  We demonstrate that the physics which resolves naturalness problems need not
take the form of new particles and can sometimes manifest itself as higher
dimensional operators. As a proof of principle, we present a simple model where
the scale of new particles is parametrically separated from that estimated via
naturalness arguments applied to self-quartic couplings. In this example, new
particles appear far above the scale $m/\sqrt{\lambda}$, where $m$ is the mass
of the particle and $\lambda$ is its self-quartic coupling. The shift symmetry
responsible for resolving the naturalness problem involves higher dimensional
operators rather than new particles.
