Couplings in coupled channels versus wave functions: application to the X(3872) resonance

We perform an analytical study of the scattering matrix and bound states in problems with many physical coupled channels. We establish the relationship of the couplings of the states to the different channels, obtained from the residues of the scattering matrix at the poles, with the wave functions for the different channels. The couplings basically reflect the value of the wave functions around the origin in coordinate space. In the concrete case of the X(3872) resonance, understood as a bound state of \ddn and \ddc (and $c.c.$), with the \ddn loosely bound, we find that the couplings to the two channels are essentially equal leading to a state of good isospin I=0 character. This is in spite of having a probability for finding the \ddn state much larger than for \ddc since the loosely bound channel extends further in space. The analytical results, obtained with exact solutions of the Schr\"odinger equation for the wave functions, can be useful in general to interpret results found numerically in the study of problems with unitary coupled channels methods.Comment: 14 pages, 4 figure

Isospin breaking effects in the dynamical generation of the X(3872)

We have studied isospin breaking effects in the X(3872) resonance and found a natural explanation for the branching fraction of the X decaying to $J/\psi$ with two and three pions being close to unit. Within our framework the X(3872) is a dynamically generated resonance in coupled channels. We also study the relationship between the couplings of the resonance to the coupled channels with its wave function, which further helps us to understand the isospin structure of the resonance.Comment: 5 pages, 1 figure. To appear in the Proceedings of XIII International Conference on Hadron Spectroscopy, November 29 - December 4, 2009, Florida State Universit

Renormalization of NN-Scattering with One Pion Exchange and Boundary Conditions

A non perturbative renormalization scheme for Nucleon-Nucleon interaction based on boundary conditions at short distances is presented and applied to the One Pion Exchange Potential. It is free of off-shell ambiguities and ultraviolet divergences, provides finite results at any step of the calculation and allows to remove the short distance cut-off in a suitable way. Low energy constants and their non-perturbative evolution can directly be obtained from experimental threshold parameters in a completely unique and model independent way when the long range explicit pion effects are eliminated. This allows to compute scattering phase shifts which are, by construction consistent with the effective range expansion to a given order in the C.M. momentum $p$. In the singlet $^1S_0$ and triplet $^3S_1- ^3D_1$ channels ultraviolet fixed points and limit cycles are obtained respectively for the threshold parameters. Data are described satisfactorily up to CM momenta of about $p \sim m_\pi$.Comment: 22 pages, 10 figures, revte

Gravitational and higher-order form factors of the pion in chiral quark models

The gravitational form factor of the pion is evaluated in two chiral quark models and confronted to the recent full-QCD lattice data. We find good agreement for the case of the Spectral Quark Model, which builds in the vector-meson dominance for the charge form factor. We derive a simple relation between the gravitational and electromagnetic form factors, holding in the considered quark models in the chiral limit. The relation implies that the gravitational mean squared radius is half the electromagnetic one. We also analyze higher-order quark generalized form factors of the pion, related to higher moments in the symmetric Bjorken X-variable of the generalized parton distribution functions, and discuss their perturbative QCD evolution, needed to relate the quark-model predictions to the lattice data. The values of the higher-order quark form factors at t=0, computed on the lattice, also agree with our quark model results within the statistical and method uncertainties.Comment: 12 pages, 4 figures, discussion and references adde

The X(3872) and other X,Y,Z Resonances as Hidden Charm Meson-Meson Molecules

We report on some ideas concerning the nature of the X(3872) resonance and the need for approximately equal charged and neutral components of $D \bar{D}^* +cc$. Then we discuss how some hidden charm states are obtained from the interaction between vector mesons with charm and can be associated to some of the charmonium-like X,Y,Z states. Finally we discuss how the nature of these states could be investigated through different types of radiative decay.Comment: Presented at the Charm2010 Workshop, Beijing, Oct. 201

Generalized Quark Transversity Distribution of the Pion in Chiral Quark Models

The transversity generalized parton distributions (tGPDs) of the the pion, involving matrix elements of the tensor bilocal quark current, are analyzed in chiral quark models. We apply the nonlocal chiral models involving a momentum-dependent quark mass, as well as the local Nambu--Jona-Lasinio with the Pauli-Villars regularization to calculate the pion tGPDs, as well as related quantities following from restrained kinematics, evaluation of moments, or taking the Fourier-Bessel transforms to the impact-parameter space. The obtained distributions satisfy the formal requirements, such as proper support and polynomiality, following from Lorentz covariance. We carry out the leading-order QCD evolution from the low quark-model scale to higher lattice scales, applying the method of Kivel and Mankiewicz. We evaluate several lowest-order generalized transversity form factors, accessible from the recent lattice QCD calculations. These form factors, after evolution, agree properly with the lattice data, in support of the fact that the spontaneously broken chiral symmetry is the key element also in the evaluation of the transversity observables.Comment: 17 pages, 17 figures, regular pape

Renormalization approach to constituent quark models of Quarkonium

Constituent quark models, while successful, require a great deal of fine tuning of the short distance interactions by introducing phenomenological gluonic form factors which are ultimately designed to accurately reproduce the spectrum. We apply and develop renormalization ideas to reduce the short distance sensitivity and show that, as naively expected, but not explicitly implemented in the models, the physics of binding is entirely linked to the string tension whereas leptonic decays depend more on the gluon exchange potential. We also show how the spectrum of S- and D- $1^{--}$ states is successfully intertwined through the singular tensor interaction.Comment: 20 pages, 11 figure

A Spatially Enhanced Data‐Driven Multimodel to Improve Semiseasonal Groundwater Forecasts in the High Plains Aquifer, USA

The aim of this paper is to improve semiseasonal forecast of groundwater availability in response to climate variables, surface water availability, groundwater level variations, and human water management using a two‐step data‐driven modeling approach. First, we implement an ensemble of artificial neural networks (ANNs) for the 300 wells across the High Plains aquifer (USA). The modeling framework includes a method to choose the most relevant input variables and time lags; an assessment of the effect of exogenous variables on the predictive capabilities of models; and the estimation of the forecast skill based on the Nash‐Sutcliffe efficiency (NSE) index, the normalized root mean square error, and the coefficient of determination (R2). Then, for the ANNs with low‐ accuracy, a MultiModel Combination (MuMoC) based on a hybrid of ANN and an instance‐based learning method is applied. MuMoC uses forecasts from neighboring wells to improve the accuracy of ANNs. An exhaustive‐search optimization algorithm is employed to select the best neighboring wells based on the cross correlation and predictive accuracy criteria. The results show high average ANN forecasting skills across the aquifer (average NSE \u3e 0.9). Spatially distributed metrics of performance showed also higher error in areas of strong interaction between hydrometeorological forcings, irrigation intensity, and the aquifer. In those areas, the integration of the spatial information into MuMoC leads to an improvement of the model accuracy (NSE increased by 0.12), with peaks higher than 0.3 when the optimization objectives for selecting the neighbors were maximized.t