Decoding the Riddle of Y(4260) and Zc(3900)

The observation of Z(c)(3900) by the BESIII Collaboration in the invariant mass spectrum of J/psi pi(+/-) in e(+)e(-) -> J/psi pi(+)pi(-) at the center of mass 4.260 GeV suggests the existence of a charged (D) over barD* + D (D) over bar* molecular state with I(J(P)) = 1(1(+)), which could be an isovector brother of the famous X(3872) and an analogue of Z(b)(10610) claimed by the Belle Collaboration. We demonstrate that this observation provides strong evidence that the mysterious Y(4260) is a (D) over barD(1)(2420) +D (D) over bar (1)(2420) molecular state. Especially, we show that the decay of this molecule naturally populates low momentum (D) over barD* pairs and leads unavoidably to a cusp at the (D) over barD* threshold. We discuss the signatures that distinguish such a (D) over barD* cusp from the presence of a true resonance.