Magnetic structure of light nuclei from lattice QCD

Emmanuel Chang
Martin J. Savage
William Detmold
Kostas Orginos, College of William and Mary

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 < = 4, along with the cross section for the M1 transition np - > d gamma, at the flavor SU(3)-symmetric point where the pion mass is m(pi) similar to 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 article [S. Beane et al., Phys. Rev. Lett. 113, 252001 (2014)]. For the charged states, the extraction of the polarizability requires careful treatment of Landau levels, which enter nontrivially in the method that is employed. The nucleon polarizabilities are found to be of similar magnitude to their physical values, with beta(p) = 5.22((+0.66)(-0.45))(0.23) x 10(-4) fm(3) and beta(n) = 1.253((+0.056)(-0.067))(0.055) x 10(-4) fm(3), exhibiting a significant isovector component. The dineutron is bound at these heavy quark masses, and its magnetic polarizability, beta(nn) = 1.872((+0.121)(-0.113))(0.082) x 10(-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) = +/- 1 deuteron states and is found to be beta(d, +/- 1) = 4.4((+1.6)(-1.5))(0.2) x 10(-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, beta(3He) = 5.4((+2.2)(-2.1))(0.2) x 10(-4) fm(3), beta(3H) = 2.6(1.7)(0.1) x 10(-4) fm(3), and beta(4He) = 3.4((+2.0)(-1.9))(0.2) x 10(-4) fm(3). Mixing between the j(z) = 0 deuteron state and the spin-singlet np state induced by the background magnetic field is used to extract the short-distance two-nucleon counterterm, (L) over bar (1), of the pionless effective theory for NN systems (equivalent to the meson-exchange current contribution in nuclear potential models) that dictates the cross section for the np - > d gamma 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.