  Hadron masses show a specific dependence on the quark masses. Therefore, the
variation of these masses can cause a resonance in a hadronic scattering
amplitude to become a bound state. Consequently, the amplitude exhibits a
non-analytic behavior at this transition. Crossed amplitudes, where the
resonance can be exchanged in the t-channel, can be shown to exhibit the same
phenomenon by s-->t analytic continuation. This entails possible kinks in
lattice quark mass extrapolations needed to compute hadronic observables.
