The hierarchy problem asks why the Higgs mass remains far below a much larger ultraviolet scale when scalar mass parameters receive additive radiative corrections proportional to that scale squared.
The technical hierarchy problem asks why a small mass scale, once chosen, remains stable under quantum corrections from much larger scales. A symmetry can protect this radiative stability without explaining the numerical origin of the scale separation. For a fundamental scalar mass, heavy thresholds often give additive corrections proportional to the heavy mass squared; supersymmetric cancellation of quadratic divergences supplies one protection mechanism when supersymmetry breaking is sufficiently soft.
Naturalness is the expectation that a dimensionless observable should not be extremely small because unrelated large contributions cancel with high precision. It is a heuristic guide to model building rather than a mathematical consistency condition.
A small mass is technically protected when its vanishing restores a symmetry that restricts the corresponding quantum corrections. Gauge protection of a vector mass, chiral protection of a fermion mass, and supersymmetry protection of scalar masses use different symmetry constraints. This is a radiative-stability statement, not a proof that all small numerical parameters require such protection.
A fermion mass that violates an otherwise restored chiral symmetry is multiplicatively rather than additively renormalized in perturbation theory: corrections vanish with the symmetry-breaking mass or coupling. A chiral gauge representation can forbid a bare mass altogether until a Higgs mechanism and Yukawa coupling make a gauge-invariant term possible. A scalar-partner bilinear may respect all those ordinary symmetries and therefore needs separate supersymmetry protection.
An unbroken gauge symmetry forbids an explicit local Proca mass for its gauge vector. A Higgs mechanism can generate that mass through a charged vacuum expectation value, but the stability of the resulting vector scale then depends on the scalar sector that fixes the expectation. Gauge invariance alone does not protect a fundamental scalar mass.
