Bi-maximal mixing at GUT, the low energy data and the leptogenesis

In the framework of the minimum supersymmetric model with right-handed neutrinos, we consider the Bi-maximal mixing which is realized at the GUT scale and discuss a question that this model can reproduce the low energy phenomena and the leptogenesis.Comment: Talk given by E. Takasugi at NuFact04, Osaka, Japan, July 26 - August 1,2004 - 3 pages, 4 figure

Yukawa Matrix for the Neutrino and Lepton Flavour Violation

We estimate the magnitude of Lepton Flavour Violation (LFV) from the phase of the neutrino Yukawa matrix. In the minimal supersymmetric standard model with right-handed neutrinos, the LFV processes l_i \to l_j \gamma can appear through the slepton mixing, which comes from the renormalization group effect on the right-handed neutrino Yukawa interaction between the Grand Unified Theory scale and the heavy right-handed neutrino mass scale. Two types of phases exist in the neutrino Yukawa matrix. One is the Majorana phase, which can change the magnitude of the LFV branching ratios by a few factor. The other phases relate for the size of the Yukawa hierarchy and its phase effect can change the LFV branching ratios by several orders of magnitude.Comment: Talk given by K. Tsumura at NuFact04, Osaka, Japan, July 26 - August 1,2004 - 3 pages, 2 figure

Phase effects from the general neutrino Yukawa matrix on lepton flavor violation

We examine contributions from Majorana phases to lepton flavor violating processes in the framework of the minimal supersymmetric standard model with heavy right-handed neutrinos. All phases in the complex neutrino Yukawa matrix are taken into account in our study. We find that in the scenario with universal soft-breaking terms sizable phase effects can appear on the lepton flavor violating processes such as $\mu \to e \gamma$, $\tau \to e \gamma$, and $\tau \to \mu \gamma$. In particular, the branching ratio of $\mu \to e \gamma$ can be considerably enhanced due to the Majorana phases, so that it can be much greater than that of $\tau \to \mu \gamma$.Comment: 14 pages, 4 eps figures, revtex

Enhancement of lepton flavor violation in a model with bi-maximal mixing at the grand unification scale

We study phenomenological predictions in the scenario with the quasi-degenerate relation among neutrino Dirac masses, m_D1 simeq m_D2 < m_D3, assuming the bi-maximal mixing at the grand unification scale in supersymmetric standard models with right-handed neutrinos. A sufficient lepton number asymmetry can be produced for successful leptogenesis. The lepton flavor violating process mu to e gamma can be enhanced due to the Majorana phase, so that it can be detectable at forthcoming experiments. The processes tau to e gamma and tau to mu gamma are suppressed because of the structure of neutrino Dirac masses, and their branching ratios are smaller than that of mu to e gamma.Comment: 15 pages, 5 figure

Noncommutative geometry and nonabelian Berry phase in the wave-packet dynamics of Bloch electrons

Motivated by a recent proposal on the possibility of observing a monopole in the band structure, and by an increasing interest on the role of Berry phase in spintronics, we studied the adiabatic motion of a wave packet of Bloch functions, under a perturbation varying slowly and incommensurately to the lattice structure. We show using only the fundamental principles of quantum mechanics that its effective wave-packet dynamics is conveniently described by a set of equations of motion (EOM) for a semiclassical particle coupled to a nonabelian gauge field associated with a geometric Berry phase. Our EOM can be viewed as a generalization of the standard Ehrenfest's theorem, and their derivation was asymptotically exact in the framework of linear response theory. Our analysis is entirely based on the concept of local Bloch bands, a good starting point for describing the adiabatic motion of a wave packet. One of the advantages of our approach is that the various types of gauge fields were classified into two categories by their different physical origin: (i) projection onto specific bands, (ii) time-dependent local Bloch basis. Using those gauge fields, we write our EOM in a covariant form, whereas the gauge-invariant field strength stems from the noncommutativity of covariant derivatives along different axes of the reciprocal parameter space. The degeneracy of Bloch bands makes the gauge fields nonabelian. We applied our formalism to the analyses on various types of Hall and polarization currents. We highlighted their behavior under time reversal (T) and space inversion (I). The concept of parity polarization current was also introduced. Together with charge/spin Hall/polarization currents, this type of orbital current is expected to be a potential probe for detecting and controling Berry phase.Comment: 39 pages. Typos corrected in the revised versio

Anomalous Hall effect in ferromagnetic semiconductors

We present a theory of the anomalous Hall effect in ferromagnetic (Mn,III)V semiconductors. Our theory relates the anomalous Hall conductance of a homogeneous ferromagnet to the Berry phase acquired by a quasiparticle wavefunction upon traversing closed paths on the spin-split Fermi surface of a ferromagnetic state. It can be applied equally well to any itinerant electron ferromagnet. The quantitative agreement between our theory and experimental data in both (In,Mn)As and (Ga,Mn)As systems suggests that this disorder independent contribution to the anomalous Hall conductivity dominates in diluted magnetic semiconductors.Comment: 4 pages, 2 figure

CP violation in scatterings, three body processes and the Boltzmann equations for leptogenesis

We obtain the Boltzmann equations for leptogenesis including decay and scattering processes with two and three body initial or final states. We present an explicit computation of the CP violating scattering asymmetries. We analyze their possible impact in leptogenesis, and we discuss the validity of their approximate expressions in terms of the decay asymmetry. In scenarios in which the initial heavy neutrino density vanishes, the inclusion of CP asymmetries in scatterings can enforce a cancellation between the lepton asymmetry generated at early times and the asymmetry produced at later times. We argue that a sizeable amount of washout is crucial for spoiling this cancellation, and we show that in the regimes in which the washouts are particularly weak, the inclusion of CP violation in scatterings yields a reduction in the final value of the lepton asymmetry. In the strong washout regimes the inclusion of CP violation in scatterings still leads to a significant enhancement of the lepton asymmetry at high temperatures; however, due to the independence from the early conditions that is characteristic of these regimes, the final value of the lepton asymmetry remains approximately unchanged.Comment: 24 pages, 6 figures. One appendix added. Some numerical results and corresponding figures (mainly fig. 3) corrected. Final version to be published in JHE

Theory of Ferromagnetism in Ca1-xLaxB6

Novel ferromagnetism in Ca$_{1-x}$La$_{x}$B$_6$ is studied in terms of the Ginzburg-Landau theory for excitonic order parameters, taking into account symmetry of the wavefunctions. We found that the minima of the free energy break both inversion and time-reversal symmetries, while the product of these two remains preserved. This explains various novelties of the ferromagnetism and predicts a number of magnetic properties, including the magnetoelectric effect, which can be tested experimentally.Comment: 5 pages, accepted for publication in Phys.Rev.Let

Chirality driven anomalous Hall effect in weak coupling regime

Anomalous Hall effect arising from non-trivial spin configuration (chirality) is studied based on the $s$-$d$ model. Considering a weak coupling case, the interaction is treated perturbatively. Scattering by normal impurities is included. Chirality is shown to drive locally Hall current and leads to overall Hall effect if there is a finite uniform chirality. This contribution is independent of the conventional spin-orbit contribution and shows distinct low temperature behavior. In mesoscopic spin glasses, chirality-induced anomalous Hall effect is expected below the spin-glass transition temperature. Measurement of Hall coefficient would be useful in experimentally confirming the chirality ordering