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
Chirality (physics) to begin with, and therefore the pions are not massless, but have small masses: they are pseudo-Goldstone bosons. For more "light" quark species, flavors in general, the corresponding chiral symmetries are "U(N)×U(N)", decomposing into and exhibiting a very analogous chiral symmetry breaking pattern. Most usually, = 3 is taken, the "u, d", and "s" quarks taken to be light (the Eightfold way (physics)), so then approximately massless for the symmetry to be meaningful to a lowest order, while the other three quarks are sufficiently heavy to barely have a residual chiral symmetry be visible for practical purposes. In theoretical physics,