Isospin properties of the X state near the DD̄* threshold

The DD̄* scattering amplitude and the production of the final states π+π-J/ψ and π+π-π0J/ψ near the D0D̄*0 threshold are discussed following the recent suggestion that the observed peaks X(3872) and X(3875) in the decays B→XK are due to a virtual state X in the D0D̄*0 channel. The strong interaction is treated using the small interaction radius approximation. It is shown that the mass difference between the charged and neutral D(*) mesons results in a distinctive behavior of the relevant isotopic amplitudes. In particular, the shape of the peak in the π+π-J/ψ channel should be significantly narrower than in the π+π-π0J/ψ channel, which property can be used for an experimental test of the virtual state hypothesis.