Spin interfaces in the Ashkin-Teller model and SLE

We investigate the scaling properties of the spin interfaces in the Ashkin-Teller model. These interfaces are a very simple instance of lattice curves coexisting with a fluctuating degree of freedom, which renders the analytical determination of their exponents very difficult. One of our main findings is the construction of boundary conditions which ensure that the interface still satisfies the Markov property in this case. Then, using a novel technique based on the transfer matrix, we compute numerically the left-passage probability, and our results confirm that the spin interface is described by an SLE in the scaling limit. Moreover, at a particular point of the critical line, we describe a mapping of Ashkin-Teller model onto an integrable 19-vertex model, which, in turn, relates to an integrable dilute Brauer model.Comment: 12 pages, 6 figure

Conformal Curves in Potts Model: Numerical Calculation

We calculated numerically the fractal dimension of the boundaries of the Fortuin-Kasteleyn clusters of the $q$-state Potts model for integer and non-integer values of $q$ on the square lattice. In addition we calculated with high accuracy the fractal dimension of the boundary points of the same clusters on the square domain. Our calculation confirms that this curves can be described by SLE$_{\kappa}$.Comment: 11 Pages, 4 figure

Neutrino Physics: Open Theoretical Questions

We know that neutrino mass and mixing provide a window to physics beyond the Standard Model. Now this window is open, at least partly. And the questions are: what do we see, which kind of new physics, and how far "beyond"? I summarize the present knowledge of neutrino mass and mixing, and then formulate the main open questions. Following the bottom-up approach, properties of the neutrino mass matrix are considered. Then different possible ways to uncover the underlying physics are discussed. Some results along the line of: see-saw, GUT and SUSY GUT are reviewed.Comment: 17 pages, latex, 12 figures. Talk given at the XXI International Symposium on Lepton and Photon Interactions at High Energies, ``Lepton Photon 2003", August 11-16, 2003 - Fermilab, Batavia, IL US

Secondary electron emission yield in the limit of low electron energy

Secondary electron emission (SEE) from solids plays an important role in many areas of science and technology.1 In recent years, there has been renewed interest in the experimental and theoretical studies of SEE. A recent study proposed that the reflectivity of very low energy electrons from solid surface approaches unity in the limit of zero electron energy2,3,4, If this was indeed the case, this effect would have profound implications on the formation of electron clouds in particle accelerators,2-4 plasma measurements with electrostatic Langmuir probes, and operation of Hall plasma thrusters for spacecraft propulsion5,6. It appears that, the proposed high electron reflectivity at low electron energies contradicts to numerous previous experimental studies of the secondary electron emission7. The goal of this note is to discuss possible causes of these contradictions.Comment: 3 pages, contribution to the Joint INFN-CERN-EuCARD-AccNet Workshop on Electron-Cloud Effects: ECLOUD'12; 5-9 Jun 2012, La Biodola, Isola d'Elba, Ital

Neutrino masses and mixing

Status of determination of the neutrino masses and mixing is formulated and possible uncertainties, especially due to presence of the sterile neutrinos, are discussed. The data hint an existence of special ``neutrino'' symmetries. If not accidental these symmetries have profound implications and can substantially change the unification program. The key issue on the way to underlying physics is relations between quarks and leptons. The approximate quark-lepton symmetry or universality can be reconciled with strongly different patterns of masses and mixings due to nearly singular character of the mass matrices or screening of the Dirac structures in the double see-saw mechanism.Comment: 11 pages, latex, iopams.sty, 3 figures. Invited talk given at TAUP2005, September 10 - 14, 2005, Zaragoza, Spai

Sterile neutrinos: direct mixing effects versus induced mass matrix of active neutrinos

Mixing of active neutrinos with sterile ones generate ``induced'' contributions to the mass matrix of active neutrinos $\sim m_S \sin^2\theta_{aS}$, where $m_S$ is the Majorana mass of the sterile neutrino and $\theta_{aS}$ is the active-sterile mixing angle. We study possible effects of the induced matrix which can modify substantially the implications of neutrino oscillation results. We have identified the regions of $m_S$ and $\sin^2\theta_{aS}$ where the induced matrix (i) provides the dominant structures, (ii) gives the sub-dominant effects and (iii) where its effects can be neglected. The induced matrix can be responsible for peculiar properties of the lepton mixing and neutrino mass spectrum, in particular, it can generate the tri-bimaximal mixing. We update and discuss bounds on the induced masses from laboratory measurements, astrophysics and cosmology. We find that substantial impact of the induced matrix is possible if $m_S \sim 0.1-1$ eV and $\sin^2\theta_{aS} \sim 10^{-3} - 10^{-2}$ or $m_S \geq 200$ MeV and $\sin^2\theta_{aS} \leq 10^{-9}$. The bounds can be relaxed in cosmological scenarios with low reheating temperature, if sterile neutrinos decay sufficiently fast, or their masses change with time.Comment: Figures updated, version to be published in Phys. Rev.

Neutrino mixing and CP violation from Dirac-Majorana bimaximal mixture and quark-lepton unification

We demonstrate that only two ansatz can produce the features of the neutrino mixing angles. The first ansatz comes from the quark-lepton grand unification; $\nu_{Di} = V_{CKM} \nu_{\alpha}$ is satisfied for left-handed neutrinos, where $\nu_{Di}$ are the Dirac mass eigenstates and $\nu_{\alpha}$ are the flavour eigenstates. The second ansatz comes from the assumption; $\nu_{Di} = U_{bimaximal} \nu_{i}$ is satisfied between the Dirac mass eigenstates $\nu_{Di}$ and the light Majorana neutrino mass eigenstates $\nu_{i}$, where $U_{bimaximal}$ is the bimaximal mixing matrix. By these two ansatz, the Maki-Nakagawa-Sakata matrix is given by $U_{MNS} = V_{CKM}^\dagger U_{bimaximal}$. We find that in this model the novel relation $\theta_{sol} + \theta_{13} = \pi/4$ is satisfied, where $\theta_{sol}$ and $\theta_{13}$ are solar and CHOOZ angle respectively. This "Solar-CHOOZ Complementarity" relation indicates that only if the CHOOZ angle $\theta_{13}$ is sizable, the solar angle $\theta_{sol}$ can deviate from the maximal mixing. We also infer the CP violation in neutrino oscillations. The leptonic Dirac CP phase $\delta_{MNS}$ is predicted as $\sin \delta_{MNS} \simeq A \lambda^2 \eta$, where $A, \lambda, \eta$ are the CKM parameters in Wolfenstein parametrization. Furthermore, we remark that the ratio of the Jarlskog CP violation factor for quarks and leptons is important, because the large uncertainty on $\eta$ is cancelled out in the ratio, $R_J \equiv J_{CKM}/J_{MNS} \simeq 4\sqrt{2} A \lambda^3 \simeq 5 \times 10^{-2}$.Comment: 9 pages, no figures; v2 references added, v3 references adde