Confined Quarks and Analyticity

We argue that confinement requires singularities in parton-hadron wave functions which are necessary for the parton-model description of physical processes and the analytic structure of hadronic amplitudes. Our arguments are supported by explicit calculations in two-dimensional quantum chromodynamics. In particular, we show, using new WKB techniques, that the amplitudes for $e^{-}h\to e^{-}X$ and $e^{+}{e}^{-}\to \mathrm{hX}$ are related by analytic continuation in their scaling regions.