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.
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