Branching ratios and CPCP asymmetries of B→χc1K(π)B\rightarrow \chi_{c1}K(\pi) decays

We investigate the exclusive nonleptonic decays $B\rightarrow \chi_{c1}K(\pi)$ in the conventional perturbative QCD (PQCD) formalism. The predictions of branching ratios and $CP$ asymmetries are given in detail. We compare our results with available experimental data as well as predictions of other theoretical studies existing in the literature. It seems that the branching ratios of $B\rightarrow \chi_{c1} K$ are more consistent with data than the earlier analyses. For the Cabibbo-suppressed $B_s$ decay, the branching ratio can reach the order of $10^{-5}$, which would be straight forward for experimental observations. The numerical results show that the direct $CP$ asymmetries of the concerned decays are rather small. The mixing-induced $CP$ asymmetry in the $B^0\rightarrow \chi_{c1}K_S$ is very close to $\sin{2\beta}$, which suggests that this channel offer an alternative method for measuring the Cabbibo-Kobayashi-Maskawa (CKM) angle $\beta$. The obtained results in the present work could be tested by further experiments in the LHCb and forthcoming Belle II.Comment: 8 pages, 1 figur

Stability Analysis of Integral Delay Systems with Multiple Delays

This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.Comment: 14 page