Is Z^+(4430) a loosely bound molecular state?

Abstract

Since $Z^{+}(4430)$ lies very close to the threshold of $D^{\ast }{\bar{D}}_1$, we investigate whether $Z^{+}(4430)$ could be a loosely bound S-wave state of $D^{\ast }{\bar{D}}_1$ or $D^{\ast }{\bar{D}}_1^{\prime }$ with $J^P=0^{-},1^{-},2^{-}$, i.e., a molecular state arising from the one-pion-exchange potential. The potential from the crossed diagram is much larger than that from the diagonal scattering diagram. With various trial wave functions, we notice that the attraction from the one pion exchange potential alone is not strong enough to form a bound state with realistic pionic coupling constants deduced from the decay widths of $D_1$ and $D_1^{\prime }$.

Comments: 8 pages, 4 figures, 4 tables. Typos corrected, more discussions added