Effects of charged charm mesons on the line shapes of the X(3872)

The quantum numbers J(PC)=1(++) of the X(3872) and the proximity of its mass to the D-*(D) over bar (0) threshold imply that it is either a loosely bound hadronic molecule whose constituents are a superposition of D-*0(D) over bar (0) and D-0(D) over bar (*0) or it is a virtual state of charm mesons. The line shapes of the X(3872) can discriminate between these two possibilities. At energies within a few MeV of the D-*0(D) over bar (0) threshold, the lines shapes of the X produced in B -> K transitions are determined by its binding energy and its width. Their normalizations are determined by a short-distance constant that is different for B+-> K+ and B-0 -> K-0. At energies comparable to the 8 MeV splitting between the D-*0(D) over bar (0) and D*+D- thresholds, the charged meson channels D*+D- and D+D*- have a significant effect on the line shapes of the X. We calculate the line shapes taking into account the resonant coupling between the charged and neutral 1(++) channels. The line shapes and their normalizations depend on one additional scattering parameter and two additional short-distance constants associated with the B -> K transitions. The line shapes of the X resonance depend on its decay channel; they are different for J/psi pi(+)pi(-), J/psi pi(+)pi(-)pi(0), and D-0(D) over bar (0)pi(0). The line shapes are also different for X produced in B+ decays and in B-0 decays. Some conceptual errors in previous work on this problem are pointed out.