The meson $Z^+(4430)$ as a tetraquark state

TL;DR

This paper uses QCD sum rules to analyze the $Z^+(4430)$ meson, suggesting it is likely a tetraquark state with $J^{P}=0^{-}$, based on mass predictions and sum rule stability.

Contribution

It applies QCD sum rules with diquark-antidiquark currents to determine the quantum numbers and mass of the $Z^+(4430)$ meson, favoring the $J^{P}=0^{-}$ assignment.

Findings

QCD sum rules yield a mass of approximately 4.52 GeV for $J^{P}=0^{-}$

Sum rules favor $J^{P}=0^{-}$ quantum numbers for $Z^+(4430)$

Acceptable Borel windows with good OPE convergence and pole dominance found

Abstract

We test the validity of the QCD sum rules applied to the meson $Z^+(4430)$, by considering a diquark-antidiquark type of current with $J^{P}=0^{-}$ and with $J^{P}=1^{-}$. We find that, with the studied currents, it is possible to find an acceptable Borel window. In such a Borel window we have simultaneously a good OPE convergence and a pole contribution which is bigger than the continuum contribution. We get $m_Z=(4.52\pm0.09)\GeV$ and $m_Z=(4.84\pm0.14)\GeV$ for the currents with $J^{P}=0^{-}$ and $J^{P}=1^{-}$ respectively. We conclude that the QCD sum rules results favors $J^{P}=0^{-}$ quantum numbers for the $Z^+(4430)$ meson.