Approximate Flavor Symmetries in the Lepton Sector

Approximate flavor symmetries in the quark sector have been used as a handle on physics beyond the Standard Model. Due to the great interest in neutrino masses and mixings and the wealth of existing and proposed neutrino experiments it is important to extend this analysis to the leptonic sector. We show that in the see-saw mechanism, the neutrino masses and mixing angles do not depend on the details of the right-handed neutrino flavor symmetry breaking, and are related by a simple formula. We propose several ans\"{a}tze which relate different flavor symmetry breaking parameters and find that the MSW solution to the solar neutrino problem is always easily fit. Further, the $\nu_\mu - \nu_\tau$ oscillation is unlikely to solve the atmospheric neutrino problem and, if we fix the neutrino mass scale by the MSW solution, the neutrino masses are found to be too small to close the Universe.Comment: 12 pages (no figures), LBL-3459

Hierarchical Quark Mass Matrices

I define a set of conditions that the most general hierarchical Yukawa mass matrices have to satisfy so that the leading rotations in the diagonalization matrix are a pair of (2,3) and (1,2) rotations. In addition to Fritzsch structures, examples of such hierarchical structures include also matrices with (1,3) elements of the same order or even much larger than the (1,2) elements. Such matrices can be obtained in the framework of a flavor theory. To leading order, the values of the angle in the (2,3) plane (s_{23}) and the angle in the (1,2) plane (s_{12}) do not depend on the order in which they are taken when diagonalizing. We find that any of the Cabbibo-Kobayashi-Maskawa matrix parametrizations that consists of at least one (1,2) and one (2,3) rotation may be suitable. In the particular case when the s_{13} diagonalization angles are sufficiently small compared to the product s_{12}s_{23}, two special CKM parametrizations emerge: the R_{12}R_{23}R_{12} parametrization follows with s_{23} taken before the s_{12} rotation, and vice versa for the R_{23}R_{12}R_{23} parametrization.Comment: LaTeX, 19 pages. References added, minor changes in text. Version published in Phys. Rev.

Simple supersymmetric solution to the strong CP problem

It is shown that the minimal supersymmetric left-right model can provide a natural solution to the strong {\it CP} problem without the need for an axion, nor any additional symmetries beyond supersymmetry and parity.Comment: Plain Latex. 10 pages, including two figures which are part of the Latex file. Shortened version, to appear in Phys. Rev. Lett. 7

Hypercharge and the Cosmological Baryon Asymmetry

Stringent bounds on baryon and lepton number violating interactions have been derived from the requirement that such interactions, together with electroweak instantons, do not destroy a cosmological baryon asymmetry produced at an extremely high temperature in the big bang. While these bounds apply in specific models, we find that they are generically evaded. In particular, the only requirement for a theory to avoid these bounds is that it contain charged particles which, during a certain cosmological epoch, carry a non-zero hypercharge asymmetry. Hypercharge neutrality of the universe then dictates that the remaining particles must carry a compensating hypercharge density, which is necessarily shared amongst them so as to give a baryon asymmetry. Hence the generation of a hypercharge density in a sector of the theory forces the universe to have a baryon asymmetry.Comment: 12 pages plus 1 Postscript figure available upon request. LBL 3482

P, C and Strong CP in Left-Right Supersymmetric Models

We systematically study the connection between P, C and strong CP in the context of both non-supersymmetric and supersymmetric left-right theories. We find that the solution to the strong CP problem requires both supersymmetry and parity breaking scales to be around the weak scale.Comment: 5 pages, RevTex, no figures. Some minor changes, final version as published in Phys. Rev. Lett. 79, 4744 (1997

Minimal Supersymmetric Scenarios for Spontaneous CP Violation

We study the possibility of spontaneous CP violation (SCPV) at the tree level in models with an extended Higgs sector. We show that the minimum equations for the complex phases of the vacuum expectation values (VEVs) have always a geometrical interpretation in terms of triangles. To illustrate our method we analyze the minimal supersymmetric (SUSY) model with R-parity violating couplings and sneutrino VEVs, where there is no SCPV. Then we study SUSY models with extra Higgs doublets and/or gauge singlets, and find that the simplest scenario with SCPV must include at least two singlet fields.Comment: LaTeX, 19 pages, 4 figure

Supersymmetry and Large Scale Left-Right Symmetry

We show that the low energy limit of the minimal supersymmetric Left-Right models is the supersymmetric standard model with an exact R-parity. The theory predicts a number of light Higgs scalars and fermions with masses much below the $B-L$ and $SU(2)_R$ breaking scales. The non-renormalizable version of the theory has a striking prediction of light doubly charged supermultiplets which may be accessible to experiment. Whereas in the renormalizable case the scale of parity breaking is undetermined, in the non-renormalizable one it must be bigger than about $10^{10} - 10^{12}$ GeV. The precise nature of the see-saw mechanism differs in the two versions, and has important implications for neutrino masses.Comment: LaTeX, 30 pages. Minor changes. Some references adde

Large Top Quark Yukawa Coupling and Horizontal Symmetries

We consider the maximal U(3) horizontal scheme as a handle on fermion masses and mixings. In particular, we attempt to explain the large top Yukawa coupling and the masses and mixing in the two heaviest generations. A simple model is constructed by enlarging the matter content of the Standard Model with that of a $10+\bar{10}$ pair of SU(5). The third generation particles get their masses when U(3) is broken to U(2). Top quark mass is naturally of order one. Bottom and tau masses are suppressed because of a hierarchy in the effective Yukawa couplings and not from the hierarchy in the Higgs doublet vacuum expectation values. The hierarchy is a consequence of the fact that the particle spectrum contains an incomplete vector-like generation and can come from hierarchies between scales of breaking of different grand unified groups. Hierarchies and mixings between the second and third generation are obtained by introducing a single parameter epsilon' representing the breaking U(2) -> U(1). As a consequence, we show that the successful (and previosuly obtained) relations V_{cb} \approx (m_s / m_b) \approx \sqrt (m_c / m_t) easily follow from our scheme.Comment: 23 pages, LaTe