Session DC: Mini-Symposium on Hybrid and Molecular Hadrons

New hadrons from Lattice QCD

Recent calculations using the lattice regularised approach to QCD can reproduce many of the systematics observed in the experimental spectrum of mesons and baryons. This pattern can, in the main, be efficiently described considering mesons as $q\bar{q}$ and baryons as $qqq$, but these calculations also predict a spectrum of hadrons featuring an excitation of the gluonic field, the hybrid mesons and baryons. Other meson states which seem to lie outside of a simple $q\bar{q}$ picture, which might be explained in terms of higher quark Fock state configurations, or as loosely bound hadron-hadron molecules, will be discussed, as will progress toward addressing the challenge of studying excited hadrons as resonances, decaying into lighter hadrons.   

Polarized Photoproduction of Hybrid Mesons with GlueX

The GlueX experiment uses a polarized 9 GeV photon beam incident on a fixed hydrogen target to generate mesons over a wide range in masses, with the goal of mapping the spectrum of exotic mesons in the light quark sector, and determining their widths and patterns of their decays. In the case of an unpolarized proton target, linear polarization of the initial-state photon provides a handle for separating the production rate of any given resonance into contributions from competing t-channel processes involving exchanges of opposite naturality. An example of how this is useful to help identify resonance behavior and extract weak resonant signals from a large background is presented. The GlueX experiment is scheduled to begin commissioning the photon beam line and detectors in Fall 2014, with the first polarized beam to follow in 2015.   

On the origin of the narrow peak and the isospin symmetry breaking of X(3872)

The $X$(3872) is investigated by a $c\bar c$-two-meson hybrid model. The two-meson state consists of the $D^0\bar D{}^{*0}$, $D^+D^{*-}$, $J/\psi\rho$, and $J/\psi\omega$. The energy dependent decay widths of the $\rho$ and $\omega$ mesons are taken into account. With reasonable assumptions we found that the $X$(3872) can be a shallowly bound state or a low-energy resonance. In either case, it is found that very narrow $J/\psi\rho$ and $J/\psi\omega$ peaks appear around the $D^0\bar D{}^{*0}$ threshold in the $B$ meson decay. Also, the isospin symmetry breaking of large size is found in the $X$(3872) decay; the strength of the $J/\psi\omega$ peak is only 2.66 times as large as that of the $J/\psi\rho$. The isospin symmetry breaking in the present model comes from the difference in the meson masses and widths. The size of the breaking in the decay becomes larger as the $c\bar c$-$D\bar D{}^*$ coupling becomes weaker. The relative strength of the $D^0\bar D{}^{*0}$ below the $D^+D^{*-}$ threshold also varies largely according to the size of this coupling. It is also found that the branching ratio of the $D^0\bar D{}^{*0}$ and the $J/\psi\rho$, which is still controversial experimentally, is a good indicator whether the $X$(3872) peak is a bound state or a threshold effect.   

Hybrid structure of X(3872) and its radiative decays

We study the radiative decays of the $X(3872)$ using a charmonium-two-meson hybrid model with the two-meson states consisting of the $D^0\bar D{}^{*0}$, $D^+D^{*-}$, $J/\psi\rho$, and $J/\psi\omega$. We can reproduce the observed mass of the X(3872) in this framework. The obtained structure of the $X(3872)$ explains many of the observed properties, such as the isospin symmetry breaking, the production rate in the $p \bar p$ collision, a lack of the existence of the $\chi_{c1}(2P)$ peak predicted by the quark model and the absence of the charged partner of the $X (3872) $. We shall report the results of the $X(3872) \to J/\psi \, \gamma$ and $X(3872) \to \psi' \, \gamma$ decay rates in our approach.   

Determination of compositeness of hadronic resonances: The $\Lambda (1405)$ radiative decay and the $a_{0}(980)$-$f_{0}(980)$ mixing

In hadron physics, one of the most important tasks is to pin down the effective degrees of freedom for the structure of individual hadrons. Especially, so as to identify the hadronic molecules, whose degrees of freedom are hadrons themselves, concept of compositeness has been constructed recently as amounts of the hadronic two-body composite states [1]. In this talk we discuss possiblities to determine the compositeness of hadronic resonances in experiments. We first investigate structure of the $\Lambda (1405)$ resonance by its radiative decay [2], and next investigate structure of the $a_{0}(980)$ and $f_{0}(980)$ resonances by their mixing intensity [3]. For this purpose we establish relations between their compositeness and the experimental observables. Then, combining the established relations and experimental data on the $\Lambda (1405)$ radiative decay width and the $a_{0}(980)$-$f_{0}(980)$ mixing intensity, we discuss $\bar{K} N$ molecular structure for the $\Lambda (1405)$ resonance and $K \bar{K}$ molecular structure for the $a_{0}(980)$ and $f_{0}(980)$ resonances. \\[4pt] [1] T. Hyodo, Int. J. Mod. Phys. A 28, 1330045 (2013).\\[0pt] [2] T. Sekihara and S. Kumano, Phys. Rev. C 89, 025202 (2014).\\[0pt] [3] T. Sekihara and S. Kumano, in preparation.   

