Supersymmetric Model of Muon Anomalous Magnetic Moment and Neutrino Masses

We propose the novel lepton-number relationship $L_\tau = L_e + L_\mu$, which is uniquely realized by the interaction $(\hat \nu_e \hat \mu - \hat e \hat \nu_\mu) \hat \tau^c$ in supersymmetry and may account for a possibly large muon anomalous magnetic moment. Neutrino masses (with bimaximal mixing) may be generated from the spontaneous and soft breaking of this lepton symmetry.Comment: 10 pages, including 2 figure

Nearly Bi-Maximal Neutrino Mixing, Muon g-2 Anomaly and Lepton-Flavor-Violating Processes

We interpret the newly observed muon g-2 anomaly in the framework of a leptonic Higgs doublet model with nearly degenerate neutrino masses and nearly bi-maximal neutrino mixing. Useful constraints are obtained on the rates of lepton-flavor-violating rare decays $\tau \to \mu \gamma$, $\mu \to e \gamma$ and $\tau \to e \gamma$ as well as the $\mu$-$e$ conversion ratio $R_{\mu e}$. We find that $\Gamma (\mu \to e \gamma)$, $\Gamma (\tau \to e \gamma)$ and $R_{\mu e}$ depend crucially on possible non-zero but samll values of the neutrino mixing matrix element $V_{e3}$, and they are also sensitive to the Dirac-type CP-violating phase. In particular, we show that $\Gamma (\tau \to \mu \gamma)/m^5_\tau$, $\Gamma (\mu \to e \gamma)/m^5_\mu$ and $\Gamma (\tau \to e \gamma)/m^5_\tau$ are approximately in the ratio $1: 2|V_{e3}|^2: 2|V_{e3}|^2$ if $|V_{e3}|$ is much larger than ${\cal O}(10^{-2})$, and in the ratio $2 (\Delta m^2_{\rm atm})^2: (\Delta m^2_{\rm sun})^2:(\Delta m^2_{\rm sun})^2$ if $|V_{e3}|$ is much lower than ${\cal O}(10^{-3})$, where $\Delta m^2_{\rm atm}$ and $\Delta m^2_{\rm sun}$ are the corresponding mass-squared differences of atmospheric and solar neutrino oscillations.Comment: LaTex 6 pages (2 PS figures). Phys. Rev. D (in printing

Flavon exchange effects in models with abelian flavor symmetry

In models with abelian flavor symmetry the small mixing angles and mass ratios of quarks and leptons are typically given by powers of small parameters characterizing the spontaneous breaking of flavor symmetry by "flavon" fields. If the scale of the breaking of flavor symmetry is near the weak scale, flavon exchange can lead to interesting flavor-violating and CP violating effects. These are studied. It is found that d_e, mu -> e + gamma, and mu-e conversion on nuclei can be near present limits. For significant range of parameters mu-e conversion can be the most sensitive way to look for such effects.Comment: 19 pages, 5 Postscript figures, LATE

Probing Left-handed Slepton Flavor Mixing at Future Lepton Colliders

It has been argued in the literature that the search for the slepton oscillation phenomenon can be a powerful probe of intergenerational mixing between sleptons, once sleptons are found at future colliders. In this article we estimate possible reach of future lepton colliders in probing left-handed slepton flavor mixing, especially mixing between the first and third generations, on which constraints imposed by other processes like $\tau \to e \gamma$ are very weak. $e^+e^-$ collider is suitable for this purpose, since it can produce, if kinematically allowed, sleptons of the first generation via t-channel, in addition to s-channel. Utilizing e^+e^- \to \tau e + 4jets + \E signal at $e^+e^-$ linear collider with integrated luminosity L=50 fb^{-1}(500 fb^{-1}) it may be possible to reach mixing angle $\sin 2\theta_{\tilde{\nu}} \gtrsim 0.06 (0.04)$ and mass difference $\Delta m_{\tilde{\nu}} \gtrsim 0.07 (0.04)$ GeV for sneutrinos in the first and third generations at the statistical significance of 5 \sigma.Comment: 27 pages, 6 figures. A new section added. Conclusion unchanged. To appear in Phys. Rev.

