[Paper Review] Exotic c c-bar Mesons

Eric Braaten|ArXiv.org|Aug 21, 2008

Quantum Chromodynamics and Particle Interactions39 references3 citations

TL;DR

This paper analyzes newly discovered $c\bar{c}$ mesons above the $D\bar{D}$ threshold, proposing that the $X(3872)$ is a weakly bound charm meson molecule with $D^{*0}\bar{D}^{0} - D^{0}\bar{D}^{*0}$ structure, while $Y(4260)$, $Y(4360)$, and $Y(4660)$ are likely charmonium hybrids, and $Z^{\pm}(4430)$ is an exotic tetraquark with $c\bar{c}u\bar{d}$ content. The $X(3872)$'s properties, including isospin violation and mass shifts in decay channels, are explained by its molecular nature and proximity to the $D^{*0}\bar{D}^{0}$ threshold.

ABSTRACT

A surprising number of new c c-bar mesons with masses above the D D-bar threshold have been discovered at the B factories. Some of them are ordinary charmonium states, but others are definitely exotic mesons. The current theoretical status of the new c c-bar mesons is summarized.

Motivation & Objective

• To understand the nature of newly discovered $c\bar{c}$ mesons above the $D\bar{D}$ threshold, particularly those that cannot be explained by conventional charmonium models.
• To determine whether exotic states like $X(3872)$, $Y(4260)$, and $Z^{\pm}(4430)$ are molecular states, tetraquarks, or hybrids.
• To explain puzzling experimental features such as isospin violation and mass shifts in $X(3872)$ decays using molecular and effective field theory frameworks.
• To provide theoretical predictions for the $J^P$ quantum numbers and decay patterns of these exotic states to guide future experiments.

Proposed method

• Uses effective field theory and universal properties of shallow bound states to model the $X(3872)$ as a weakly bound $D^{*0}\bar{D}^{0} - D^{0}\bar{D}^{*0}$ molecule.
• Applies the relation $\langle r\rangle_{X} = 1/(8\mu E_X)^{1/2}$ to estimate the mean separation of constituents based on binding energy.
• Analyzes $B$-meson decay line shapes to infer the $X(3872)$'s position relative to the $D^{*0}\bar{D}^{0}$ threshold, distinguishing between bound and virtual states.
• Evaluates the $B^+ \to K^+ + X$ and $B^0 \to K^0 + X$ production rate ratio using the inverse scattering length $\gamma_1$ and $\kappa_1 = 125$ MeV in the $I=1$ channel.
• Proposes that $Y(4260)$, $Y(4360)$, and $Y(4660)$ are charmonium hybrids by analyzing their lack of resonance peaks in inclusive and exclusive $e^+e^-$ cross sections.
• Uses heavy quark symmetry to argue that $b\bar{b}$ exotic mesons should exist with larger binding energies than their $c\bar{c}$ counterparts.

Experimental results

Research questions

• RQ1 Is the $X(3872)$ an ordinary charmonium state or a molecular state composed of $D^{*0}\bar{D}^{0}$ and $D^{0}\bar{D}^{*0}$?
• RQ2 Why does the $X(3872)$ exhibit isospin violation in its decays to $J/\psi\pi^+\pi^-$ and $J/\psi\pi^+\pi^-\pi^0$ final states?
• RQ3 Why is the $X(3872)$ mass measured to be 3.8 ± 1.1 MeV higher in the $D^0\bar{D}^0\pi^0$ decay channel than in the $J/\psi\pi^+\pi^-$ channel?
• RQ4 Are the $Y(4260)$, $Y(4360)$, and $Y(4660)$ states best described as charmonium hybrids or as molecular states?
• RQ5 What is the quark content and $J^P$ quantum number of the $Z^{\pm}(4430)$, and how does it relate to the $X(3872)$?

Key findings

• The $X(3872)$ is a weakly bound charm meson molecule with a binding energy $E_X < 0.4$ MeV, implying a mean separation $\langle r\rangle_X > 3.5$ fm between its constituents.
• The $X(3872)$'s wavefunction is an equal superposition of $I=0$ and $I=1$ states: $X = \frac{1}{\sqrt{2}}(D^{*0}\bar{D}^{0} - D^{0}\bar{D}^{*0})$, explaining its isospin-violating decays.
• The mass shift of $3.8 \pm 1.1$ MeV between decay channels arises from different line shapes: a resonance below the $D^{*0}\bar{D}^{0}$ threshold in $J/\psi\pi^+\pi^-$ and a threshold enhancement above it in $D^0\bar{D}^0\pi^0$.
• The $X(3872)$ is likely a bound state below the $D^{*0}\bar{D}^{0}$ threshold, with a predicted zero in the $B^+ \to K^+ + J/\psi\pi^+\pi^-$ line shape about 6 MeV above the threshold and in $B^0 \to K^0 + J/\psi\pi^+\pi^-$ about 2 MeV below it.
• The $Y(4260)$, $Y(4360)$, and $Y(4660)$ are strong candidates for charmonium hybrids, with their lack of resonance peaks in $e^+e^-$ cross sections supporting this interpretation.
• The $Z^{\pm}(4430)$ is an exotic tetraquark meson with $c\bar{c}u\bar{d}$ quark content and $I^G = 1^+$, and is the charged member of an isospin multiplet.