Abstract
Two-pion induced self-energy contributions to the $\rho$-meson mass are examined in relation to the quenched approximation of QCD, where the physics associated with two-pion intermediate states has been excluded from vector-isovector correlation functions. Corrections to quenched QCD calculations of the $\rho$-meson mass are estimated to be small at the order of a few percent of the $\rho$-meson mass. The two-pion contributions display nonanalytic behavior as a function of the pion mass as the two-pion cut is encountered. The implications of this nonanalytic behavior in extrapolations of full QCD calculations are also discussed. We note that for full QCD, the error made in making a linear extrapolation of the $\rho$ mass, neglecting nonanalytic behavior, increases as one approaches the two-pion cut.
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