Hadron mass scaling near an s-wave threshold

We study the influence of a two-hadron threshold when the hadron mass scales with respect to some QCD parameters. We derive the general behavior of the energy of the bound state and resonance near the two-body threshold from the expansion of the Jost function at zero energy. For a threshold in $p$- or higher partial waves, the scaling low of the stable bound state continues across the threshold describing the real part of the resonance energy. In contrast, the leading contribution of the scaling is forbidden by the nonperturbative dynamics near an $s$-wave threshold, and the bound state cannot directly turn into a resonance. This universal behavior is a consequence of the vanishing of the field renormalization constant of the zero energy bound state in $s$-wave.   

Investigating representations of high-spin hadron wave function in the Regge framework

The vector-spinor $\psi^{\mu}=\psi \otimes e^{\mu}$ is the standard representation of Rarita-Schwinger field for particle of spin-3/2. In this work we search for the solution for spin-3/2 spinor legitimate to describe hadron reactions at high energy and show that the representation of $1 \otimes {1\over2}$ state composed of each helicity eigenstate should yield the same result as the one combined by the momentum states from boosting spin-1 and spin-1/2, respectively. Proofs are given in numerical consequences of differential cross section and spin density matrix elements in the $\gamma + N\to\pi +\Delta(1232)$ process. In the similar fashion, the two respresntations discussed above are applied for tensor field $e^{\mu\nu}=e^{\mu}\otimes e^{\nu}$ and numerical results in the process $\gamma+ N\to f_2(a_2) +N$ are presented for proof of equality.   

The properties of the lightest scalar mesons in a holographic QCD model

We study a mixing structure of light scalar mesons corresponding to the two-quark state, four-quark state and the glueball state using a bottom-up holographic QCD model. In our model, the geometry of the five dimensional space-time and the vacuum expectation value of the glueball field are determined through the Einstein equation by requiring that the dilaton potential can reproduce the asymptotic freedom of QCD and the glueball field arises as the fluctuation with respect to the gravity background. By using the geometry as a background, we add the scalar field corresponding to the two-quark state and four-quark state. Using this model, we study the spectra of the light iso-scalar scalar mesons and the mixing among the glueball, the two-quark states and four-quark states.   

$\sigma$ and $\kappa$ mesons as broad dynamical resonances in one-meson-exchange model

The existences of broad scalar $\mathrm{\sigma (600)}$ and $\mathrm{\kappa (700)}$ mesons have been discussed intensively in the experimental and theoretical studies on $\mathrm{\pi \pi }$ and $\mathrm{\pi K}$ scatterings. By using chiral perturbation model, J. Oller, A. G\'omez and J. R. Pel\'aez confirmed the existence of these mesons as dynamical resonances. In meson-exchange models, their existence has not been established yet. In this talk, using the quasi-potential of meson-exchange model and Lippmann-Schwinger equation, we determine the T and S -matrices, from which we could find the positions of poles in physical amplitudes in the complex E-plane. With the full treatment of meson-meson interactions ($\mathrm{\pi \pi -\pi K-\pi \eta -\eta \eta }$ and $\mathrm{\pi K-\eta K})$, for the first time, the existence of the scalar $\mathrm{\sigma (600)}$ and $\mathrm{\kappa (700)}$ mesons are confirmed in one-meson-exchange model. There are two kinds of form factors in our model: the monopole and the Gaussian. Our recent results show that the poles $\sigma $ and $\kappa $ appear at around $\mathrm{410-i540}$MeV and $\mathrm{650-i20}$MeV for monopole form factors, respectively. For Gaussian form factors, the poles $\sigma $ and $\kappa $, respectively, are at $\mathrm{360-i510}$MeV and $\mathrm{649-i190}$MeV.   

Spin degeneracy in the heavy meson molecules

In the heavy quark limit, spin degeneracies emerge in the system of heavy hadrons as a consequence of heavy quark symmetry. We study the heavy meson molecules containing hidden heavy quarks in the heavy quark limit and clarify the mass spectrum and spin partners of them. This study also provides the information about the properties of heavy mesons such as the fractions of wavefunctions and the ratios of the productions and decays. The specific exotic hadrons that would be heavy meson molecules are discussed from the point of view of heavy quark spin symmetry.   

Search for the $\eta^\prime$-n bound state in the $\gamma$(d,p) reaction

A strong attractive force between a $\eta^\prime$ meson and a nucleon is theoretically suggested in the linear $\sigma$ model, which explains the partial restoration of chiral symmetry. In the same framework as the calculation of $\Lambda$(1405) which is treated as a quasibound state of $\bar{K}$N, a $\eta^\prime$-N bound state is expected with a binding energy of 6--10 MeV. The LEPS experiments at SPring-8 utilizes a photon beam up to 2.9 GeV, so that a $\eta^\prime$ meson can be photoproduced with a small recoil momentum. We searched for the $\eta^\prime$-n bound state by injecting the photon beam into a liquid deuterium target and detecting a proton at extremely forward angles with the LEPS spectrometer. The analysis status and results will be reported in this talk.