The mechanism of channel coupling via decay products is used to study energy shifts, level mixing as well as the possibility of new near-threshold resonances in $c\overline{c}$, $b\overline{b}$ systems. The Weinberg eigenvalue method is formulated in the multichannel problems, which allows one to describe coupled-channel resonances and wave functions in a unitary way, and to predict new states due to channel coupling. Realistic wave functions for all single-channel states and decay matrix elements computed earlier are exploited, and no new fitting parameters are involved. Examples of level shifts, widths, and mixings are presented; the dynamical origin of $X(3872)$ and the destiny of the single-channel $2{}^{3}P_1(c\overline{c})$ state are clarified. As a result a sharp and narrow peak in the state with quantum numbers $J^{PC}=1^{++}$ is found at 3.872 GeV, while the single-channel resonance originally around 3.940 GeV becomes increasingly broad and disappears with growing coupling to open channels.

• Received 13 September 2009

DOI:https://doi.org/10.1103/PhysRevD.81.074027