Novel Compact Three-Way Filtering Power Divider Using Net-Type Resonators

In this paper, we present a novel compact three-way power divider with bandpass responses. The proposed power divider utilizes folded net-type resonators to realize dual functions of filtering and power splitting as well as compact size. Equal power ratio with low magnitude imbalance is achieved due to the highly symmetric structure. For demonstration, an experimental three way filtering power divider is implemented. Good filtering and power division characteristics are observed in the measured results of the circuit. The area of the circuits is 14.5 mm x 21.9 mm or 0.16 λg x 0.24 λg, where the λg is the guide wavelength of the center frequency at 2.1 GHz

Understanding the newly observed heavy pentaquark candidates

We find that several thresholds can contribute to the enhancements of the newly observed heavy pentaquark candidates $P_c^+(4380)$ and $P_c^+(4450)$ via the anomalous triangle singularity (ATS) transitions in the specific kinematics of $\Lambda_b\to J/\psi K^- p$. Apart from the observed two peaks we find that another peaks around 4.5 GeV can also be produced by the ATS. We also show that the $\Sigma_c^{(*)}$ can be produced at leading order in $\Lambda_b$ decay. This process is different from the triangle diagram and its threshold enhancement only appears as CUSP effects if there is no pole structure or the ATS involved. The threshold interaction associated with the presence of the ATS turns out to be a general phenomenon and plays a crucial role in the understanding of candidates for exotic states.Comment: 9 pages, 6 figures, 4 tables; published version in PL