Quenched approximation in the quark model

We present a model calculation of some effects of virtual $q\overline{q}$ pairs in mesons. Specifically, using a model for pair creation that has previously been shown to give a good description of strong meson decays, we calculate the energy shift of a static quark-antiquark pair due to the presence of virtual quark-antiquark pairs. The shift is large and approximately proportional to the distance between the static sources. The linearity of the correction suggests that pair-creation effects can be absorbed into a renormalization of the mesonic string tension. However, this masking can only be approximate, as we show by considering the dependence of the energy shift on the spin state of the sources. We conclude by pointing out the relevance of our results to the "$\frac{N}{\rho }$" problem encountered in lattice QCD calculations.