Considerations on the Schmid theorem for triangle singularities

We investigate the Schmid theorem, which states that if one has a tree level mechanism with a particle decaying to two particles and one of them decaying posteriorly to two other particles, the possible triangle singularity developed by the mechanism of elastic rescattering of two of the three decay particles does not change the cross section provided by the tree level. We investigate the process in terms of the width of the unstable particle produced in the first decay and determine the limits of validity and violation of the theorem. One of the conclusions is that the theorem holds in the strict limit of zero width of that resonance, in which case the strength of the triangle diagram becomes negligible compared to the tree level. Another conclusion, on the practical side, is that for realistic values of the width, the triangle singularity can provide a strength comparable or even bigger than the tree level, which indicates that invoking the Schmid theorem to neglect the triangle diagram stemming from elastic rescattering of the tree level should not be done. Even then, we observe that the realistic case keeps some memory of the Schmid theorem, which is visible in a peculiar interference pattern with the tree level.Comment: 13 pages, 13 figure

Molecular Ωb\Omega_b states

Motivated by the recent finding of five $\Omega_c$ states by the LHCb collaboration, and the successful reproduction of three of them in a recent approach searching for molecular states of meson-baryon with the quantum numbers of $\Omega_c$, we extend these ideas and make predictions for the interaction of meson-baryon in the beauty sector, searching for poles in the scattering matrix that correspond to physical states. We find several $\Omega_b$ states: two states with masses 6405~MeV and 6465~MeV for $J^P= \frac{1}{2}^-$; two more states with masses 6427~MeV and 6665~MeV for $\frac{3}{2}^-$; and three states between 6500 and 6820~MeV, degenerate with $J^P=\frac{1}{2}^-,\,\frac{3}{2}^-$, stemming from the interaction of vector-baryon in the beauty sector.Comment: 11 pages, 9 tables; v2: discussion added, version accepted for publication in NP

Production and mixing of scalar mesons in ηc\eta_c and χc1\chi_{c1} decays

We briefly discuss how the chiral unitary approach in coupled channels and $SU(3)$ symmetry can be used to describe the production of $f_0(500)$, $f_0(980)$ and $a_0(980)$ in the $\chi_{c1} \to \eta \pi^+ \pi^-$ reaction, recently measured by the BESIII collaboration. In this reaction a very strong peak for the $a_0(980)$ can be seen in the $\eta\pi$ invariant mass, while clear signals for the $f_0(500)$ and $f_0(980)$ appear in the one of $\pi^+\pi^-$. Next, we show the predictions made with the same model for the analogous decay $\eta_c \to \eta \pi^+ \pi^-$, which could also be measured experimentally. We discuss the differences of these two reactions which are interesting to test the picture where these scalar mesons are dynamically generated from the interaction of pairs of pseudoscalars. Furthermore, we comment on a new recent work where the same model was used to study the $a_0(980) - f_0(980)$ mixing in the $\chi_{c1} \to \pi^0 \pi^0 \eta$ and $\chi_{c1} \to \pi^0 \pi^+ \pi^-$ reactions, showing that quantitative agreement with the experimental measurement of this mixing, also performed by BESIII, can be obtained, revealing interesting aspects of the dynamics of this process and the importance of coupled channels.Comment: Talk presented at the XVII International Conference on Hadron Spectroscopy and Structure - Hadron2017, 25-29 September, 2017, University of Salamanca, Salamanca, Spain. arXiv admin note: substantial text overlap with arXiv:1707.0722

Study of the DKKDK K and DKKˉDK \bar{K} systems

Using the Fixed Center Approximation to Faddeev equations we have investigated the $DKK$ and $DK\bar{K}$ three-body systems, considering that the $D^*_{s0}(2317)$ acts as the heavy cluster in both cases, generated from the $DK$ interaction in isospin 0. For the $DK\bar{K}$ system we have found evidence of a state with $I(J^P)=1/2(0^-)$ and mass about $2833 - 2858$ MeV, above the threshold of $D^*_{s0}(2317)\bar{K}$. Our results indicate that this state is dominated by a $Df_0(980)$ component, then it could be searched for in the $\pi \pi D$ invariant mass. On the other hand, no clear evidence related to a state from the $DKK$ interaction is found.Comment: Talk presented at the XVII International Conference on Hadron Spectroscopy and Structure - Hadron2017, 25-29 September, 2017, University of Salamanca, Salamanca, Spai