820 research outputs found

### Form factors of the isovector scalar current and the $\eta\pi$ 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

### $Z_c(3900)$: 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

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