Form factors of the isovector scalar current and the ηπ\eta\pi scattering phase shifts

A model for S-wave $\eta\pi$ scattering is proposed which could be realistic in an energy range from threshold up to above one GeV, where inelasticity is dominated by the $K\bar{K}$ channel. The $T$-matrix, satisfying two-channel unitarity, is given in a form which matches the chiral expansion results at order $p^4$ exactly for the $\eta\pi\to\eta\pi$, $\eta\pi\to K\bar{K}$ amplitudes and approximately for $K\bar{K}\to K\bar{K}$. It contains six phenomenological parameters. Asymptotic conditions are imposed which ensure a minimal solution of the Muskhelishvili-Omn\`es problem, thus allowing to compute the $\eta\pi$ and $K\bar{K}$ form factor matrix elements of the $I=1$ scalar current from the $T$-matrix. The phenomenological parameters are determined such as to reproduce the experimental properties of the $a_0(980)$, $a_0(1450)$ resonances, as well as the chiral results of the $\eta\pi$ and $K\bar{K}$ scalar radii which are predicted to be remarkably small at $O(p^4)$. This $T$-matrix model could be used for a unified treatment of the $\eta\pi$ final-state interaction problem in processes such as $\eta'\to \eta \pi\pi$, $\phi\to\eta\pi\gamma$, or the $\eta\pi$ initial-state interaction in $\eta\to3\pi$.Comment: 33 pages, 14 figures. v2: Some clarifications and corrections of typo

Identification of a Scalar Glueball

We have performed a coupled channel study of the meson-meson S-waves involving isospins (I) 0, 1/2 and 3/2 up to 2 GeV. For the first time the channels \pi\pi, K\bar{K}, \eta\eta, \sigma\sigma, \eta\eta', \eta'\eta', \rho\rho, \omega\omega, \omega\phi$, \phi\phi, a_1\pi and \pi^*\pi are considered. All the resonances with masses below 2 GeV for I=0 and 1/2 are generated by the approach. We identify the f_0(1710) and a pole at 1.6 GeV, which is an important contribution to the f_0(1500), as glueballs. This is based on an accurate agreement of our results with predictions of lattice QCD and the chiral suppression of the coupling of a scalar glueball to \bar{q}q. Another nearby pole, mainly corresponding to the f_0(1370), is a pure octet state not mixed with the glueball.Comment: 5 pages, 1 figure. More data are included and reproduced. Some discussions have been rephrase

Scalar-Pseudoscalar scattering and pseudoscalar resonances

The interactions between the f_0(980) and a_0(980) scalar resonances and the lightest pseudoscalar mesons are studied. We first obtain the interacting kernels, without including any ad hoc free parameter, because the lightest scalar resonances are dynamically generated. These kernels are unitarized, giving the final amplitudes, which generate pseudoscalar resonances, associated with the K(1460), \pi(1300), \pi(1800), \eta(1475) and X(1835). We also consider the exotic channels with I=3/2 and I^G=1^+ quantum numbers. The former could be also resonant in agreement with a previous prediction.Comment: 3 pages, 2 figures; Contributed oral presentation in (QCHS09) The IX International Conference on Quark Confinement and Hadron Spectrum - Madrid, Spain, 30 Aug 2010 - 03 Sep 201

Zc(3900)Z_c(3900): Confronting theory and lattice simulations

We consider a recent $T$-matrix analysis by Albaladejo {\it et al.}, [Phys.\ Lett.\ B {\bf 755}, 337 (2016)] which accounts for the $J/\psi\pi$ and $D^\ast\bar{D}$ coupled--channels dynamics, and that successfully describes the experimental information concerning the recently discovered $Z_c(3900)^\pm$. Within such scheme, the data can be similarly well described in two different scenarios, where the $Z_c(3900)$ is either a resonance or a virtual state. To shed light into the nature of this state, we apply this formalism in a finite box with the aim of comparing with recent Lattice QCD (LQCD) simulations. We see that the energy levels obtained for both scenarios agree well with those obtained in the single-volume LQCD simulation reported in Prelovsek {\it et al.} [Phys.\ Rev.\ D {\bf 91}, 014504 (2015)], making thus difficult to disentangle between both possibilities. We also study the volume dependence of the energy levels obtained with our formalism, and suggest that LQCD simulations performed at several volumes could help in discerning the actual nature of the intriguing $Z_c(3900)$ state

