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

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 $m_Z=(4.52\pm 0.09)\text{GeV}$ and $m_Z=(4.84\pm 0.14)\text{GeV}$ 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.

Comments: version accepted for publication at Phys. Lett. B