1/Nc expansion and the spin-flavor structure of the quark interaction in the constituent quark model

TL;DR

This paper investigates the hierarchy of coefficients in the 1/Nc expansion for negative parity excited baryons within the constituent quark model, focusing on the spin-flavor structure of quark interactions and their implications.

Contribution

It demonstrates that different spin-flavor structures of quark interactions converge to a single operator in the zero-range limit, explaining the dominance of this operator and proposing a test for spin-flavor dependence.

Findings

All spin-flavor structures match onto the same operator in the zero-range limit.

Both pion and gluon exchange models are compatible with experimental data.

The dominance of the $S_c^2$ operator is explained by the zero-range interaction limit.

Abstract

We study the hierarchy of the coefficients in the 1/Nc expansion for the negative parity L=1 excited baryons from the perspective of the constituent quark model. This is related to the problem of determining the spin-flavor structure of the quark interaction. The most general two-body scalar interaction between quarks contains the spin-flavor structures $t_1^a t_2^a, \vec s_1\cdot \vec s_2$ and $ \vec s_1\cdot \vec s_2 t_1^a t_2^a$. We show that in the limit of a zero range interaction all these structures are matched onto the same hadronic mass operator $S_c^2$, which gives a possible explanation for the dominance of this operator in the 1/Nc expansion for the L=1 states and implies that in this limit it is impossible to distinguish between these different spin-flavor structures. Modeling a finite range interaction through the exchange of a vector and pseudoscalar meson, we propose a test for the spin-flavor dependence of the quark forces. For the scalar part of the quark interaction we find that both pion exchange and gluon exchange are compatible with data.