Abstract: We make a theoretical study of the eta(1405) -> pi(0)f(0)(980) and eta(1405) -> pi(0)a(0)(980) reactions with an aim to determine the isospin violation and the mixing of the f(0)(980) and a(0)(980) resonances. We make use of the chiral unitary approach where these two resonances appear as composite states of two mesons, dynamically generated by the meson-meson interaction provided by chiral Lagrangians. We obtain a very narrow shape for the f(0)(980) production in agreement with a BES experiment. As to the amount of isospin violation, or f(0)(980) and a(0)(980) mixing, assuming constant vertices for the primary eta(1405) -> pi K-0 (K) over bar and eta(1405) -> pi(0)pi(0)eta production, we find results which are much smaller than found in the recent experimental BES paper, but consistent with results found in two other related BES experiments. We have tried to understand this anomaly by assuming an I = 1 mixture in the eta(1405) wave function, but this leads to a much bigger width of the f(0)(980) mass distribution than observed experimentally. The problem is solved by using the primary production driven by eta' -> K*(K) over bar followed by K* -> K pi, which induces an extra singularity in the loop functions needed to produce the f(0)(980) and a(0)(980) resonances. Improving upon earlier work along the same lines, and using the chiral unitary approach, we can now predict absolute values for the ratio Gamma(pi(0), pi(+)pi(-))/Gamma(pi(0), pi(0)eta) which are in fair agreement with experiment. We also show that the same results hold if we had the eta(1475) resonance or a mixture of these two states, as seems to be the case in the BES experiment.

Abstract: The aim of this paper is to investigate an efficient strategy that allows one to obtain pi pi phase shifts and rho meson properties from QCD lattice data with high precision. For this purpose we evaluate the levels of the pi pi system in the rho channel in finite volume using chiral unitary theory. We investigate the dependence on the pi mass and compare this with other approaches which use QCD lattice calculations and effective theories. We also illustrate the errors induced by using the conventional Luscher approach instead of a more accurate one that was recently developed that takes into account exactly the relativistic two-meson propagators. Finally, we make use of this latter approach to solve the inverse problem, getting pi pi phase shifts from “synthetic” lattice data, providing an optimal strategy and showing which accuracy is needed in these data to obtain the rho properties with a desired accuracy.

Abstract: In a recent paper the authors make a study on the determination of the S-matrix elements for scattering of particles in the infinite volume from the energy levels in a finite box for the case of multiple channels. The study is done with a toy model in 1+1 dimension and the authors find that there is some ambiguity in the sign of nondiagonal matrix elements, casting doubts on whether the needed observables in the infinite volume can be obtained from the energy levels of the box. In this paper I present an easy derivation, confirming the ambiguity of the sign and argue that this, however, does not put restrictions in the determination of observables.

Abstract: In analogy to the f(0)(500), which appears as a pi pi resonance in chiral unitary theory, and the f(0)(980), which appears as a quasibound K (K) over bar state, the extension of this approach to the charm sector also predicts a quasibound D (D) over bar state with mass around 3720 MeV, named as X(3700), for which some experimental support is seen in the e(+)e(-) -> J/psi D (D) over bar reaction close to the D (D) over bar threshold. In the present work we propose three different experiments to observe it as a clear peak. The first one is the radiative decay of the psi(3770), psi(3770) -> gamma X(3700) -> gamma eta eta'. The second one proposes the analogous reaction psi(4040) -> gamma X(3700) -> gamma eta eta' and the third reaction is the e(+)e(-) -> J/psi X(3700) -> J/psi eta eta'. Neat peaks are predicted for all the reactions and the calculated rates are found within measurable range in present facilities.

Abstract: In the present paper we address the interaction of pairs of charmed mesons with hidden charm in a finite box. We use the interaction from a recent model based on heavy-quark spin symmetry that predicts molecules of hidden charm in the infinite volume. The energy levels in the box are generated within this model, and from them some synthetic data are generated. These data are then employed to study the inverse problem of getting the energies of the bound states and phase shifts for D (D) over bar or D*(D) over bar*. Different strategies are investigated using the lowest two levels for different values of the box size, and the errors produced are studied. Starting from the upper level, fits to the synthetic data are carried out to determine the scattering length and effective range plus the binding energy of the ground state. A similar strategy using the effective range formula is considered with a simultaneous fit to the two levels-one above and the other one below the threshold. This method turns out to be more efficient than the previous one. Finally, a method based on the fit to the data by means of a potential and a conveniently regularized loop function, turns out to be very efficient and allows us to produce accurate results in the infinite volume starting from levels of the box with errors far larger than the uncertainties obtained in the final results. A regularization method based on Gaussian wave functions turns out to be rather efficient in the analysis and as a byproduct a practical and fast method to calculate the Luscher function with high precision is presented.