fact that it is necessary to take into account the precise experimental method if one is to identify correctly the weak phase that one is about to measure.
I present a new form of spontaneous CP violation in which, in analogy with the left-right-symmetric model, CP breaking results from the inequality of two real vacuum expectation values. In my model there is no scalar-pseudoscalar mixing, and the smallness of strong CP violation finds a natural explanation.
I put forward a model with vectorlike isosinglet quarks in which soft breaking of CP leads to strong CP violation only arising at two-loop level.
I put forward an SU(2)_L x SU(2)_R x U(1) model in which spontaneously broken parity symmetry makes it that strong CP violation only arises at three-loop level. All leptons and up-type quarks are in doublets either of SU(2)_L or of SU(2)_R, but there are singlet down-type quarks. A bi-doublet of scalars is introduced which has only one component with non-vanishing expectation value, thereby avoiding W_L-W_R mixing. The scalar potential is such that scalar-pseudoscalar mixing does not occur either.
We consider the time dependence of the decays of tagged $D^0$ and $\bar{D}^0$ into CP-conjugate final states $f$ and $\bar{f}$, or into a CP eigenstate $F$. We expand each decay width as $\exp (- Γt)$ times a series in $Γt$, where $Γ$ is the average decay width of the mass eigenstates $D_H$ and $D_L$, and examine the first three terms of the series. We show that experimental information on the coefficients of these terms allows in principle to compute all the relevant mixing parameters. In particular, depending on CP violation or conservation, we discuss the different possibilities to extract $Δm$ and $ΔΓ$, i.e., the mass and decay-width differences of the mass eigenstates. We also comment on consistency conditions among the coefficients of the various decay-width expansions.
We build a class of two-Higgs-doublet models in which the flavour-changing couplings of the neutral scalars are related in an exact way to elements of the quark mixing matrix. In this framework, we explore the different possibilities for CP violation and find some interesting scenarios, like a realization of the superweak idea without CP violation in the $B$-meson system. In another scenario the neutral scalars can be relatively light, and their contributions to the $B^0$--$\bar{B}^0$ transitions can alter the standard-model predictions for CP violation in that system.
We perform a systematic study of CP-violating observables in \ddbar\ decays. We show that given a final state, which may be a CP eigenstate or not, all the observables can in principle be measured if decay-time information is available and if, for CP non-eigenstates, both decay rates into $f$ and $\bar f$ are considered. As an illustration of our analysis we discuss an effective superweak scenario.
We investigate the effects of the new scalars in a two-Higgs-doublet model on the weak magnetic dipole moments of the fermions at the $Z$ peak. Proportionality of the Yukawa couplings to the fermion masses, and to $\tanβ$, makes such effects more important for the third family, and potentially relevant. For the $τ$ lepton, the new diagrams are suppressed by $v_τ= 2 \sin^2 θ_W - 1/2$, or by powers of $m_τ/M_Z$, but may still be comparable to the SM electroweak contributions. In contrast, we find that the new contributions for the bottom quark may be much larger than the SM electroweak contributions. These new effects may even compete with the gluonic contribution, if the extra scalars are light and $\tan β$ is large. We also comment on the problem of the gauge dependence of the vertex, arising when the $Z$ is off mass shell. We compute the contributions from the new scalars to the magnetic dipole moments for top-quark production at the NLC, and for bottom and $ τ$ production at LEP2. In the case of the top, we find that the SM electroweak and gluonic contributions to the $Z t {\bar t}$ vertex are comparable. The new contributions may be of the same order of magnitude as the standard-model ones, but not much larger.
In a general two-scalar-doublet model without fermions, there is a unique source of CP violation, $ J_1 $, in the gauge interactions of the scalars. It arises in the mixing of the three neutral physical scalars $ X_1 $, $ X_2 $ and $ X_3 $. CP violation may be observed via different decay rates for $ X_1 \rightarrow H^+ W^- $ and $ X_1 \rightarrow H^- W^+ $ (or, alternatively, for $ H^+ \rightarrow X_1 W^+ $ and $ H^- \rightarrow X_1 W^- $ --- depending on which decays are kinematically allowed). I compute the part of those CP-violating decay-rate differences which is proportional to $ J_1 $. The CP-invariant final-state-interaction phase is provided by the absorptive parts of the one-loop diagrams. I check the gauge invariance of the whole calculation.
I discuss methods to identify the presence of dicrete symmetries in the two-Higgs-doublet model by observing the masses and the cubic and quartic interactions of the scalars. The symmetries considered are a $ Z_2 $ symmetry under which $ ϕ_2 \rightarrow - ϕ_2 $, and a CP symmetry which enforces real coupling constants in the Higgs potential. Those symmetries are spontaneously broken, and the $ Z_2 $ symmetry may also be softly broken. I identify the signatures in the interactions of the scalars that these symmetries leave after their breaking.
We consider a SU(2)$ \otimes $U(1) gauge theory with many scalar doublets, but without fermions. We devise a systematic method of constructing quantities which are invariant under changes of basis of the scalar fields, but acquire a minus sign under a general CP transformation. Those quantities provide a basis-independent way of checking for the existence of CP violation.
In the SUSY GUT scenario, it is natural to assume the right-handed-neutrino Majorana-mass scale to be $10^{16}$ GeV. This will in principle lead, by the seesaw mechanism, to a $ ν_τ $ mass of order $ m_t^2 / (10^{16}\, {\rm GeV}) \sim 3 \times 10^{-3}\, {\rm eV} $. This suggests that the solution of the solar-neutrino puzzle should be either the MSW effect in $ν_e$--$ν_τ$ oscillations, with $ m_{ν_τ}^2 \sim 10^{-5}\, {\rm eV}^2 $, or long-wavelength $ν_e$--$ν_μ$ oscillations, with $ m_{ν_μ}^2 \sim 10^{-10}\, {\rm eV}^2 $. These solutions require unexpectedly large mixings of $ ν_e $ with $ ν_τ $ and $ ν_μ $, respectively. I suggest a variation of the Dimopoulos--Hall--Raby model for the fermion mass matrices which can accomodate such large mixings.
In the extension of the Dimopoulos--Hall--Raby model of the fermion mass matrices to the neutrino sector, there is an entry in the up-quark and neutrino Dirac mass matrices which can be assumed to arise from the Yukawa coupling of a {\bf 120}, instead of a {\bf 10} or a {\bf 126}, of SO(10). Although this assumption leads to an extra undetermined complex parameter in the model, the resulting lepton mixing matrix exhibits the remarkable feature that the $ ν_τ $ does not mix with the other two neutrinos. Making a reasonable assumption about the extra parameter, we are able to fit the large-mixing-angle MSW solution of the solar-neutrino problem, and we obtain $ m_{ν_τ} \sim 10 $ eV, the right mass range to close the Universe. Other possibilities for explaining the solar-neutrino deficit are also discussed.
We compute the oblique parameters, including the three new parameters $ V $, $ W $ and $ X $ introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin $ J $ and weak hypercharge $ Y $. We show that, when the masses of the heaviest and lightest components of the multiplet remain constant, but $ J $ increases, the oblique parameter $ U $ and the three new oblique parameters increase like $ J^3 $, while $ T $ only increases like $ J $. For large multiplets with masses not much higher than $ m_Z $, the oblique parameters $ U $ and $ V $ may become much larger than $ T $ and $ S $.
Analysis of the model of Babu and Mohapatra for the mass matrices in SO(10), with survey of the different types of neutrino spectra possible in that model