Nucleon-Quark Diquark-exchange Interaction

TL;DR

This paper derives the nucleon-quark diquark-exchange interaction using Feynman propagators, revealing a sign difference from quark-antiquark exchange, and applies it to nuclear-quark matter calculations.

Contribution

It introduces a derivation of the axial-vector diquark propagator and highlights the sign difference due to fermion loops, with applications to nuclear matter.

Findings

Derived the axial-vector diquark propagator with a sign difference from quark-antiquark exchange.

Found the diquark exchange leads to a repulsive potential in nucleon-quark interactions.

Applied the interaction to nuclear-quark matter, showing its relevance in such systems.

Abstract

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.