Electromagnetic characteristics of $A \leq 3$ physical and lattice nuclei

Abstract

We analyze the quark-mass dependence of electromagnetic properties of two and three-nucleon states. To that end, we apply the pionless effective field theory to experimental data and numerical lattice calculations which simulate QCD at pion masses of 450~MeV and 806~MeV. At the physical pion mass, we postdict the magnetic moment of helium-3, $\mu_{^3He}=-2.13~$nNM, and the magnetic polarizability of deuterium, $\beta_D=7.33~10^{-2}~$fm$^3$. Magnetic polarizabilities of helium-3, $\beta_{^3He}=9.7~10^{-4}~$fm$^3$, and the triton, $\beta_{^3H}=8.2~10^{-4}~$fm$^3$, are predictions. Postdictions of the effective theory for the magnetic moments are found consistent with QCD simulations at 806~MeV pion mass while our EFT result $\beta_D=2.92~10^{-2}~$fm$^3$ was not extracted from the lattice. The deuteron would thus be relatively pliable compared to a three-nucleon state for which we postdict $\beta_{^3H}=3.9~10^{-5}~$fm$^3$. At $m_\pi=450~$MeV, the magnetic moment of the triton is predicted, $\mu_{^3He}=-2.15(5)~$nNM, based on a conjecture of its binding energy, $B_{^3H}\cong 30$~MeV. For all three pion masses, we compare the point-charge radii of the two and three-nucleon bound states. The sensitivity of the electromagnetic properties to the Coulomb interaction between protons is studied in anticipation of lattice calculations with dynamical QED.