  Small weakly-bound droplets determine a number of properties of ultracold
Bose and Fermi gases. For example, Efimov trimers near the atom-atom-atom and
atom-dimer thresholds lead to enhanced losses from bosonic clouds.
Generalizations to four- and higher-body systems have also been considered.
Moreover, Efimov trimers have been predicted to play a role in the Bose polaron
with large boson-impurity scattering length. Motivated by these considerations,
the present work provides a detailed theoretical analysis of weakly-bound
$N$-body clusters consisting of $N-1$ identical bosons (denoted by "B") of mass
$m$ that interact with a single distinguishable impurity particle (denoted by
"X") of mass $M$. The system properties are analyzed as a function of the mass
ratio $\kappa$ (values from $\kappa=1$ to $50$ are considered), where $\kappa$
is equal to $m/M$, and the two-body $s$-wave scattering length $a_{\text{BX}}$
between the bosons and the impurity. To reach the universal Efimov regime in
which the size of the BBX trimer as well as those of larger clusters is much
larger than the length scales of the underlying interaction model, three
different approaches are considered: resonance states are determined in the
absence of BB and BBX interactions, bound states are determined in the presence
of repulsive three-body boson-boson-impurity interactions, and bound states are
determined in the presence of repulsive two-body boson-boson interactions. The
universal regime, in which the details of the underlying interaction model
become irrelevant, is identified.
