Determination of SU(6) Clebsch-Gordan Coefficients and Baryon Mass and Electromagnetic Moment Relations

Abstract

We compute and tabulate the Clesbsch--Gordan coefficients of the $SU(6)\supset SU(3)\times SU(2)$ product $\overline{56}\otimes 56$, which are relevant to the nonrelativistic spin-flavor symmetry of the lightest baryons. Under the assumption that the largest representation in this product, the $2695$, gives rise to operators in a chiral expansion that produce numerically small effects, we obtain a set of relations among the masses of the baryons, as well as among their magnetic dipole and higher multipole moments. We compare the mass relations to experiment, and find numerical predictions for the ${\Sigma }^0$-$\Lambda$ mass mixing parameter and eighteen of the twenty-seven magnetic moments in the $56$.

33 pages, latex (aps revtex), no figures

References in corpus (14)

• The 1/N Expansion for Baryons
• Baryon-Pion Couplings from Large-N QCD
• Spin-Flavor Structure of Large N Baryons
• 1/N Corrections to the Baryon Axial Currents in QCD
• Baryons from Quarks in the $1/N$ Expansion
• On Spin Independence in Large $N_c$ Baryons
• Baryon Hyperfine Mass Splittings in Large N QCD
• Baryon Magnetic Moments in a Simultaneous Expansion in $1/N$ and $m_s$
• Light Quark Spin-Flavor Symmetry for Baryons Containing a Heavy Quark in Large N QCD
• Baryon Magnetic Moments in the 1/N Expansion
• Hyperfine Mass Splittings of Baryons Containing a Heavy Quark in Large N QCD
• Baryon decuplet mass relations in chiral perturbation theory
• Baryon Masses at Second Order in Chiral Perturbation Theory
• Baryons with Many Colors and Flavors

Cited by in corpus (22)

• Baryon Mass Splittings in the 1/N_c Expansion
• Charmed and strange baryon resonances with heavy-quark spin symmetry
• Hidden charm N and Delta resonances with heavy-quark symmetry
• Large N_c Limit of Spin-Flavor Breaking in Excited Baryon Levels
• SU(6) Extension of the Weinberg-Tomozawa Meson-Baryon Lagrangian
• Quadrupole moments of baryons
• Baryon Charge Radii and Quadrupole Moments in the 1/N_c Expansion: The 3-Flavor Case
• Electromagnetic N->Delta transition and neutron form factors
• Electromagnetic form factors of the Delta with D-waves
• Complete Analysis of Baryon Magnetic Moments in 1/N_c
• Chiral extrapolations for nucleon electric charge radii
• Chiral extrapolations for nucleon magnetic moments
• Power Counting Regime of Chiral Effective Field Theory and Beyond
• Baryon resonances in large $N_c$ QCD
• Spin of ground state baryons
• Finite-volume corrections to charge radii
• Resonances and the Weinberg--Tomozawa 56-baryon --35-meson interaction
• Electromagnetic multipole moments of baryons
• Heavy Baryons in SU(2) $\times$ SU(6)
• Three quark currents and baryon spin
• Ernest Henley and the shape of baryons
• Excited nucleon electromagnetic form factors from broken spin-flavor symmetry