Magnetic Moments of Light Nuclei from Lattice Quantum Chromodynamics

We present the results of lattice QCD calculations of the magnetic moments of the lightest nuclei, the deuteron, the triton, and ${}^3\mathrm{He}$, along with those of the neutron and proton. These calculations, performed at quark masses corresponding to $m_{\pi }\sim 800\text{MeV}$, reveal that the structure of these nuclei at unphysically heavy quark masses closely resembles that at the physical quark masses. In particular, we find that the magnetic moment of ${}^3\mathrm{He}$ differs only slightly from that of a free neutron, as is the case in nature, indicating that the shell-model configuration of two spin-paired protons and a valence neutron captures its dominant structure. Similarly a shell-model-like moment is found for the triton, ${\mu }_{{}^3\mathrm{H}}\sim {\mu }_p$. The deuteron magnetic moment is found to be equal to the nucleon isoscalar moment within the uncertainties of the calculations. Furthermore, deviations from the Schmidt limits are also found to be similar to those in nature for these nuclei. These findings suggest that at least some nuclei at these unphysical quark masses are describable by a phenomenological nuclear shell model.

Figure 1

The correlator ratios $R(B)$ as a function of time slice for the various states ($p$, $n$, $d$, ${}^3\mathrm{He}$, and ${}^3\mathrm{H}$) for $\tilde{n}=+1,-2,+4$. Fits to the ratios are also shown.

Figure 2

The calculated $\delta E^{(B)}$ of the proton and neutron (upper panel) and light nuclei (lower panel) in lattice units as a function of $|\tilde{n}|$. The shaded regions corresponds to fits of the form $\delta E^{(B)}=-2\mu |\mathbf{B}|+\gamma |\mathbf{B}{|}^3$ and their uncertainties. The dashed lines correspond to the linear contribution alone.

Figure 3

The magnetic moments of the proton, neutron, deuteron, ${}^3\mathrm{He}$, and triton. The results of the lattice QCD calculation at a pion mass of $m_{\pi }\sim 806\mathrm{MeV}$, in units of natural nuclear magnetons ($e/2M_N^{\text{latt}}$), are shown as the solid bands. The inner bands corresponds to the statistical uncertainties, while the outer bands correspond to the statistical and systematic uncertainties combined in quadrature, and include our estimates of the uncertainties from lattice spacing and volume. The red dashed lines show the experimentally measured values at the physical quark masses.

Figure 4

The differences between the nuclear magnetic moments and the predictions of the naive shell model. The results of the lattice QCD calculation at a pion mass of $m_{\pi }\sim 806\mathrm{MeV}$, in units of natural nuclear magnetons ($e/2M_N^{\text{latt}}$), are shown as the solid bands. The inner band corresponds to the statistical uncertainties, while the outer bands correspond to the statistical and systematic uncertainties combined in quadrature, including estimates of the uncertainties from lattice spacing and volume. The red dashed lines show the experimentally measured differences.