  We address some new issues concerning spontaneous symmetry breaking. We
define classical Higgs fields for gauge-natural invariant Yang--Mills type
Lagrangian field theories through the requirement of the existence of {\em
canonical} covariant gauge-natural conserved quantities. As an illustrative
example we consider the `gluon Lagrangian', i.e. a Yang--Mills Lagrangian on
the $(1,1)$-order gauge-natural bundle of $SU(3)$-principal connections, and
canonically define a `gluon' classical Higgs field through the split reductive
structure induced by the kernel of the associated gauge-natural Jacobi
morphism.
