Spin contribution to light baryons in different large-$N$ limits

TL;DR

This paper analyzes how spin contributions to light baryons scale in different large-N limits using a relativistic constituent quark model with perturbative spin-dependent interactions, confirming theoretical scaling laws.

Contribution

It provides an analytical proof of the scaling behavior of spin contributions in various large-N limits within a relativistic quark model framework.

Findings

Spin contributions scale as S(S+1)/n_q in all large-N limits.

Both spin-dependent potentials produce S-independent contributions that scale at most as O(n_q).

The results agree with diagrammatic methods.

Abstract

We investigate the spin contribution to light baryon ground states in three inequivalent large-$N$ limits: 't Hooft, QCD antisymmetric and QCD symmetric. Our framework is a constituent quark model with a relativistic Hamiltonian containing a stringlike confinement and a one-gluon exchange term. Two spin-dependent potentials are considered and treated as perturbations: the color magnetic interaction stemming from the one-gluon exchange process and the chiral boson exchange interaction. We analytically prove that the spin contributions scale like $S(S+1)/n_q$, where $S$ is the total spin and $n_q$ is the number of quark, in agreement with diagrammatic methods. Both potentials yield also $S$-independent contributions which scale at most as O$(n_q)$.