Scale Invariance in Heavy Hadron Molecules

We discuss a scenario in which the $P_c(4450)^{+}$ heavy pentaquark is a $\Sigma_c \bar{D}^*$-$\Lambda_{c}(2595) \bar{D}$ molecule. The $\Lambda_{c1} \bar{D} \to \Sigma_c \bar{D}^*$ transition is mediated by the exchange of a pion almost on the mass shell that generates a long-range $1/r^2$ potential. This is analogous to the effective force that is responsible for the Efimov spectrum in three-boson systems interacting through short-range forces. The equations describing this molecule exhibit approximate scale invariance, which is anomalous and broken by the solutions. If the $1/r^2$ potential is strong enough this symmetry survives in the form of discrete scale invariance, opening the prospect of an Efimov-like geometrical spectrum in two-hadron systems. For a molecular pentaquark with quantum numbers $\frac{3}{2}^{-}$ the attraction is not enough to exhibit discrete scale invariance, but this prospect might very well be realized in a $\frac{1}{2}^{+}$ pentaquark or in other hadron molecules involving transitions between particle channels with opposite intrinsic parity and a pion near the mass shell. A very good candidate is the $\Lambda_{c}(2595) \bar{\Xi}_b - \Sigma_c \bar{\Xi}_b'$ molecule. Independently of this, the $1/r^2$ force is expected to play a very important role in the formation of this type of hadron molecule, which points to the existence of $\frac{1}{2}^{+}$ $\Sigma_c D^*$-$\Lambda_{c}(2595) D$ and $1^+$ $\Lambda_{c}(2595) {\Xi}_b - \Sigma_c {\Xi}_b'$ molecules and $0^{+}$/$1^{-}$ $\Lambda_{c}(2595) \bar{\Xi}_b - \Sigma_c \bar{\Xi}_b'$ baryonia.Comment: 6 pages, 1 figure, corresponds to published versio

Octet-baryon masses in finite space

We report on a recent study of finite-volume effects on the lowest-lying octet baryon masses using the covariant baryon chiral perturbation theory up to next-to-leading order by analysing the latest $n_f = 2 + 1$ lattice QCD results from the NPLQCD Collaboration.Comment: 4 pages, 1 figure; parallel talk delivered by XLR at the 14th national conference on nuclear structure, April 12nd - 16th, 2012, Huzhou, Chin

Weak decays of heavy hadrons into dynamically generated resonances

In this paper, we present a review of recent works on weak decay of heavy mesons and baryons with two mesons, or a meson and a baryon, interacting strongly in the final state. The aim is to learn about the interaction of hadrons and how some particular resonances are produced in the reactions. It is shown that these reactions have peculiar features and act as filters for some quantum numbers which allow to identify easily some resonances and learn about their nature. The combination of basic elements of the weak interaction with the framework of the chiral unitary approach allow for an interpretation of results of many reactions and add a novel information to different aspects of the hadron interaction and the properties of dynamically generated resonances Read More: http://www.worldscientific.com/doi/10.1142/S021830131630001