Electromagnetic characteristics of $A\le 3$ 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, ${\mu }_{{}^{3}He}=-2.13$nNM, and the magnetic polarizability of deuterium, ${\beta }_D=7.3310^{-2}$fm${}^3$. Magnetic polarizabilities of helium-3, ${\beta }_{{}^{3}He}=9.710^{-4}$fm${}^3$, and the triton, ${\beta }_{{}^{3}H}=8.210^{-4}$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 ${\beta }_D=2.9210^{-2}$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 ${\beta }_{{}^{3}H}=3.910^{-5}$fm${}^3$. At $m_{\pi }=450$MeV, the magnetic moment of the triton is predicted, ${\mu }_{{}^{3}He}=-2.15(5)$nNM, based on a conjecture of its binding energy, $B_{{}^{3}H}\cong 30$~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.

25 pages, 7 figures

References in corpus (4)

• Light Nuclei and Hypernuclei from Quantum Chromodynamics in the Limit of SU(3) Flavor Symmetry
• Power Counting of Contact-Range Currents in Effective Field Theory
• Effective Field Theory for Few-Boson Systems
• Octet Baryon Magnetic Moments from Lattice QCD: Approaching Experiment from a Three-Flavor Symmetric Point

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• Resolving the $\Lambda$ hypernuclear overbinding problem in pionless effective field theory
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• The onset of $\Lambda \Lambda$ hypernuclear binding
• Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory
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• Cold Neutron-Deuteron Capture and Wigner-SU(4) Symmetry
• Effective field theory analysis of boson-trimer bond lengths to next-to-leading order
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