  The role of an intrinsic four-body scale in universal few-boson systems is
the subject of active debate. We study these systems within the framework of
effective field theory. For systems of up to six bosons we establish that no
four-body scale appears at leading order (LO). However, we find that at
next-to-leading (NLO) order a four-body force is needed to obtain renormalized
results for binding energies. With the associated parameter fixed to the
binding energy of the four-boson system, this force is shown to renormalize the
five- and six-body systems as well. We present an original ansatz for the
short-distance limit of the bosonic $A$-body wave function from which we
conjecture that new $A$-body scales appear at N$^{A-3}$LO. As a specific
example, calculations are presented for clusters of helium atoms. Our results
apply more generally to other few-body systems governed by a large scattering
length, such as light nuclei and halo states, the low-energy properties of
which are independent of the detailed internal structure of the constituents.
