Detecting the pure triangle sigularity effect through the $psi(2S) to p bar{p} eta / p bar{p} pi^0$ process

In this work, the triangle singularity mechanism is investigated in the $psi(2S) to p bar{p} eta / p bar{p} pi^0$ process. The triangle loop composed by $J/psi$, $eta$ and $p$ has a singularity in the physical kinematic range for the $psi(2S) to p bar{p} eta / p bar{p} pi^0$ process, and it would generate a very narrow peak in the invariant mass spectrum of $peta (pi)$ around $1.56387$ GeV, which is far away from both the threshold and relative resonances. In these processes, all the involved vertices are constrained by the experimental data. Thus, we can make a precise model independent prediction here. It turns out that the peak in the $peta$ invariant mass spectrum is visible, while it is very small in the $ppi^0$ invariant mass spectrum. We expect this effect shown in $p bar{p} eta$ final state can be observed by the Beijing Spectrometer (BESIII) and Super Tau-Charm Facility (STCF) in the future.

Exploring possible triangle singularities in the $Xi^-_{b} to K^- J/psi Lambda$ decay

We analyze possible singularities in the $J/psi Lambda$ invariant mass distribution of the $Xi^-_{b}~to~K^- J/psi Lambda$ process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with $Xi^*$-charmonium-$Lambda$ intermediate states, the one from the $chi_{c1} Xi(2120) Lambda$ loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs $S$- and $P$-waves in $chi_{c1} Lambda$ and $J/psi Lambda$ systems, respectively, when the quantum numbers of these systems are $1/2^+$ or $3/2^+$. When the quantum numbers of the $Xi(2120)$ are $J^P=1/2^+$, $1/2^-$ or $3/2^+$, the peak structure should be sharper than the other $J^P$ choices. This suggests that although the whole strength is unknown, we should pay attention to the contributions from the $Xi^*$-charmonium-$Lambda$ triangle diagram if structures are observed in the $J/psi Lambda$ invariant mass spectrum experimentally. In addition, a few triangle diagrams with the $D_{s1}^*(2700)$ as one of the intermediate particles can also produce singularities in the $J/psiLambda$ distribution, but at higher energies above 4.9 GeV.

Graphic Method for Arbitrary $n$-body Phase Space

In quantum field theory, the phase space integration is an essential part in all theoretical calculations of cross sections and decay widths. It is also needed for computing the imaginary part of a physical amplitude. A key problem is to get the phase space formula expressed in terms of any chosen invariant masses in an $n$-body system. We propose a graphic method to quickly get the phase space formula of any given invariant masses intuitively for an arbitrary $n$-body system in general $D$-dimensional spacetime, with the involved momenta in any reference frame. The method also greatly simplifies the phase space calculation just as what Feynman diagrams do in calculating scattering amplitudes.

Decay behaviors of Pc hadronic molecules

The $P_c(4380)$ and $P_c(4450)$ states observed recently by LHCb experiment were proposed to be either $bar{D} Sigma_c^*$ or $bar{D}^* Sigma_c$ S-wave bound states of spin parity $J^P={frac32}^-$. We analyze the decay behaviors of such two types of hadronic molecules within the effective Lagrangian framework. With branching ratios of ten possible decay channels calculated, it is found that the two types of hadronic molecules have distinguishable decay patterns. While the $bar{D} Sigma_c^*$ molecule decays dominantly to $bar{D}^* Lambda_c$ channel with a branching ratio by 2 orders of magnitude larger than to $bar{D}Lambda_c$, the $bar{D}^* Sigma_c$ molecule decays to these two channels with a difference of less than a factor of 2. Our results show that the total decay width of $P_c(4380)$ as the spin-parity-${frac32}^-$ $bar{D} Sigma_c^*$ molecule is about a factor of 2 larger than the corresponding value for the $bar{D}^* Sigma_c$ molecule. It suggests that the assignment of $bar{D} Sigma_c^*$ molecule for $P_c(4380)$ is more favorable than the $bar{D}^* Sigma_c$ molecule. In addition, $P_c(4450)$ seems to be a $bar{D}^* Sigma_c$ molecule with $J^P={frac52}^+$ in our scheme. Based on these partial decay widths of $P_c(4380)$, we estimate the cross sections for the reactions $gamma p to J/psi p $ and $ pi pto J/psi p $ through the s-channel $P_c(4380)$ state. The forthcoming $gamma p$ experiment at JLAB and $pi p$ experiment at JPARC should be able to pin down the nature of these $P_c$ states.