Naturalness without new particles

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 $$ m/\sqrt{\lambda } $$ m / λ , where m is the mass of the particle and λ is its self-quartic coupling. The shift symmetry responsible for resolving the naturalness problem involves higher dimensional operators rather than new particles.