Lepton Flavor Violation in the SUSY-GUT Models with Lopsided Mass Matrix

The tiny neutrino masses measured in the neutrino oscillation experiments can be naturally explained by the supersymmetric see-saw mechanism. If the supersymmetry breaking is mediated by gravity, the see-saw models may predict observable lepton flavor violating effects. In this work, we investigate the lepton flavor violating process $\mu\to e\gamma$ in the kind of neutrino mass models based on the idea of the ``lopsided'' form of the charged lepton mass matrix. The constraints set by the muon anomalous magnetic moment are taken into account. We find the present models generally predict a much larger branching ratio of $\mu\to e\gamma$ than the experimental limit. Conversely, this process may give strong constraint on the lepton flavor structure. Following this constraint we then find a new kind of the charged lepton mass matrix. The feature of the structure is that both the elements between the 2-3 and 1-3 generations are ``lopsided''. This structure produces a very small 1-3 mixing and a large 1-2 mixing in the charged lepton sector, which naturally leads to small $Br(\mu\to e\gamma)$ and the LMA solution for the solar neutrino problem.Comment: 24 pages, 8 figure

Lepton Flavor Violation in Z and Lepton Decays in Supersymmetric Models

The observation of charged lepton flavor non-conservation would be a clear signature of physics beyond the Standard Model. In particular, supersymmetric (SUSY) models introduce mixings in the sneutrino and the charged slepton sectors which could imply flavor-changing processes at rates accessible to upcoming experiments. In this paper we analyze the possibility to observe Z --> lep_I lep_J in the GigaZ option of TESLA at DESY. We show that although models with SUSY masses above the current limits could predict a branching ratio BR(Z --> mu e) accessible to the experiment, they would imply an unobserved rate of mu --> e gamma and thus are excluded. In models with a small mixing angle between the first and the third (or the second and the third) slepton families GigaZ could observe Z --> tau mu (or Z --> tau e) consistently with present bounds on lep_J --> lep_I gamma. In contrast, if the mixing angles between the three slepton families are large the bounds from mu --> e gamma push these processes below the reach of GigaZ. We show that in this case the masses of the three slepton families must be strongly degenerated (with mass differences of order 10^{-3}). We update the limits on the slepton mass insertions delta_{LL,RR,LR} and discuss the correlation between flavor changing and g_mu-2 in SUSY models.Comment: 23 pages, 6 figures. Version to appear in Phys. Rev.

A Complete Theory of Grand Unification in Five Dimensions

A fully realistic unified theory is constructed, with SU(5) gauge symmetry and supersymmetry both broken by boundary conditions in a fifth dimension. Despite the local explicit breaking of SU(5) at a boundary of the dimension, the large size of the extra dimension allows precise predictions for gauge coupling unification, alpha_s(M_Z) = 0.118 \pm 0.003, and for Yukawa coupling unification, m_b(M_Z) = 3.3 \pm 0.2 GeV. A complete understanding of the MSSM Higgs sector is given; with explanations for why the Higgs triplets are heavy, why the Higgs doublets are protected from a large tree-level mass, and why the mu and B parameters are naturally generated to be of order the SUSY breaking scale. All sources of d=4,5 proton decay are forbidden, while a new origin for d=6 proton decay is found to be important. Several aspects of flavor follow from an essentially unique choice of matter location in the fifth dimension: only the third generation has an SU(5) mass relation, and the lighter two generations have small mixings with the heaviest generation. The entire superpartner spectrum is predicted in terms of only two free parameters. The squark and slepton masses are determined by their location in the fifth dimension, allowing a significant experimental test of the detailed structure of the extra dimension. Lepton flavor violation is found to be generically large in higher dimensional unified theories with high mediation scales of SUSY breaking. In our theory this forces a common location for all three neutrinos, predicting large neutrino mixing angles. Rates for mu -> e gamma, mu -> e e e, mu -> e conversion and tau -> mu gamma are larger in our theory than in conventional 4D supersymmetric GUTs. Proposed experiments probing mu -> e transitions will probe the entire interesting parameter space of our theory.Comment: 51 pages, late

The Complexity of the Empire Colouring Problem

We investigate the computational complexity of the empire colouring problem (as defined by Percy Heawood in 1890) for maps containing empires formed by exactly $r > 1$ countries each. We prove that the problem can be solved in polynomial time using $s$ colours on maps whose underlying adjacency graph has no induced subgraph of average degree larger than $s/r$. However, if $s \geq 3$, the problem is NP-hard even if the graph is a forest of paths of arbitrary lengths (for any $r \geq 2$, provided $s < 2r - \sqrt(2r + 1/4+ 3/2)$. Furthermore we obtain a complete characterization of the problem's complexity for the case when the input graph is a tree, whereas our result for arbitrary planar graphs fall just short of a similar dichotomy. Specifically, we prove that the empire colouring problem is NP-hard for trees, for any $r \geq 2$, if $3 \leq s \leq 2r-1$ (and polynomial time solvable otherwise). For arbitrary planar graphs we prove NP-hardness if $s<7$ for $r=2$, and $s < 6r-3$, for $r \geq 3$. The result for planar graphs also proves the NP-hardness of colouring with less than 7 colours graphs of thickness two and less than $6r-3$ colours graphs of thickness $r \geq 3$.Comment: 23 pages, 12 figure