Diquark size effects in the quark-diquark approximation for baryons

TL;DR

This paper evaluates the accuracy of the quark-diquark approximation for baryons by comparing it with a three-body model, analyzing baryon masses and distances, and proposing a method to refine the diquark potential.

Contribution

It introduces an original procedure to improve the quark-diquark potential and assesses the approximation's validity against a three-body model.

Findings

Diquark compactness is not essential for accurate baryon masses.

The quark-diquark approximation can be reliable even with non-compact diquarks.

A new method to establish the quark-diquark potential enhances model precision.

Abstract

Baryons can be described within several theoretical frameworks. Among them, the constituent approach is widely used. In this context, we aim to evaluate the accuracy of a particular model of baryons: the quark-diquark approximation. It consists in separating the three-body system into two subsequent two-body ones: a pair of two quarks, the diquark, and a second system consisting of the diquark and the third quark. This approximation is widely used, but its accuracy is rarely evaluated. The goal of this work is to perform this evaluation by comparing the quark-diquark model with a three-body model, both using the same semi-relativistic interaction. The baryon masses and some characteristic distances are computed and analysed within both approaches. Additionally, an original procedure to establish the quark-diquark potential will be presented with the aim to increase the precision of this approximation. It is shown that a diquark must not necessarily be compact to obtain good baryon masses.