Probing the nature of Y(4260) in the isospin violating process Y(4260) → J/ψηπ0

The isospin violation process Y(4260) -> J/psi eta pi(0) is studied assuming that Y(4260) is a D-1(D) over bar +c.c. hadronic molecule. In association with the production of the Z(c)(3900), which is treated as a D (D) over bar c.c. hadronic molecule, this process can help us distinguish the molecular nature of Y(4260) from other scenarios since the incomplete cancellation between the charged and neutral- meson loops, which are prominent in the molecular picture only, produces a peak in the e(+)e(-) -> Y(4260) -> J/psi eta pi(0) cross section at the D-1(D) over bar c.c. threshold and a very prominent peak in the J/psi eta pi(0) invariant mass spectrum in between the D (D) over bar + c.c. thresholds, the latter being much narrower than the corresponding one in the isospin conserving channel, i.e. J/psi pi(+)pi(-). The partial width of Y(4260) -> J/psi eta pi(0) is about 4 x 10(-4) times that of Y(4260) -> J/psi eta pi(0). The cross section of e(+)e(-) -> Y(4260) -> J/psi eta pi(0) at the D-1(D) over bar + c.c. threshold is about 0.05 pb, which is much larger than that produced by the nearby resonances. These features are the direct consequence of the assumed nature of these two states, especially for the Y(4260), which might be accessible at high- statistics experiments such as BESIII and LHCb.