Algebraic polynomials and moments of stochastic integrals

We propose an algebraic method for proving estimates on moments of stochastic integrals. The method uses qualitative properties of roots of algebraic polynomials from certain general classes. As an application, we give a new proof of a variation of the Burkholder-Davis-Gundy inequality for the case of stochastic integrals with respect to real locally square integrable martingales. Further possible applications and extensions of the method are outlined.Comment: Published in Statistics and Probability Letters by the Elsevier. Permanent link: http://dx.doi.org/10.1016/j.spl.2011.01.022 Preliminary version of this paper appeared on October 27, 2009 as EURANDOM Report 2009-03

Dynamical picture for the exotic XYZ states

We present a dynamical approach for description of the multi-quark states that is based on an effective interaction Lagrangian describing the coupling of hadrons to their constituent quarks. First, we explore the consequences of treating the $X(3872)$ meson as a tetraquark bound state. We calculate the decay widths of the observed channels and conclude that for reasonable values of the size parameter of the $X(3872)$ one finds consistency with the available experimental data. Then we have critically checked the tetraquark picture for the $Z_c(3900)$ state by analyzing its strong decays. We found that $Z_c(3900)$ has a much more stronger coupling to $DD^\ast$ than to $J/\psi\pi$ that is in discord with experiment. As an alternative we have employed a molecular-type four-quark current to describe the decays of the $Z_c(3900)$ state as the charged particle in the isotriplet. We found that a molecular-type current gives the values of the above decays in accordance with the experimental observation. By using molecular-type four-quark currents for the recently observed resonances $Z_b(10610)$ and $Z_b(10650)$, we have calculated their two-body decay rates into a bottomonium state plus a light meson as well as into B-meson pairs.Comment: 7 pages, 4 figures, some references adde