Baryon magnetic moment in large-$N_c$ chiral perturbation theory: Complete analysis for $N_c=3$

TL;DR

This paper calculates baryon magnetic moments using large-$N_c$ chiral perturbation theory at one-loop order, including specific corrections, and compares the results to existing approaches, highlighting the importance of non-degenerate baryon effects.

Contribution

It provides a complete analytical framework for baryon magnetic moments at $N_c=3$ including all relevant operator structures and corrections, improving upon previous partial calculations.

Findings

Theoretical expressions agree with existing results at $N_c=3$.

Numerical fits reveal the importance of non-degenerate baryon effects.

Results suggest refined parameter determination requires considering baryon mass differences.

Abstract

Baryon magnetic moments are computed in baryon chiral perturbation theory in the large-$N_c$ limit at one-loop order, where $N_c$ is the number of color charges. Orders $\mathcal{O}(m_q^{1/2})$ and $\mathcal{O}(m_q \ln m_q)$ corrections are both evaluated including all the operator structures that participate at the physical value $N_c=3$. The complete expressions for octet and decuplet baryon magnetic moments in addition to decuplet-octet baryon transition moments are thus compared to their available counterparts obtained in heavy baryon chiral perturbation theory for degenerate intermediate baryons in the loops. Theoretical expressions fully agree at the physical values $N_c=3$ and $N_f=3$ flavors of light quarks. Some numerical evaluations are produced via a least-squares fit to explore the free parameters in the analysis. Results point out the necessity of incorporating the effects of non-degenerate intermediate baryons in the loops for a consistent determination of these free parameters.