Download 12.5.2. QCD

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.