  Near two-body unitarity, the three-boson system is characterized by an
approximate discrete scale invariance manifest in a geometric tower of bound
states (the Efimov effect). In the absence of a strong four-body force, the
four-boson system has two states associated with each Efimov state, one very
nearly unstable, the other several times deeper. We study correlations between
the excited- and ground-state properties, such as binding energies and radii,
up to next-to-leading order in an effective field theory for short-range
forces. We obtain the parameters in these correlations from similar
correlations arising from existing precise calculations based on short-range
potentials. We also derive correlations among excited-state properties that
emerge from the proximity of the state to the break-up threshold into a boson
and a three-boson bound state, using an effective field theory for "halo"
states.
