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

TL;DR

This paper investigates whether the $Z^+(4430)$ particle can be a loosely bound molecular state of $D^*$ and $D_1$ mesons, concluding that one-pion-exchange alone is insufficient to form such a bound state.

Contribution

The study analyzes the potential for $Z^+(4430)$ to be a molecular state via one-pion-exchange, finding it unlikely with realistic coupling constants.

Findings

One-pion-exchange potential alone does not produce a bound state.

Crossed diagram contributions are significantly larger than diagonal scattering.

Realistic pionic coupling constants are insufficient for binding.

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 $D^\ast{\bar D}^\prime_1$ 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 $D^\prime_1$.