Nucleon magnetic moments beyond the perturbative chiral regime

The quark mass dependence of nucleon magnetic moments is explored over a wide range. Quark masses currently accessible to lattice QCD, which lie beyond the regime of chiral perturbation theory $(\ensuremath{\chi}\mathrm{PT})$, are accessed via the cloudy bag model (CBM). The latter reproduces the leading nonanalytic behavior of $\ensuremath{\chi}\mathrm{PT}$, while modeling the internal structure of the hadron under investigation. We find that the predictions of the CBM are succinctly described by the simple formula ${\ensuremath{\mu}}_{N}{(m}_{\ensuremath{\pi}})={\ensuremath{\mu}}_{N}^{(0)}/(1+\ensuremath{\alpha}{m}_{\ensuremath{\pi}}+\ensuremath{\beta}{m}_{\ensuremath{\pi}}^{2})$, which reproduces the lattice data, as well as the leading nonanalytic behavior of $\ensuremath{\chi}\mathrm{PT}$. As this form also incorporates the anticipated Dirac moment behavior in the limit ${m}_{\ensuremath{\pi}}\ensuremath{\rightarrow}\ensuremath{\infty}$, it constitutes a powerful method for extrapolating lattice results to the physical mass regime.