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 $\left(\chi \mathrm{PT}\right)$, are accessed via the cloudy bag model (CBM). The latter reproduces the leading nonanalytic behavior of $\chi \mathrm{PT}$, 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 ${\mu }_N{(m}_{\pi })={\mu }_N^{\mathrm{}\left(0\right)\mathrm{}}/(1+\alpha m_{\pi }+\beta m_{\pi }^2)$, which reproduces the lattice data, as well as the leading nonanalytic behavior of $\chi \mathrm{PT}$. As this form also incorporates the anticipated Dirac moment behavior in the limit $m_{\pi }\to \infty$, it constitutes a powerful method for extrapolating lattice results to the physical mass regime.

• Received 7 October 1998

DOI:https://doi.org/10.1103/PhysRevD.60.034014