Prediction of an exotic state around 4240 MeV with $J^{PC}=1^{-+}$ as C-parity partner of Y(4260) in molecular picture

TL;DR

This paper predicts an exotic charmonium-like state around 4240 MeV with quantum numbers $J^{PC}=1^{-+}$, based on molecular state modeling of $Dar D_1(2420)$ interactions, suggesting new avenues for experimental searches.

Contribution

It introduces a molecular model prediction of an exotic $J^{PC}=1^{-+}$ state near 4240 MeV, expanding the understanding of possible charmonium-like exotic states.

Findings

An attractive potential for $Dar D_1(2420)$ states with $J^{PC}=1^{--}$ and $1^{-+}$.

Prediction of a new exotic state $ ext{η}_{c1}(4240)$ with $J^{PC}=1^{-+}$.

Estimated decay modes suggest search channels in $ ext{η}η_c$ and $ ext{η}χ_{c1}$.

Abstract

The possibility of the Y(4260) being the molecular state of $D\bar D_1(2420)+\mathrm{c.c.}$ is investigated in the one boson exchange model. It turns out that the potential of $J^{PC}=1^{--}$ state formed by $D\bar D_1(2420)+\mathrm{c.c.}$ is attractive and strong enough to bind them together when the momentum cutoff $\Lambda \gtrsim 1.4$ GeV. To produce the Y(4260) with correct binding energy, we need $\Lambda\approx 2.1$ GeV. Besides, $D\bar D_1(2420)+\mathrm{c.c.}$ can also form a state with exotic quantum numbers, $J^{PC}=1^{-+}$, and its potential similar with that of the $J^{PC}=1^{--}$ state. Therefore, an exotic state with mass around 4240 MeV (called $\eta_{c1}(4240)$) is predicted to exist. Our estimation of the mass of the $J^{PC}=1^{-+}$ state in charmonium region is in agreement with those predicted by the chiral quark model and the lattice QCD. The possible decay modes and their relative widths are estimated and the results suggest that this exotic state can be searched for in $\eta\eta_c$ and $\eta\chi_{c1}$ channels.