The Magnetic Structure of Light Nuclei from Lattice QCD

Emmanuel Chang; William Detmold; Kostas Orginos; Assumpta Parreno; Martin J. Savage; Brian C. Tiburzi; Silas R. Beane

doi:10.1103/PhysRevD.92.114502

paper

The Magnetic Structure of Light Nuclei from Lattice QCD

arXiv:1506.05518 · doi:10.1103/PhysRevD.92.114502

Abstract

Lattice QCD with background magnetic fields is used to calculate the magnetic moments and magnetic polarizabilities of the nucleons and of light nuclei with $A \leq 4$ , along with the cross-section for the $M 1$ transition $n p \to d γ$ , at the flavor SU(3)-symmetric point where the pion mass is $m_{π} \sim 806$ MeV. These magnetic properties are extracted from nucleon and nuclear energies in six uniform magnetic fields of varying strengths. The magnetic moments are presented in a recent Letter. For the charged states, the extraction of the polarizability requires careful treatment of Landau levels, which enter non-trivially in the method that is employed. The nucleon polarizabilities are found to be of similar magnitude to their physical values, with $β_{p} = 5.22 (+ 0.66/ - 0.45) (0.23) \times 1 0^{- 4}$ fm $^{3}$ and $β_{n} = 1.253 (+ 0.056/ - 0.067) (0.055) \times 1 0^{- 4}$ fm $^{3}$ , exhibiting a significant isovector component. The dineutron is bound at these heavy quark masses and its magnetic polarizability, $β_{nn} = 1.872 (+ 0.121/ - 0.113) (0.082) \times 1 0^{- 4}$ fm $^{3}$ differs significantly from twice that of the neutron. A linear combination of deuteron scalar and tensor polarizabilities is determined by the energies of the $j_{z} = \pm 1$ deuteron states, and is found to be $β_{d, \pm 1} = 4.4 (+ 1.6/ - 1.5) (0.2) \times 1 0^{- 4}$ fm $^{3}$ . The magnetic polarizabilities of the three-nucleon and four-nucleon systems are found to be positive and similar in size to those of the proton, $β_{^{3} He} = 5.4 (+ 2.2/ - 2.1) (0.2) \times 1 0^{- 4}$ fm $^{3}$ , $β_{^{3} H} = 2.6 (1.7) (0.1) \times 1 0^{- 4}$ fm $^{3}$ , $β_{^{4} He} = 3.4 (+ 2.0/ - 1.9) (0.2) \times 1 0^{- 4}$ fm $^{3}$ . Mixing between the $j_{z} = 0$ deuteron state and the spin-singlet $n p$ state induced by the background magnetic field is used to extract the short-distance two-nucleon counterterm, $L ˉ_{1}$ , of the pionless effective theory for $N N$ systems (equivalent to the meson-exchange current contribution in nuclear potential models), that dictates the cross-section for the $n p \to d γ$ process near threshold. Combined with previous determinations of NN scattering parameters, this enables an ab initio determination of the threshold cross-section at these unphysical masses.

49 pages, 24 figures

The Magnetic Structure of Light Nuclei from Lattice QCD

Abstract

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