Diquark size effects in the quark-diquark approximation for baryons

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.

Some numbers in Table 4 to 13 are corrected. The conclusions remain unchanged, except for one point. The lowest quark-diquark mass is now always given by the configuration with the largest component in the 3-body wave functions