A family of complex potentials with real spectrum

We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters the hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other PT symmetric models, which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.Comment: Six figures and four table

LHCb pentaquarks in constituent quark models

The recently discovered $P_c(4380)^+$ and $P_c(4450)^+$ states at LHCb have masses close to the $\bar D\Sigma_c^*$ and $\bar D^*\Sigma_c$ thresholds, respectively, which suggest that they may have significant meson-baryon molecular components. We analyze these states in the framework of a constituent quark model which has been applied to a wide range of hadronic observables, being the model parameters, therefore, completely constrained. The $P_c(4380)^+$ and $P_c(4450)^+$ are studied as molecular states composed by charmed baryons and open charm mesons. Several bound states with the proper binding energy are found in the $\bar D\Sigma_c^*$ and $\bar D^*\Sigma_c$ channels. We discuss the possible assignments of these states from their decay widths. Moreover, two more states are predicted, associated with the $\bar D\Sigma_c$ and $\bar D^* \Sigma_c^*$ thresholds.Comment: 5 pages, 2 table

Heavy mesons in the Quark Model

Since the discovery of the $J/\psi$, the quark model was very successful in describing the spectrum and properties of heavy mesons including only $q\bar q$ components. However since 2003, with the discovery of the $X(3872)$, many states that can not be accommodated on the naive quark model have been discovered, and they made unavoidable to include higher Fock components on the heavy meson states. We will give an overview of the success of the quark model for heavy mesons and point some of the states that are likely to be more complicated structures such as meson-meson molecules.Comment: Contribution to the Proceedings of the 15th International Workshop on Meson Physics - MESON201

The X(3872) and other possible XYZXYZ molecular states

We perform a coupled channel calculation of the $DD^*$ and $c\bar c$ sectors in the framework of a constituent quark model. The interaction for the $DD^*$ states is obtained using the Resonant Group Method (RGM) and the underlying quark interaction model. The coupling with the two quark system is performed using the $^3 P_0$ model. The X(3872) is found as a molecular state with a sizable $c\bar c$ component. A comparison with Belle and BaBar data has been done, finding a good agreement. Other possible molecular molecular states are discussed.Comment: 5 pages, 5 figures, Proceedings to the Hadron 2009 - XIII International Conference on Hadron Spectroscopy, Florida State University (USA

On electrons and hydrogen-bond connectivity in liquid water

The network connectivity in liquid water is revised in terms of electronic signatures of hydrogen bonds (HBs) instead of geometric criteria, in view of recent X-ray absorption studies. The analysis is based on ab initio molecular-dynamics simulations at ambient conditions. Even if instantaneous thread-like structures are observed in the electronic network, they continuously reshape in oscillations reminiscent of the r and t modes in ice (tau~170 fs). However, two water molecules initially joint by a HB remain effectively bound over many periods regardless of its electronic signature.Comment: 4 pages, 4 figure

Quark Cluster Model Study of Isospin-Two Dibaryons

Based on a quark cluster model for the non-strange sector that reproduces reasonably well the nucleon-nucleon system and the excitation of the $\Delta$ isobar, we generate a nucleon-$\Delta$ interaction and present the predictions for the several isospin two channels. The only attractive channels are $0^+$ and $0^-$, but not attractive enough to generate a resonance. If a resonance is artificially generated and is required to have the observed experimental mass, then our model predicts a width that agrees with the experimental result.Comment: 12 pages, 5 poscript figures available under request. To appear in Phys. Rev.

Variational collocation on finite intervals

In this paper we study a new family of sinc--like functions, defined on an interval of finite width. These functions, which we call ``little sinc'', are orthogonal and share many of the properties of the sinc functions. We show that the little sinc functions supplemented with a variational approach enable one to obtain accurate results for a variety of problems. We apply them to the interpolation of functions on finite domain and to the solution of the Schr\"odinger equation, and compare the performance of present approach with others.Comment: 12 pages, 8 figures, 1 tabl

Does the quark cluster model predict any isospin two dibaryon resonance?

We analyze the possible existence of a resonance in the $J^P=0^-$ channel with isospin two by means of nucleon-$\Delta$ interactions based on the constituent quark model. We solve the bound state and the scattering problem using two different potentials, a local and a non-local one. The non-local potential results to be the more attractive, although not enough to generate the experimentally predicted resonance.Comment: 9 pages in Latex (revtex), 2 eps figures available under reques