Chiral Magnetism of the Nucleon

TL;DR

This paper develops a chiral effective field theory with explicit pions, nucleons, and Δ(1232) resonances to study the quark-mass dependence of nucleon magnetic moments. By promoting the isovector NΔ M1 transition to leading order and adopting a modified power counting, it reveals important non-analytic $m_\pi$-dependence that significantly shapes chiral extrapolations of lattice QCD data. The authors show that their scheme C can describe quenched lattice results at larger $m_\pi$ and remains consistent with Adelaide's Padé fits, providing a framework for extrapolations over a wider range of quark masses. They also discuss quenching effects and the need for more low-mass lattice data to further test and refine the approach, highlighting implications for future lattice simulations and EFT analyses.

Abstract

We study the quark mass expansion of the magnetic moments of the nucleon in a chiral effective field theory including nucleons, pions and delta resonances as explicit degrees of freedom. We point out that the usual powercounting applied so far to this problem misses important quark mass structures generated via an intermediate isovector M1 nucleon-delta transition. We propose a modified powercounting and compare the resulting chiral extrapolation function to available (quenched) lattice data. The extrapolation is found to work surprisingly well, given that the lattice data result from rather large quark masses. Our calculation raises the hope that extrapolations of lattice data utilizing chiral effective field theory might be applicable over a wider range in quark masses than previously thought, and we discuss some open questions in this context. Furthermore, we observe that within the current lattice data uncertainties the extrapolations presented here are consistent with the Pade fit ansatz introduced by the Adelaide group a few years ago.

Figures (7)

• Figure 1: Diagrams contributing to the anomalous magnetic moment of the nucleon at leading-one-loop order.
• Figure 2: Pion mass dependence of the isovector anomalous magnetic moment in nuclear magnetons. The curves shown denote the standard NLO Heavy Baryon ChPT (dashed line, scheme A, see Eq.(\ref{['sa']})) and the NLO Small Scale Expansion calculation (dot-dashed line, scheme B, see Eq.(\ref{['sb']})). The solid line denotes the LO Relativistic BChPT result discussed in Appendix \ref{['B']}. The lattice data are taken from Ref.adelaide. The physical $\kappa_v=3.706$ [n.m] is displayed by the full circle.
• Figure 3: Pion mass dependence of the isovector anomalous magnetic moment in nuclear magnetons. The full curve denotes the NLO calculation in the modified expansion scheme C of Eq.(\ref{['sc']}). The lattice data are taken from Ref.adelaide. The physical $\kappa_v=3.706$ [n.m] is displayed by the full circle.
• Figure 4: Pion mass dependence of the isoscalar anomalous magnetic moment in nuclear magnetons. The full curve represents the suggested pion mass dependence of the modified expansion scheme C of Eq.(\ref{['eq:kappascalar']}). The lattice data are taken from Ref.adelaide. The physical $\kappa_s=-0.1202$ [n.m] is displayed by the full circle.
• Figure 5: Pion mass dependence of the magnetic moments of proton (upper curves) and neutron (lower curves) in nuclear magnetons. The full curve represents the best fit in the modified expansion scheme, whereas the dashed curve denotes the Pade extrapolation formula Eq.(\ref{['eq:pade']}). Our error estimate is given by the dotted curves. The lattice data are taken from Ref.adelaide. The physical values $\mu_p=2.793$ [n.m], $\mu_n=-1.913$ [n.m] are displayed by the full circles.