Channel coupling in heavy quarkonia: energy levels, mixing, widths and new states

Abstract

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 $c\bar c, b\bar b$ systems. The Weinberg eigenvalue method is formulated in the multichannel problems, which allows 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 $2^3P_1(c\bar c)$ 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.