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12.5.2. QCD The existence of 3 quarks colors provides the basis for the current theory of strong interactions known as quantum chromodynamics (QCD). To begin, the 3 colors of each quark flavor form a triplet, e.g., ur u u g u b dr d d g d b etc (12.62) 1 The set of unitary transformations exp i α x λ , which rearranges the color 2 components within a given flavor, constitutes the color gauge group SU(3). This group has 8 generators so that there are 8 Hermitian matrices, analogous to the Pauli matrices for SU(2). The correspondent gauge theory thus contains 8 independent gauge fields with 8 associated gauge bosons. The latter are called gluons since they glue the quarks together to form hadrons. Like the quarks, these gluons seem to be confined permanently inside the hadrons. Evidence of the existence of gluons can be gleaned from the structure functions of deep inelastic scattering. The functions fi x in eqs(12.54-5) represent the probabilities that the ith constituent species carries a fraction x of the proton’s total 1 momentum. Since the total fraction must be 1, we have dx x f x 1 . i i 0 However, when the fi x deduced from measurements are put into this ‘sum rule’, the total is only about 0.5. Thus, some 50% of the momentum is carried by electrically neutral constituents, which do not interact with the virtual photon and hence do not show up in the structure functions. According to QCD, these neutral constituents are gluons.