  The hierarchy problem in the Standard Model is usually understood as both a
technical problem of stability of the calculation of the quantum corrections to
the masses of the Higgs sector and of the unnatural difference between the
Planck and gauge breaking scales. Leaving aside the gauge sector, we implement
on a purely scalar model a mechanism for generating naturally light scalar
particles where both of these issues are solved. In this model, on top of terms
invariant under a continuous symmetry, a highly non-renormalizable term is
added to the action that explicitly breaks this symmetry down to a discrete
one. In the spontaneously broken phase, the mass of the pseudo-Goldstone is
then driven by quantum fluctuations to values that are non-vanishing but that
are generically, that is, without fine-tuning, orders of magnitude smaller than
the UV scale.
