We examine how the binding of light (A <= 8) nuclei depends on possible variations of hadronic masses, including meson, nucleon, and nucleon-resonance masses. Small variations in hadronic masses may have occurred over time; the present results should help evaluate the consequences for primordial nucleosynthesis. Larger variations may be relevant to current attempts to extrapolate properties of nucleon-nucleon interactions from lattice QCD calculations. As an example, we employ a particular set of relations obtained from a Dyson-Schwinger study of hadron masses and sigma terms. We find that nuclear binding decreases moderately rapidly as the quark mass increases, with the deuteron becoming unbound when the pion mass is increased by ~50%. In the other direction, the dineutron becomes bound if the pion mass is decreased by ~10%.
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