On the nature of the lightest scalar resonances

We briefly review the recent progresses in the new unitarization approach being developed by us. Especially we discuss the large $N_c$ $\pi\pi$ scatterings by making use of the partial wave $S$ matrix parametrization form. We find that the $\sigma$ pole may move to the negative real axis on the second sheet of the complex $s$ plane, therefore it raises the interesting question that this `$\sigma$' pole may be related to the $\sigma$ in the linear $\sigma$ model.Comment: Talk presented by Zheng at ``Quark Confinement and Hadron Spectroscopy VI'', 21--25 Sept. 2004, Cagliari, Italy. 3 pages with 2 figure

Moderate deviations in Poisson approximation: a first attempt

Poisson approximation using Stein's method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for right-tail probabilities of sums of dependent indicators. We obtain results under certain general conditions for local dependence as well as for size-bias coupling. These results are then applied to independent indicators, 2-runs, and the matching problem.Comment: 21 page

Is the σ\sigma meson dynamically generated?

We study the problem whether the $\sigma$ meson is generated `dynamically'. A pedagogical analysis on the toy O(N) linear sigma model is performed and we find that the large $N_c$ limit and the $m_\sigma\to \infty$ limit does not commute. The sigma meson may not necessarily be described as a dynamically generated resonance. On the contrary, the sigma meson may be more appropriately described by considering it as an explicit degree of freedom in the effective lagrangian.Comment: Contribution to ``Quark Confinement and Hadron Spectrum VII'', 2--7 Sept. 2006, Ponta Delgada, Acores, Portuga

On the scalar nonet in the extended Nambu Jona-Lasinio model

We discuss the lightest scalar resonances, $f_0(600)$, $\kappa(800)$, $a_0(980)$ and $f_0(980)$ in the extended Nambu Jona-Lasinio model. We find that the model parameters can be tuned, but unnaturally, to accommodate for those scalars except the $f_0(980)$. We also discuss problems encountered in the K Matrix unitarization approximation by using $N_c$ counting technique.Comment: 23 pages 3 eps figures, To appear in Nucl. Phys.

Is the f0(600)f_0(600) meson a dynamically generated resonance? -- a lesson learned from the O(N) model and beyond

O(N) linear $\sigma$ model is solvable in the large $N$ limit and hence provides a useful theoretical laboratory to test various unitarization approximations. We find that the large $N_c$ limit and the $m_\sigma\to \infty$ limit do not commute. In order to get the correct large $N_c$ spectrum one has to firstly take the large $N_c$ limit. We argue that the $f_0(600)$ meson may not be described as generated dynamically. On the contrary, it is most appropriately described at the same level as the pions, i.e, both appear explicitly in the effective lagrangian. Actually it is very likely the $\sigma$ meson responsible for the spontaneous chiral symmetry breaking in a lagrangian with linearly realized chiral symmetry.Comment: 15 pages, 3 figurs; references added; discussions slightly modified; revised version accepted by IJMP

Local spin polarisation of electrons in Rashba semiconductor nanowires: effects of the bound state

The local spin polarisation (LSP) of electrons in two typical semiconductor nanowires under the modulation of Rashba spin-orbit interaction (SOI) is investigated theoretically. The influence of both the SOI- and structure-induced bound states on the LSP is taken into account via the spin-resolved lattice Green function method. It is discovered that high spin-density islands with alternative signs of polarisation are formed inside the nanowires due to the interaction between the bound states and the Rashba effective magnetic field. Further study shows that the spin-density islands caused by the structure-induced bound state exhibit a strong robustness against disorder. These findings may provide an efficient way to create local magnetic moments and store information in semiconductors.Comment: 8 pages, 3 figure