Baryon Magnetic Moments in a QCD-based Quark Model with loop corrections

Abstract

We study meson loop corrections to the baryon magnetic moments starting from a QCD-based quark model derived earlier in a quenched approximation to QCD. The model reproduces the standard quark model with extra corrections for the binding of the quarks. The loop corrections are necessary to remove the quenching. Our calculations use heavy baryon perturbation theory with chiral baryon-meson couplings and a form factor characterizing the structure of baryons as composite particles. The form factor reflects soft wave function effects with characteristic momenta $\approx 400$ MeV, well below the usual chiral cutoff of $\approx 1$ GeV. The resulting model involves only three parameters, the quark moments $μ_u$ and $μ_s$ and a parameter $λ$ that sets the momentum scale in the wavefunctions. We find that this approach substantially improves the agreement between the theoretical and experimental values of the octet baryon magnetic moments, with an average difference between the theoretical and experimental moments of 0.05$μ_N$. An extension to the decuplet states using the same input predicts a moment of 1.97 $μ_N$ for the $Ω^-$ hyperon, in excellent agreement with the measured moment of $2.02\pm0.05 μ_N$.