Revisiting the Ω(2012)\Omega(2012) as a hadronic molecule and its strong decays

Recently, the Belle collaboration measured the ratios of the branching fractions of the newly observed $\Omega(2012)$ excited state. They did not observe significant signals for the $\Omega(2012) \to \bar{K} \Xi^*(1530) \to \bar{K} \pi \Xi$ decay, and reported an upper limit for the ratio of the three body decay to the two body decay mode of $\Omega(2012) \to \bar{K} \Xi$. In this work, we revisit the newly observed $\Omega(2012)$ from the molecular perspective where this resonance appears to be a dynamically generated state with spin-parity $3/2^-$ from the coupled channels interactions of the $\bar{K} \Xi^*(1530)$ and $\eta \Omega$ in $s$-wave and $\bar{K} \Xi$ in $d$-wave. With the model parameters for the $d$-wave interaction, we show that the ratio of these decay fractions reported recently by the Belle collaboration can be easily accommodated.Comment: Published version. Published in Eur.\ Phys.\ J.\ C {\bf 80}, 361 (2020

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we can realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed by a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial-linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks and find both the existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.Comment: 14 pages, 6 figure