Gauge boson more complicated group "SU"(3) has eight generators, corresponding to the eight gluons. The three W and Z bosons correspond (roughly) to the three generators of "SU"(2) in GWS theory. For technical reasons involving gauge invariance, gauge bosons are described mathematically by field equations for massless particles. Therefore, at a naïve theoretical level, all gauge bosons are required to be massless, and the forces that they describe are required to be long-ranged. The conflict between this idea and experimental evidence that the weak and strong interactions have a very short range requires further theoretical insight. According to the Standard Model, the
W and Z bosons particles, starting with and , all denote quarks and antiquarks (factor "N" is applied). The various "V" denote the corresponding CKM matrix coefficients. Unitarity of the CKM matrix implies that Z bosons decay into a fermion and its antiparticle. As the Z boson is a mixture of the pre-symmetry-breaking W and B bosons (see weak mixing angle), each vertex factor includes a factor "T" − "Q" sin"θ" where "T" is the third component of the weak isospin of the fermion, "Q "is the electric charge of the fermion (in units of the elementary charge), and "θ" is the weak mixing