Interpretation of imaginary channel weights for resonant states

Characterize the detailed physical meaning of the imaginary parts of channel component weights obtained from the non-Hermitian complex-scaled description of charmonium-like resonances.

Background

The complex scaling method describes resonances using a non-Hermitian Hamiltonian and a c-product rather than the usual Hermitian inner product. Consequently, the channel component weights of resonant states can be complex, and individual weights need not be real, positive, or directly interpretable as probabilities. The paper states that although the real parts can sometimes indicate the relative importance of channels when the imaginary parts are small, the detailed physical interpretation of the imaginary parts remains unresolved.