An interactively recurrent functional neural fuzzy network with fuzzy differential evolution and its applications

In this paper, an interactively recurrent functional neural fuzzy network (IRFNFN) with fuzzy differential evolution (FDE) learning method was proposed for solving the control and the prediction problems. The traditional differential evolution (DE) method easily gets trapped in a local optimum during the learning process, but the proposed fuzzy differential evolution algorithm can overcome this shortcoming. Through the information sharing of nodes in the interactive layer, the proposed IRFNFN can effectively reduce the number of required rule nodes and improve the overall performance of the network. Finally, the IRFNFN model and associated FDE learning algorithm were applied to the control system of the water bath temperature and the forecast of the sunspot number. The experimental results demonstrate the effectiveness of the proposed method

Tcc+T_{cc}^+ and X(3872)X(3872) with the complex scaling method and DD(Dˉ)πDD(\bar{D})\pi three-body effect

We use the leading order (LO) contact interactions and OPE potentials to investigate the newly observed double-charm state $T_{cc}^+$. The $DD\pi$ three-body effect is important in this system since the intermediate states can go on shell. We keep the dependence of the pion propagators on the center-of-mass energy, which results in a unitary cut of the OPE potential at the $DD\pi$ three-body threshold. By solving the complex scaled Schr\"odinger equation, we find a pole corresponding to the $T_{cc}^+$ on the physical Riemann sheet. Its width is around 80 keV and nearly independent of the choice of the cutoff. Assuming the $D\bar{D}\pi$ and $D\bar{D}^*$ channels as the main decay channels, we apply the similar calculations to the $X(3872)$, and find its width is even smaller. Besides, the isospin breaking effect is significant for the $X(3872)$ while its impact on the $T_{cc}^+$ is relatively small.Comment: 25 pages, 10 figures, 6 table

PcP_c states and their open-charm decays with the complex scaling method

A partial width formula is proposed using the analytical extension of the wave function in momentum space. The distinction of the Riemann sheets is explained from the perspective of the Schrodinger equation. The analytical form in coordinate space and the partial width are derived subsequently. Then a coupled-channel analysis is performed to investigate the open-charm branching ratios of the $P_c$ states, involving the contact interactions and one-pion-exchange potential with the three-body effects. The low energy constants are fitted using the experimental masses and widths as input. The $P_c(4312)$ is found to decay mainly to $\Lambda_c\bar{D}^*$, while the branching ratios of the $P_c(4440)$ and $P_c(4457)$ in different channels are comparable. Under the reasonable assumption that the off-diagonal contact interactions are small, the $J^P$ quantum numbers of the $P_c(4440)$ and the $P_c(4457)$ prefer $\frac{1}{2}^-$ and $\frac{3}{2}^-$ respectively. Three additional $P_c$ states at 4380 MeV, 4504 MeV and 4516 MeV, together with their branching ratios, are predicted. A deduction of the revised one-pion-exchange potential involving the on-shell three-body intermediate states is performed.Comment: 16 pages, 5 figure