  The mass-in-mass (MiM) lattice consists of an infinite chain of identical
beads that are both nonlinearly coupled to their nearest neighbors and linearly
coupled to a distinct resonator particle; it serves as a prototypical model of
wave propagation in granular crystals and metamaterials. We study traveling
waves in an MiM lattice whose bead interaction is governed by the cubic
Fermi-Pasta-Ulam-Tsingou potential and whose resonator mass is small compared
to the bead mass. Excluding a countable number of "antiresonance" resonator
masses accumulating at 0, we prove the existence of nanopteron traveling waves
in this small mass limit. The profiles of these waves consist of the
superposition of an exponentially localized core and a small amplitude periodic
oscillation that itself is a traveling wave profile for the lattice. Our
arguments use functional analytic techniques originally developed by Beale for
a capillary-gravity water wave problem and recently employed in a number of
related nanopteron constructions in diatomic Fermi-Pasta-Ulam-Tsingou lattices.
