New Insights on Low Energy πN\pi N Scattering Amplitudes

The $S$- and $P$- wave phase shifts of low-energy pion-nucleon scatterings are analysed using Peking University representation, in which they are decomposed into various terms contributing either from poles or branch cuts. We estimate the left-hand cut contributions with the help of tree-level perturbative amplitudes derived in relativistic baryon chiral perturbation theory up to $\mathcal{O}(p^2)$. It is found that in $S_{11}$ and $P_{11}$ channels, contributions from known resonances and cuts are far from enough to saturate experimental phase shift data -- strongly indicating contributions from low lying poles undiscovered before, and we fully explore possible physics behind. On the other side, no serious disagreements are observed in the other channels.Comment: slightly chnaged version, a few more figures added. Physical conclusions unchange

Massive Dirac fermions and spin physics in an ultrathin film of topological insulator

We study transport and optical properties of the surface states which lie in the bulk energy gap of a thin-film topological insulator. When the film thickness is comparable with the surface state decay length into the bulk, the tunneling between the top and bottom surfaces opens an energy gap and form two degenerate massive Dirac hyperbolas. Spin dependent physics emerges in the surface bands which are vastly different from the bulk behavior. These include the surface spin Hall effects, spin dependent orbital magnetic moment, and spin dependent optical transition selection rule which allows optical spin injection. We show a topological quantum phase transition where the Chern number of the surface bands changes when varying the thickness of the thin film.Comment: 7 pages, 5 figure

New Insights on Low Energy πN\pi N Scattering Amplitudes: Comprehensive Analyses at O(p3)\mathcal{O}(p^3) Level

A production representation of partial-wave $S$ matrix is utilized to construct low-energy elastic pion-nucleon scattering amplitudes from cuts and poles on complex Riemann sheets. Among them, the contribution of left-hand cuts is estimated using the $\mathcal{O}(p^3)$ results obtained in covariant baryon chiral perturbation theory within the extended-on-nass-shell scheme. By fitting to data on partial-wave phase shifts, it is indicated that the existences of hidden poles in $S_{11}$ and $P_{11}$ channels, as conjectured in our previous paper~\citep{Wang:2017agd}, are firmly established. Specifically, the pole mass of the $S_{11}$ hidden resonance is determined to be $(895\pm81)-(164\pm23)i$ MeV, whereas, the virtual pole in the $P_{11}$ channel locates at $(966\pm18)$ MeV. It is found that analyses at the $\mathcal{O}(p^3)$ level improves significantly the fit quality, comparing with the previous $\mathcal{O}(p^2)$ one. Quantitative studies with cautious physical discussions are also conducted for the other $S$- and $P$-wave channels.Comment: 38 pages. Published in Chinese Physics

On the Existence of N∗(890)N^*(890) Resonance in S11S_{11} Channel of πN\pi N Scatterings

Low-energy partial-wave $\pi N$ scattering data is reexamined with the help of the production representation of partial-wave $S$ matrix, where branch cuts and poles are thoroughly under consideration. The left-hand cut contribution to the phase shift is determined, with controlled systematic error estimates, by using the results of $\mathcal{O}(p^3)$ chiral perturbative amplitudes obtained in the extended-on-mass-shell scheme. In $S_{11}$ and $P_{11}$ channels, severe discrepancies are observed between the phase shift data and the sum of all known contributions. Statistically satisfactory fits to the data can only be achieved by adding extra poles in the two channels. We find that a $S_{11}$ resonance pole locates at $\sqrt{z_{r}}=(0.895\pm0.081)-(0.164\pm0.023)i$ GeV, on the complex $s$-plane. On the other hand, a $P_{11}$ virtual pole, as an accompanying partner of the nucleon bound-state pole, locates at $\sqrt{z_{v}}=(0.966\pm0.018)$ GeV, slightly above the nucleon pole on the real axis below threshold. Physical origin of the two newly established poles is explored to the best of our knowledge. It is emphasized that the $\mathcal{O}(p^3)$ calculation greatly improves the fit quality comparing with the previous $\mathcal{O}(p^2)$ one.Comment: 7 Page