Study of Λb→Λ(ϕ,η(′))\Lambda_b\to \Lambda (\phi,\eta^{(\prime)}) and Λb→ΛK+K−\Lambda_b\to \Lambda K^+K^- decays

We study the charmless two-body $\Lambda_b\to \Lambda (\phi,\eta^{(\prime)})$ and three-body $\Lambda_b\to \Lambda K^+K^-$ decays. We obtain ${\cal B}(\Lambda_b\to \Lambda\phi)=(3.53\pm 0.24)\times 10^{-6}$ to agree with the recent LHCb measurement. However, we find that ${\cal B}(\Lambda_b\to \Lambda(\phi\to)K^+ K^-)=(1.71\pm 0.12)\times 10^{-6}$ is unable to explain the LHCb observation of ${\cal B}(\Lambda_b\to\Lambda K^+ K^-)=(15.9\pm 1.2\pm 1.2\pm 2.0)\times 10^{-6}$, which implies the possibility for other contributions, such as that from the resonant $\Lambda_b\to K^- N^*,\,N^*\to\Lambda K^+$ decay with $N^*$ as a higher-wave baryon state. For $\Lambda_b\to \Lambda \eta^{(\prime)}$, we show that ${\cal B}(\Lambda_b\to \Lambda\eta,\,\Lambda\eta^\prime)= (1.47\pm 0.35,1.83\pm 0.58)\times 10^{-6}$, which are consistent with the current data of $(9.3^{+7.3}_{-5.3},<3.1)\times 10^{-6}$, respectively. Our results also support the relation of ${\cal B}(\Lambda_b\to \Lambda\eta) \simeq {\cal B}(\Lambda_b\to\Lambda\eta^\prime)$, given by the previous study.Comment: 8 pages, 1 figure, revised version accepted by EPJ

The capacity region of classes of product broadcast channels

We establish a new outer bound for the capacity region of product broadcast channels. This outer bound matches Marton's inner bound for a variety of classes of product broadcast channels whose capacity regions were previously unknown. These classes include product of reversely semi-deterministic and product of reversely more-capable channels. A significant consequence of this new outer bound is that it establishes, via an example, that the previously best known outer-bound is strictly suboptimal for the general broadcast channel. Our example is comprised of a product broadcast channel with two semi-deterministic components in reverse orientation.Comment: full version of isit pape