Solar neutrinos and 1-3 leptonic mixing

Effects of the 1-3 leptonic mixing on the solar neutrino observables are studied and the signatures of non-zero $\theta_{13}$ are identified. For this we have re-derived the formula for $3\nu$-survival probability including all relevant corrections and constructed the iso-contours of observables in the $\sin^2 \theta_{12} - \sin^2 \theta_{13}$ plane. Analysis of the solar neutrino data gives $\sin^2\theta_{13} = 0.007^{+ 0.080}_{-0.007}$ (90% C.L.) for $\Delta m^2 = 8 \cdot 10^{-5}$ eV$^2$. The combination of the ratio CC/NC at SNO and gallium production rate selects $\sin^2\theta_{13} = 0.017 \pm 0.026$ ($1\sigma$). The global fit of all oscillation data leads to zero best value of $\sin^2 \theta_{13}$. The sensitivity ($1\sigma$ error) of future solar neutrino studies to $\sin^2 \theta_{13}$ can be improved down to 0.01 - 0.02 by precise measurements of the pp-neutrino flux and the CC/NC ratio as well as spectrum distortion at high ($E > 4$ MeV) energies. Combination of experimental results sensitive to the low and high energy parts of the solar neutrino spectrum resolves the degeneracy of angles $\theta_{13}$ and $\theta_{12}$. Comparison of $\sin^2 \theta_{13}$ as well as $\sin^2 \theta_{12}$ measured in the solar neutrinos and in the reactor/accelerator experiments may reveal new effects which can not be seen otherwise.Comment: 36 pages, latex, 10 figures. Analysis and figures are updated with new (salt phase II) SNO results, several clarifications added, typos correcte

Nodal Domain Statistics for Quantum Maps, Percolation and SLE

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated by numerical computations for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general hamiltonian systems, where the validity of the underlying assumptions is much less clear. We also demonstrate that the nodal domains of the perturbed cat maps obey the Cardy crossing formula and find evidence that the boundaries of the nodal domains are described by SLE with $\kappa$ close to the expected value of 6, suggesting that quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.Comment: 4 pages, 5 figure

Solar neutrino spectrum, sterile neutrinos and additional radiation in the Universe

Recent results from the SNO, Super-Kamiokande and Borexino experiments do not show the expected upturn of the energy spectrum of events (the ratio $R \equiv N_{obs}/N_{SSM}$) at low energies. At the same time, cosmological observations testify for possible existence of additional relativistic degrees of freedom in the early Universe: $\Delta N_{eff} = 1 - 2$. These facts strengthen the case of very light sterile neutrino, $\nu_s$, with $\Delta m^2_{01} \sim (0.7 - 2) \cdot 10^{-5}$ eV$^2$, which mixes weakly with the active neutrinos. The $\nu_s$ mixing in the mass eigenstate $\nu_1$ characterized by $\sin^2 2\alpha \sim 10^{-3}$ can explain an absence of the upturn. The mixing of $\nu_s$ in the eigenstate $\nu_3$ with $\sin^2 \beta \sim 0.1$ leads to production of $\nu_s$ via oscillations in the Universe and to additional contribution $\Delta N_{eff} \approx 0.7 - 1$ before the big bang nucleosynthesis and later. Such a mixing can be tested in forthcoming experiments with the atmospheric neutrinos as well as in future accelerator long baseline experiments. It has substantial impact on conversion of the supernova neutrinos.Comment: 27 pages, LaTeX, 14 eps figures, 3 figures and additional considerations adde

Free field representation for the O(3) nonlinear sigma model and bootstrap fusion

The possibility of the application of the free field representation developed by Lukyanov for massive integrable models is investigated in the context of the O(3) sigma model. We use the bootstrap fusion procedure to construct a free field representation for the O(3) Zamolodchikov- Faddeev algebra and to write down a representation for the solutions of the form-factor equations which is similar to the ones obtained previously for the sine-Gordon and SU(2) Thirring models. We discuss also the possibility of developing further this representation for the O(3) model and comment on the extension to other integrable field theories.Comment: 14 pages, latex, revtex v3.0 macro package, no figures Accepted for publication in Phys. Rev.

Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $gl(N)$. Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide with certain components of WZW conformal block for primary fields. We introduce the symmetrized version of the Drinfeld associator by dropping the odd terms. The symmetrized associator gives the same knot invariants, but has a simpler structure and is fully characterized by one symmetric function which we call the Drinfeld prepotential.Comment: 14 pages, 2 figures; several flaws indicated by referees correcte

The Tails of the Crossing Probability

The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails of the crossing probability far from the critical point have shape $\pi_{hs}(p) \simeq D \exp(c L[p-p_{c}]^{\nu})$ where $\nu$ is the correlation length index, $p=1-\exp(-\beta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical change

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

Dirac equation in the magnetic-solenoid field

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian in both above dimensions and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.Comment: 23 pages, 2 figures, LaTex fil