Abstract
In this paper, we develop a formalism for incorporating hadron loops into the quark model. We derive expressions for mass shifts, continuum components, and mixing amplitudes of “quenched” quark model states due to hadron loops, as perturbation series in the valence-continuum coupling Hamiltonian. We prove three general theorems regarding the effects of hadron loops, which show that given certain constraints on the external “bare” quark model states, the valence-continuum coupling, and the hadrons summed in the loops, the following results hold: (1) The loop mass shifts are identical for all states within a given multiplet. (2) These states have the same total open-flavor decay widths. (3) Loop-induced valence configuration mixing vanishes provided that or . The charmonium system is used as a numerical case study, with the decay model providing the valence-continuum coupling. We evaluate the mass shifts and continuum mixing numerically for all , and charmonium valence states due to loops of , and meson pairs. We find that the mass shifts are quite large but numerically similar for all the low-lying charmonium states, as suggested by the first theorem. Thus, loop mass shifts may have been “hidden” in the valence quark model by a change of parameters. The two-meson continuum components of the physical charmonium states are also found to be large, creating challenges for the interpretation of the constituent quark model.
- Received 7 December 2007
DOI:https://doi.org/10.1103/PhysRevC.77.055206
©2008 American Physical Society