Constraining the neutrino magnetic moment with anti-neutrinos from the Sun

We discuss the impact of different solar neutrino data on the spin-flavor-precession (SFP) mechanism of neutrino conversion. We find that, although detailed solar rates and spectra allow the SFP solution as a sub-leading effect, the recent KamLAND constraint on the solar antineutrino flux places stronger constraints to this mechanism. Moreover, we show that for the case of random magnetic fields inside the Sun, one obtains a more stringent constraint on the neutrino magnetic moment down to the level of \mu_\nu \lsim few \times 10^{-12}\mu_B, similar to bounds obtained from star cooling.Comment: 4 pages, 3 figures. Final version to appear in Phys. Rev. Let

Universality and tree structure of high energy QCD

Using non-trivial mathematical properties of a class of nonlinear evolution equations, we obtain the universal terms in the asymptotic expansion in rapidity of the saturation scale and of the unintegrated gluon density from the Balitsky-Kovchegov equation. These terms are independent of the initial conditions and of the details of the equation. The last subasymptotic terms are new results and complete the list of all possible universal contributions. Universality is interpreted in a general qualitative picture of high energy scattering, in which a scattering process corresponds to a tree structure probed by a given source.Comment: 4 pages, 3 figure

Fluctuations effects in high-energy evolution of QCD

Recently, Iancu and Triantafyllopoulos have proposed a hierarchy of evolution equations in QCD at high energy which generalises previous approaches by including the effects of gluon number fluctuations and thus the pomeron loops. In this paper, we present the first numerical simulations of the Langevin equation which reproduces that hierarchy. This equation is formally the Balitsky-Kovchegov equation supplemented with a noise term accounting for the relevant fluctuations. In agreement with theoretical predictions, we find that the effects of the fluctuations is to reduce the saturation exponent and to induce geometric scaling violations at high energy.Comment: 12 pages, 7 figures, minor corrections, version appeared in Phys. Rev.

QCD traveling waves beyond leading logarithms

We derive the asymptotic traveling-wave solutions of the nonlinear 1-dimensional Balitsky-Kovchegov QCD equation for rapidity evolution in momentum-space, with 1-loop running coupling constant and equipped with the Balitsky-Kovchegov-Kuraev-Lipatov kernel at next-to-leading logarithmic accuracy, conveniently regularized by different resummation schemes. Traveling waves allow to define "universality classes" of asymptotic solutions, i.e. independent of initial conditions and of the nonlinear damping. A dependence on the resummation scheme remains, which is analyzed in terms of geometric scaling properties.Comment: 10 pages, 5 figures; typos corrected, references updated, final Phys.Rev. D versio

Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable subsystems with one-dimensional unstable dynamics or critically stable dynamics. Systems of this type arise in problems of nonlinear output regulation, parameter estimation and adaptive control. In addition to providing boundedness and convergence criteria the results allow to derive domains of initial conditions corresponding to solutions leaving a given neighborhood of the origin at least once. In contrast to other works addressing convergence issues in unstable systems, our results require neither input-output characterizations for the stable part nor estimates of convergence rates. The results are illustrated with examples, including the analysis of phase synchronization of neural oscillators with heterogenous coupling

Front Propagation up a Reaction Rate Gradient

We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the expedient of a cutoff in the reaction rate below some critical density to capture the essential role of fl uctuations in the system. For large density, the velocity is large, which allows for an approximate analytic treatment. We derive an analytic approximation for the front velocity depe ndence on bulk particle density, showing that the velocity indeed diverge s in the infinite density limit. The form in which diffusion is impleme nted, namely nearest-neighbor hopping on a lattice, is seen to have an essential impact on the nature of the divergence

Field Theory of Propagating Reaction-Diffusion Fronts

The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at the results already confirmed by numerical simulations

Effects of gluon number fluctuations on photon - photon collisions at high energies

We investigate the effects of gluon number fluctuations on the total $\gamma\gamma$, $\gamma^*\gamma^*$ cross sections and the photon structure function $F_2^\gamma(x,Q^2)$. Considering a model which relates the dipole-dipole and dipole-hadron scattering amplitudes, we estimate these observables by using event-by-event and physical amplitudes. We demonstrate that both analyses are able to describe the LEP data, but predict different behaviours for the observables at high energies, with the gluon fluctuations effects decreasing the cross sections. We conclude that the study of $\gamma \gamma$ interactions can be useful to constrain the QCD dynamics.Comment: 9 pages, 6 figures. Improved version with two new figures. Version to be published in Physical Review

Space-Time Complexity in Hamiltonian Dynamics

New notions of the complexity function C(epsilon;t,s) and entropy function S(epsilon;t,s) are introduced to describe systems with nonzero or zero Lyapunov exponents or systems that exhibit strong intermittent behavior with ``flights'', trappings, weak mixing, etc. The important part of the new notions is the first appearance of epsilon-separation of initially close trajectories. The complexity function is similar to the propagator p(t0,x0;t,x) with a replacement of x by the natural lengths s of trajectories, and its introduction does not assume of the space-time independence in the process of evolution of the system. A special stress is done on the choice of variables and the replacement t by eta=ln(t), s by xi=ln(s) makes it possible to consider time-algebraic and space-algebraic complexity and some mixed cases. It is shown that for typical cases the entropy function S(epsilon;xi,eta) possesses invariants (alpha,beta) that describe the fractal dimensions of the space-time structures of trajectories. The invariants (alpha,beta) can be linked to the transport properties of the system, from one side, and to the Riemann invariants for simple waves, from the other side. This analog provides a new meaning for the transport exponent mu that can be considered as the speed of a Riemann wave in the log-phase space of the log-space-time variables. Some other applications of new notions are considered and numerical examples are presented.Comment: 27 pages, 6 figure

Approximated maximum likelihood estimation in multifractal random walks

We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the dependency structure for the latent volatility. The procedure is implemented as a package in the R computer language. Its performance is tested on synthetic data and compared to an inference approach based on the generalized method of moments. The method is applied to estimate parameters for various financial stock indices.Comment: 8 pages, 3 figures, 2 table