It seems necessary to have at least one more type of particle (and one more type of interaction). This interaction has little to do with the forces between the particles, but is essential for the generation of mass and for the symmetry-breaking that yields different masses for the W (and Z) and for the photon.
The particle associated with this interaction is called the "Higgs boson." The Higgs boson has not yet been observed.
However, we do know that particles have masses. Exactly how it happens is one of the puzzles that we hope to solve by studying processes that occur at future colliders.
