Abstract: We present a way to evaluate the scattering of unstable particles quantized in a finite volume with the aim of extracting physical observables for infinite volume from lattice data. We illustrate the method with the pi rho scattering which generates dynamically the axial-vector a(1)(1260) resonance. Energy levels in a finite box are evaluated both considering the rho as a stable and unstable resonance and we find significant differences between both cases. We discuss how to solve the problem to get the physical scattering amplitudes in the infinite volume, and hence phase shifts, from possible lattice results on energy levels quantized inside a finite box.

Abstract: We present a strategy to extract the position of the two Lambda(1405) poles from experimental photoproduction data measured recently at different energies in the gamma p -> K+pi(0)Sigma(0) reaction at Jefferson Laboratory. By means of a chiral dynamics motivated potential with free parameters, we solve the Bethe-Salpeter equation in the coupled channels (K) over barN and pi Sigma in isospin I = 0 and parametrize the amplitude for the photonuclear reaction in terms of a linear combination of the pi Sigma -> pi Sigma and (K) over barN -> pi Sigma scattering amplitudes in I = 0, with a different linear combination for each energy. Good fits to the data are obtained with some sets of parameters, by means of which one can also predict the cross section for the K- p -> pi(0)Sigma(0) reaction. These later results help us decide among the possible solutions. The result is that the different solutions lead to two poles similar to those found in the chiral unitary approach. With the best result we find the two Lambda(1405) poles at 1385 – 68i MeV and 1419 – 22i MeV.

Abstract: We present a coupled channel unitary approach to obtain states dynamically generated from the meson-baryon interaction with hidden charm, using constraints of heavy quark spin symmetry. As a basis of states, we use (D) over barB, (D) over bar *B states, with B baryon charmed states belonging to the 20 representations of SU(4) with J(P) = 1/2(+), 3/2(+). In addition we also include the eta N-c and J/psi N states. The inclusion of these coupled channels is demanded by heavy quark spin symmetry, since in the large m(Q) limit the D and D* states are degenerate and are obtained from each other by means of a spin rotation, under which QCD is invariant. The novelty in the work is that we use dynamics from the extrapolation of the local hidden gauge model to SU(4), and we show that this dynamics fully respects the constraints of heavy quark spin symmetry. With the full space of states demanded by the heavy quark spin symmetry and the dynamics of the local hidden gauge, we look for states dynamically generated and find four basic states that are bound, corresponding to (D) over bar Sigma(c), (D) over bar Sigma(c)*, (D) over bar*Sigma(c) and (D) over bar*Sigma*(c) decaying mostly into eta N-c and J/psi N. All the states appear in isospin I = 1/2, and we find no bound states or resonances in I = 3/2. The (D) over bar Sigma(c) state appears in J = 1/2 and the (D) over bar Sigma*(c) in J = 3/2; the (D) over bar*Sigma(c) appears nearly degenerate in J = 1/2, 3/2 and the (D) over bar*Sigma*(c) appears nearly degenerate in J = 1/2, 3/2, 5/2, with the peculiarity that in J = 5/2 the state has zero width in the space of states chosen. All the states are bound with about 50 MeV with respect to the corresponding (D) over barB thresholds, and the width, except for the J = 5/2 state, is also of the same order of magnitude. Finally, we discuss the uncertainties stemming from the expected breaking of SU(4) and the heavy quark spin symmetry.

Abstract: In this paper, we examine the interaction of (B) over barN, (B) over bar Delta, (B) over bar *N, and (B) over bar*Delta states, together with their coupled channels, by using a mapping from the light meson sector. The assumption that the heavy quarks act as spectators at the quark level automatically leads us to the results of the heavy quark spin symmetry for pion exchange and reproduces the results of the Weinberg Tomozawa term, coming from light vector exchanges in the extended local hidden gauge approach. With this dynamics we look for states dynamically generated from the interaction and find two states with nearly zero width, which we associate to the A(b)(5912) and A(b)(5920) states. The states couple mostly to (B) over bar *N, which are degenerate with the Weinberg Tomozawa interaction. The difference of masses between these two states, with J = 1/2 and 3/2, respectively, is due to pion exchange connecting these states to intermediate (B) over barN states. In addition to these two A(b) states, we find three more states with I = 0, one of them nearly degenerate in two states of J = 1/2, 3/2. Furthermore, we also find eight more states in I = 1, two of them degenerate in J = 1/2, 3/2, and another two degenerate in J = 1/2, 3/2, 5/2.

Abstract: We study the interaction of rho, D* and (D) over bar* with spins aligned using the fixed center approximation to the Faddeev equations. We select a cluster of D*(D) over bar*, which is found to be bound in I = 0 and can be associated to the X(3915), and let the rho meson orbit around the D* and (D) over bar*. In this case we find an I = 1 state with mass around 4340 MeV and narrow width of about 50MeV. We also investigate the case with a cluster of rho D* and let the (D) over bar * orbit around the system of the two states. The rho D* cluster is also found to bind and leads to the D-2*(2460) state. The addition of the extra (D) over bar* produces further binding and we find, with admitted uncertainties, a state of I = 0 around 4000MeV, and a less bound narrow state with I = 1 around 4200 MeV.