QCD

Simple Examples

1. Quark-Antiquark Interaction
   
2. Quark-Quark Interaction
   As a second example quark-quark scattering is discussed.
   
   The corresponding Feynman diagram is depicted in This QCD amplitude is like the electron-muon scattering amplitude where both particles have equal charges and once again with the replacement: α -> C_Fα_s. The quark-quark potential (again at small distances) is hence given by:
   In contrast to the quark-antiquark case, here one needs to consider the direct product of a colour triplet and a another colour triplet. The result is the direct sum of a colour sextet and a colour anti-triplet:
   
   There are again two possibilities for C_F. One finds
   
   C_F(sextet)=+1/3
   C_F(antitriplet)=-2/3
   
   As a consequence, the quark-quark scattering potential at short distances is attractive in the anti-triplet configuration and repulsive in the sextet configuration. When a third quark is added the direct product of this anti-triplet with the added colour triplet leads to an octect and a colour singlet. The direct product of the sextet with the triplet results in a decuplet and an octet.
   
   The net effect in the decuplet is a repulsive force whereas in the singlet configuration the force is attractive and more attractive than in the octet configuration.