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

TL;DR

This paper investigates how channel coupling affects energy levels, mixing, and the emergence of new states in heavy quarkonia, using the Weinberg eigenvalue method to predict and analyze resonances without additional fitting parameters.

Contribution

It introduces a multichannel Weinberg eigenvalue approach to study coupled-channel resonances in heavy quarkonia, clarifying the nature of states like X(3872) and predicting new near-threshold resonances.

Findings

Identifies a narrow peak at 3.872 GeV with quantum numbers J^{PC}=1^{++}.

Shows the broadening and disappearance of the 3.940 GeV resonance with increased channel coupling.

Clarifies the dynamical origin of the X(3872) state.

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.