Nucleon-Quark Diquark-exchange Interaction

In this note the nucleon-quark diquark-exchange interaction is derived using the Feynman-propagator for axial-vector diquark (D) exchange. The Feynman diquark propagator is derived and the result is a (-)-sign difference w.r.t. quark-antiquark exchange. This is due to the (-)-sign for a closed fermion loop, present in for example vector and axial-vector quark-antiquark exchange, but absent in the case of D-exchange. The calculations in these notes follow closely those for vacuum polarisation in the literature. Taking into account that the diquark D is a color \left{\bar{3}_c\right\}-state giving a factor +2. The result is an effective axial-vector diquark propagator. Application to $QN \rightarrow NQ$ gives a repulsive potential, which has been used in mixed nuclear-quark matter calculation.