  In this paper we develop a formalism for incorporating hadron loops in 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 N,L multiplet. (2) These states have the same total open-flavor decay
widths. (3) Loop-induced valence configuration mixing vanishes provided that
${\L}_i \neq \L_f$ or $\S_i \neq \S_f$. The charmonium system is used as a
numerical case study, with the $^3\P_0$ decay model providing the
valence-continuum coupling. We evaluate the mass shifts and continuum mixing
numerically for all 1S, 1P and 2S charmonium valence states due to loops of D,
D$^*$, D$_s$ and D$_s^*$ meson pairs. We find that the mass shifts are quite
large, but are 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.
