Line shapes of the X(3872)

If the quantum numbers of the X(3872) are J(PC)=1(++), the measurement of its mass implies that it is either a loosely bound hadronic molecule whose constituents are a superposition of the charm mesons pairs (DD0)-D-*0 and (DD*0)-D-0 or else it is a virtual state of these charm mesons. Its binding energy is small enough that the decay width of a constituent D-*0 or D-*0 has a significant effect on the line shapes of the X resonance. We develop a simple approximation to the line shapes that takes into account the effect of the D-*0 width as well as inelastic scattering channels of the charm mesons. We carry out a simultaneous fit to the line shapes in the J/psi pi(+)pi(-) and (DD0)-D-0 pi(0) channels measured in the decays B+-> K++X by the Belle Collaboration. The best fit corresponds to the X(3872) being a bound state just below the (DD0)-D-*0 threshold, but a virtual state just above the (DD0)-D-*0 threshold is not excluded.