The key idea to the Higgs mechanism is somewhat more theoretical and abstract. Theoretical physics shows that every particle inside some interaction field behaves exactly like its energy or momentum has changed. This concept is called
canonical momentum, in contrast to the usual (kinetic) momentum
For example, in the magnetic field the canonical momentum is
and in the static electric field the canonical energy is
(these formulas are non-relativistic). The latter is most simply understood, because we are used to call
potential energy. A force acts on the particle when such additional term changes with spatial position.
Variations of this idea depend on the tensor type of the interaction field. The electromagnetic field is a vector field, and the Higgs field is a scalar field. (The other types of fields are also possible, for example, the gravitational field in GR is a tensor field of order 2.) That leads to an important fact: the energy and the momentum change by the same factor (in the relativistic sense), which is the same as the mass would change.
and
where
is the coupling constant.
Thus, wherever some scalar interaction field gets a non-zero value, particles move like they have gained some mass. And the Higgs field does have a constant non-zero value all over the Universe,
Thus, all particles have their Higgs masses, and they can have no explicit mass besides it, and the theory supposes so.
