Baryon magnetic moments in large-$N_c$ chiral perturbation theory: Effects of the decuplet-octet mass difference and flavor symmetry breaking

The magnetic and transition magnetic moments of the ground-state baryons are computed in heavy baryon chiral perturbation theory in the large-$N_c$ limit, where $N_c$ is the number of colors. SU(3) symmetry breaking is systematically studied twofold: On the one hand, one-loop nonanalytic corrections of orders $m_q^{1/2}$ and $m_q\ln m_q$ are included, with contributions of baryon intermediate states from both flavor octet and flavor decuplet multiplets, assuming degeneracy between baryon states within a given flavor multiplet but nondegeneracy between baryons of different multiplets. On the other hand, perturbative SU(3) symmetry breaking is also analyzed by including all relevant leading-order operators that explicitly break SU(3) at linear order. The resultant expressions are compared with the available experimental data and with other determinations in the context of conventional heavy baryon chiral perturbation theory for three flavors of light quarks and at the physical value $N_c=3$. The agreement reached is quite impressive.

Figure 1

Feynman diagrams which yield nonanalytic $m_q^{1/2}$ corrections to the magnetic moments of octet baryons. Dashed lines denote mesons, and single and double solid lines denote octet and decuplet baryons, respectively. For decuplet baryons and decuplet-octet transitions, the diagrams are similar.

Figure 2

Feynman diagrams which yield nonanalytic $m_q\ln m_q$ corrections to the magnetic moments of octet baryons. Dashed lines denote mesons, and single and double solid lines denote octet and decuplet baryons, respectively. The wave function renormalization graphs are omitted in the figure but are nevertheless considered in the analysis. For decuplet baryons and decuplet-octet transitions, the diagrams are similar.

Figure 3

Deviation of baryon magnetic moments (in units of ${\mu }_N$) relative to the SU(3) symmetric fit. The open circles are from fit B. The open diamonds are from the experimental values. The baryon labels are indicated in the horizontal axis, cf. Table 1.

Figure 4

Deviation of baryon magnetic moments (in units of ${\mu }_N$) relative to the SU(3) symmetric fit. The open circles are from fit C. The open diamonds are from the experimental values. The baryon labels are indicated in the horizontal axis, cf. Table 1.

Figure 5

Deviation of baryon magnetic moments (in units of ${\mu }_N$) relative to the SU(3) symmetric fit. The open circles are from fit D. The open diamonds are from the experimental values. The baryon labels are indicated in the horizontal axis, cf. Table 1.