${\rm Z}^{+}(4430)$ and Analogous Heavy Flavor States

TL;DR

This paper investigates the structure of the ${ m Z}^+(4430)$ as a possible ${ m D^{*}ar{D}_1}$ molecular state, predicts properties of related heavy flavor states, and explores the existence of other exotic molecules using a quark model.

Contribution

The study introduces a dynamic multichannel Schrödinger equation approach to analyze heavy flavor molecular states and predicts their properties, including ${ m Z}^+(4430)$ and analogous states.

Findings

${ m Z}^+(4430)$ likely has quantum numbers ${ m J^{P}=0^{-}}$

Predicted masses of ${ m Z}^{+}_{bb}$ and ${ m Z}^{++}_{bc}$ agree with other models

Exotic ${ m DD^{*}}$ molecules do not exist under the studied conditions

Abstract

The proximity of ${\rm Z}^+(4430)$ to the ${\rm D^{*}\bar{D}_1}$ threshold suggests that it may be a ${\rm D^{*}\bar{D}_1}$ molecular state. The ${\rm D^{*}\bar{D}_1}$ system has been studied dynamically from quark model, and state mixing effect is taken into account by solving the multichannel Schr$\ddot{\rm o}$dinger equation numerically. We suggest the most favorable quantum number is ${\rm J^{P}=0^{-}}$, if future experiments confirm ${\rm Z}^+(4430)$ as a loosely bound molecule state. More precise measurements of ${\rm Z}^+(4430)$ mass and width, partial wave analysis are helpful to understand its structure. The analogous heavy flavor mesons ${\rm Z}^{+}_{bb}$ and ${\rm Z}^{++}_{bc}$ are studied as well, and the masses predicted in our model are in agreement with the predictions from potential model and QCD sum rule. We further apply our model to the ${\rm D\bar{D}^{*}}$ and ${\rm DD^{*}}$ system. We find the exotic ${\rm DD^{*}}$ bound molecule doesn't exist, while the $1^{++}$ ${\rm D\bar{D}^{*}}$ bound state solution can be found only if the screening mass $\mu$ is smaller than 0.17 GeV. The state mixing effect between the molecular state and the conventional charmonium should be considered to understand the nature of X(3872).