A Light Sterile Neutrino from Friedberg-Lee Symmetry

Light sterile neutrinos of mass about an eV with mixing $\tilde U_{ls}$ of a few percent to active neutrinos may solve some anomalies shown in experimental data related to neutrino oscillation. How to have light sterile neutrinos is one of the theoretical problems which have attracted a lot of attentions. In this article we show that such an eV scale light sterile neutrino candidate can be obtained in a seesaw model in which the right-handed neutrinos satisfy a softly-broken Friedberg-Lee (FL) symmetry. In this model a right-handed neutrino is guaranteed by the FL symmetry to be light comparing with other two heavy right-handed neutrinos. It can be of eV scale when the FL symmetry is softly broken and can play the role of eV scale sterile neutrino needed for explaining the anomalies of experimental data. This model predicts that one of the active neutrino is massless. We find that this model prefers inverted hierarchy mass pattern of active neutrinos than normal hierarchy. An interesting consequence of this model is that realizing relatively large $|{\tilde U}_{es}|$ and relatively small $|{\tilde U}_{\mu s}|$ in this model naturally leads to a relatively small $|{\tilde U}_{\tau s}|$. This interesting prediction can be tested in future atmospheric or solar neutrino experiments.Comment: 14 pages, references added, version for publication in PL

Variational equalities of entropy in nonuniformly hyperbolic systems

In this paper we prove that for an ergodic hyperbolic measure $\omega$ of a $C^{1+\alpha}$ diffeomorphism $f$ on a Riemannian manifold $M$, there is an $\omega$-full measured set $\widetilde{\Lambda}$ such that for every invariant probability $\mu\in \mathcal{M}_{inv}(\widetilde{\Lambda},f)$, the metric entropy of $\mu$ is equal to the topological entropy of saturated set $G_{\mu}$ consisting of generic points of $\mu$: $$h_\mu(f)=h_{\top}(f,G_{\mu}).$$ Moreover, for every nonempty, compact and connected subset $K$ of $\mathcal{M}_{inv}(\widetilde{\Lambda},f)$ with the same hyperbolic rate, we compute the topological entropy of saturated set $G_K$ of $K$ by the following equality: $$\inf\{h_\mu(f)\mid \mu\in K\}=h_{\top}(f,G_K).$$ In particular these results can be applied (i) to the nonuniformy hyperbolic diffeomorphisms described by Katok, (ii) to the robustly transitive partially hyperbolic diffeomorphisms described by ~Ma{\~{n}}{\'{e}}, (iii) to the robustly transitive non-partially hyperbolic diffeomorphisms described by Bonatti-Viana. In all these cases $\mathcal{M}_{inv}(\widetilde{\Lambda},f)$ contains an open subset of $\mathcal{M}_{erg}(M,f)$.Comment: Transactions of the American Mathematical Society, to appear,see http://www.ams.org/journals/tran/0000-000-00/S0002-9947-2016-06780-X

Anomaly inflow mechanism using Wilson line

It is shown that the anomaly inflow mechanism can be implemented using Wilson line in odd dimensional gauge theories. An action of Wess-Zumino-Witten (WZW) type can be constructed using Wilson line. The action is understood in the odd dimensional bulk space-time rather than in the even dimensional boundary. This action is not gauge invariant. It gives anomalous gauge variations of the consistent form on boundary space-times. So it can be used to cancel the quantum anomalies localized on boundary space-times. This offers a new way to cancel the gauge anomaly and construct anomaly-free gauge theory in odd dimensional space-time.Comment: 4 pages, 1 figure; title changed; text and figure improved; references adde