Enhanced breaking of heavy quark spin symmetry

Heavy quark spin symmetry is useful to make predictions on ratios of decay or production rates of systems involving heavy quarks. The breaking of spin symmetry is generally of the order of $O({\Lambda_{\rm QCD}/m_Q})$, with $\Lambda_{\rm QCD}$ the scale of QCD and $m_Q$ the heavy quark mass. In this paper, we will show that a small $S$- and $D$-wave mixing in the wave function of the heavy quarkonium could induce a large breaking in the ratios of partial decay widths. As an example, we consider the decays of the $\Upsilon(10860)$ into the $\chi_{bJ}\omega\, (J=0,1,2)$, which were recently measured by the Belle Collaboration. These decays exhibit a huge breaking of the spin symmetry relation were the $\Upsilon(10860)$ a pure $5S$ bottomonium state. We propose that this could be a consequence of a mixing of the $S$-wave and $D$-wave components in the $\Upsilon(10860)$. Prediction on the ratio $\Gamma(\Upsilon(10860)\to\chi_{b0}\omega)/\Gamma(\Upsilon(10860)\to\chi_{b2}\omega)$ is presented assuming that the decay of the $D$-wave component is dominated by the coupled-channel effects.Comment: 13 pages, 5 figures. Discussion extended, version to appear in Phys.Lett.

"Multiproduct Duopoly with Vertical Differentiation"

The paper investigates a two-stage competition in a vertical differentiated industry, where each firm produces an arbitrary number of similar qualities and sells them to heterogeneous consumers. We show that, when unit costs of quality are increasing and quadratic, each firm has an incentive to provide an interval of qualities. The finding is in sharp contrast to the single-quality outcome when the market coverage is exogenously determined. We also show that allowing for an interval of qualities intensifies competition, lowers the profits of each firm and raises the consumer surplus and the social welfare in comparison to the single-quality duopoly.

Anomalous Electron Trajectory in Topological Insulators

We present a general theory about electron orbital motions in topological insulators. An in-plane electric field drives spin-up and spin-down electrons bending to opposite directions, and skipping orbital motions, a counterpart of the integer quantum Hall effect, are formed near the boundary of the sample. The accompanying Zitterbewegung can be found and controlled by tuning external electric fields. Ultrafast flipping electron spin leads to a quantum side jump in the topological insulator, and a snake-orbit motion in two-dimensional electron gas with spin-orbit interactions. This feature provides a way to control electron orbital motion by manipulating electron spin.Comment: 5 pages and 4 figures for the letter, 6 pagers for the online supplemental materia