Low-energy $D^{*+}D^0_1$ Scattering and the Resonance-like Structure
  $Z^+(4430)$

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Abstract

Low-energy scattering of $D^*$ and $D_1$ meson are studied using quenched lattice QCD with improved lattice actions on anisotropic lattices. The calculation is performed within L\"uscher's finite-size formalism which establishes the relation between the scattering phase in the infinite volume and the exact energy level in the finite volume. The threshold scattering parameters, namely the scattering length $a_0$ and the effective range $r_0$, for the s-wave scattering in $J^P=0^-$ channel are extracted. After the chiral and continuum extrapolations, we obtain: $a_0=2.52(47)$fm and $r_0=0.7(1)$fm where the errors are purely statistical. Based on these results, we discuss the possibility of a shallow bound state for the two charmed mesons within the non-relativistic potential scattering model. It is argued that, albeit the interaction between the two charmed mesons being attractive, it is unlikely that they can form a shallow bound state in this channel. This calculation provides some useful information on the nature of the newly discovered resonance-like structure $Z^+(4430)$ by the Belle Collaboration.

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Line Shapes of the Z(4430)

Meng Lu, Eric Braaten (2007)

The Belle Collaboration recently discovered the first manifestly exotic meson: Z^+(4430), which decays into psi' pi^+ and therefore has quark content c c-bar u d-bar. The proximity of its mass to the D_1 D-bar^* threshold has motivated the interpretation of the Z^+ as a charm meson molecule whose constituents are an S-wave superposition of D_1^+ D-bar^{*0}$ and D^{*+} D-bar_1^0$. If this interpretation is correct, the small ratio of the binding energy of the Z^+ to the width Gamma_1 of its constituent D_1 can be exploited to predict properties of its line shapes. Its full width at half maximum in the channel psi' pi^+ should be approximately sqrt{3} Gamma_1 = 35 MeV, which is consistent with the measured width of the Z^+. The Z^+ should also decay into D^* D-bar^* pi through decay of its constituent D_1. The peak in the line shape for D^* D-bar^* pi should be at a higher energy than the peak in the line shape for psi' pi^+ by about Gamma_1/sqrt{12} = 6 MeV. The line shape in D^* D-bar^* pi should also be broader and asymmetric, with a shoulder on the high energy side that can be attributed to a threshold enhancement in the production of D_1 D-bar^*.

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$Z^+(4430)$ as a $D_1'{D}^* $ ($D_1{D}^* $) molecular state

Xiang Liu, Shi-Lin Zhu, Wei-Zhen Deng … (2008)

We reexamine whether $Z^+(4430)$ could be a $D_1'-{D}^*$ or $D_1-{D}^*$ molecular state after considering both the pion and $\sigma$ meson exchange potentials and introducing the form factor to take into account the structure effect of the interaction vertex. Our numerical analysis with Matlab package MATSLISE indicates the contribution from the sigma meson exchange is small for the $D_1'-{D}^*$ system and significant for the $D_1-{D}^*$ system. The S-wave $D_1-\bar{D}^*$ molecular state with only $J^{P}=0^-$ and $D_1'-{D}^*$ molecular states with $J^P=0^-,1^-,2^-$ may exist with reasonable parameters. One should investigate whether the broad width of $D_1'$ disfavors the possible formation of molecular states in the future. The bottom analog $Z_B$ of $Z^+(4430)$ has a larger binding energy, which may be searched at Tevatron and LHC. Experimental measurement of the quantum number of $Z^+(4430)$ may help uncover its underlying structure.

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A Uniform Description of the States Recently Observed at B-factories

Cong-Feng Qiao (2007)

The newly found states Y(4260), Y(4361), Y(4664) and Z$^\pm$(4430) stir broad interest in the study of spectroscopy in a typical charmonium scale. The Y(4260) which was observed earlier has been interpreted as hybrid, molecular state, and baryonium, etc. In this note we show for the first time that these new structures, which are hard to be interpreted as charmonium states, can be systematically embedded into an extended baryonium picture. According to this assignment, the so far known characters of these states are understandable. And, in the same framework, we make some predictions for experimenters to measure in the future.