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.
Highlights
In the limit of exact SUð3Þ flavor symmetry, Coleman and Glashow [1] first derived a set of relations among magnetic moments of the octet baryons
When the method was applied to the renormalization of the baryon axial current, chiral logarithmic corrections to the axial couplings in hyperon semileptonic decays were found to be as large as the lowest order values when only intermediate octet baryons were included in the loops [5]
Baryon magnetic moments get corrections at one-loop order from the diagrams displayed in Figs. 1 and 2, which contribute to orders Oðm1=2 q Þ and Oðmq ln mq Þ, respectively
Summary
In the limit of exact SUð3Þ flavor symmetry, Coleman and Glashow [1] first derived a set of relations among magnetic moments of the octet baryons. When the method was applied to the renormalization of the baryon axial current, chiral logarithmic corrections to the axial couplings in hyperon semileptonic decays were found to be as large as the lowest order values when only intermediate octet baryons were included in the loops [5]. The earliest analysis of the magnetic moments of octet baryons in HBCHPT to orders Oðm1=2 q Þ and Oðmq ln mq Þ was presented in Ref. The main contribution of this paper is to explicitly show that baryon chiral perturbation theory in the large-N c limit and HBCHPT analyses of baryon octet magnetic moments fully agree at the physical value N c 1⁄4 3 for N f 1⁄4 3 flavors of light quarks. The paper is complemented by five appendixes where the complete lengthy formulas of baryon magnetic moments are relegated
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