Quantum chromodynamics observed particles make isospin and SU(3) multiplets. The approximate flavor symmetries do have associated gauge bosons, observed particles like the rho and the omega, but these particles are nothing like the gluons and they are not massless. They are emergent gauge bosons in an approximate string description of QCD. The dynamics of the quarks and gluons are controlled by the quantum chromodynamics Lagrangian. The gauge invariant QCD Lagrangian is where formula_1 is the quark field, a dynamical function of spacetime, in the fundamental representation of the SU(3) gauge group, indexed by formula_2; formula_3 is the gauge covariant derivative; the γ
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