Nucleon-Nucleon Interactions from Dispersion Relations: Coupled Partial Waves

We consider nucleon-nucleon interactions from chiral effective field theory applying the N/D method. The case of coupled partial waves is now treated, extending Ref. [1] where the uncoupled case was studied. As a result three N/D elastic-like equations have to be solved for every set of three independent partial waves coupled. As in the previous reference the input for this method is the discontinuity along the left-hand cut of the nucleon-nucleon partial wave amplitudes. It can be calculated perturbatively in chiral perturbation theory because it involves only irreducible two-nucleon intermediate states. We apply here our method to the leading order result consisting of one-pion exchange as the source for the discontinuity along the left-hand cut. The linear integral equations for the N/D method must be solved in the presence of L - 1 constraints, with L the orbital angular momentum, in order to satisfy the proper threshold behavior for L>= 2. We dedicate special attention to satisfy the requirements of unitarity in coupled channels. We also focus on the specific issue of the deuteron pole position in the 3S1-3D1 scattering. Our final amplitudes are based on dispersion relations and chiral effective field theory, being independent of any explicit regulator. They are amenable to a systematic improvement order by order in the chiral expansion.Comment: 11 pages. Extends the work of uncoupled partial waves of M. Albaladejo and J. A. Oller, Phys. Rev. C 84, 054009 (2011) to the case of coupled partial waves. This version matches the published version. Discussion about the deuteron enlarged. Some references adde

Heavy-to-light scalar form factors from Muskhelishvili-Omn\`es dispersion relations

By solving the Muskhelishvili-Omn\`es integral equations, the scalar form factors of the semileptonic heavy meson decays $D\to\pi \bar \ell \nu_\ell$, $D\to \bar{K} \bar \ell \nu_\ell$, $\bar{B}\to \pi \ell \bar\nu_\ell$ and $\bar{B}_s\to K \ell \bar\nu_\ell$ are simultaneously studied. As input, we employ unitarized heavy meson-Goldstone boson chiral coupled-channel amplitudes for the energy regions not far from thresholds, while, at high energies, adequate asymptotic conditions are imposed. The scalar form factors are expressed in terms of Omn\`es matrices multiplied by vector polynomials, which contain some undetermined dispersive subtraction constants. We make use of heavy quark and chiral symmetries to constrain these constants, which are fitted to lattice QCD results both in the charm and the bottom sectors, and in this latter sector to the light-cone sum rule predictions close to $q^2=0$ as well. We find a good simultaneous description of the scalar form factors for the four semileptonic decay reactions. From this combined fit, and taking advantage that scalar and vector form factors are equal at $q^2=0$, we obtain $|V_{cd}|=0.244\pm 0.022$, $|V_{cs}|=0.945\pm 0.041$ and $|V_{ub}|=(4.3\pm 0.7)\times10^{-3}$ for the involved Cabibbo-Kobayashi-Maskawa (CKM) matrix elements. In addition, we predict the following vector form factors at $q^2=0$: $|f_+^{D\to\eta}(0)|=0.01\pm 0.05$, $|f_+^{D_s\to K}(0)|=0.50 \pm 0.08$, $|f_+^{D_s\to\eta}(0)|=0.73\pm 0.03$ and $|f_+^{\bar{B}\to\eta}(0)|=0.82 \pm 0.08$, which might serve as alternatives to determine the CKM elements when experimental measurements of the corresponding differential decay rates become available. Finally, we predict the different form factors above the $q^2-$regions accessible in the semileptonic decays, up to moderate energies amenable to be described using the unitarized coupled-channel chiral approach.Comment: includes further discussions and references; matches the accepted versio