Magnetic structure of light nuclei from lattice QCD

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 M 1 transition np → dγ, at the flavor SU(3)-symmetric point where the pion mass is mπ ∼ 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 [1]. 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 βp = 5.22 Mixing between the jz = 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,L1, 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 np → dγ 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.

Baryons as relativistic three-quark bound states

“…[644][645][646][647][648][649] and Refs. therein, the main theoretical tools to address CS are 'hadronic' descriptions such as chiral perturbation theory, which provides a systematic expansion of the CS amplitude at low energies and low momenta, and dispersion relations which establish a direct link to experimental data.…”

Unitary Limit of Two-Nucleon Interactions in Strong Magnetic Fields

“…In this work, the numerical technique of lattice QCD (LQCD) is applied to study two-nucleon systems in uniform, time-independent background magnetic fields, following methods used in previous studies of the magnetic moments [10] and polarizabilities [11] of nucleons and light nuclei up to atomic number A ¼ 4. To understand the phenomenological effects of the strong fields in nuclear environments, a first task is to ascertain the effects on the two-nucleon interactions.…”

“…States with the quantum numbers of h ¼ n, p, nn, pp, d jj z j¼1 are accessed from correlation functions C h ðt; BÞ ¼ h0jχ h ðtÞχ h ð0Þj0i B computed in the presence of the background magnetic field B from source and sink interpolating operators with the requisite quantum numbers, as discussed in detail in Ref. [11]. Representative correlation functions for the heavier mass ensemble can be found in Ref.…”

“…Representative correlation functions for the heavier mass ensemble can be found in Ref. [11] for each hadron or nucleus and background magnetic field. Ratios of these correlation functions to those without the magnetic field, R h ðt; BÞ ≡ C h ðt; BÞ=C h ðt; 0Þ, are also shown in Ref.…”

“…Ratios of these correlation functions to those without the magnetic field, R h ðt; BÞ ≡ C h ðt; BÞ=C h ðt; 0Þ, are also shown in Ref. [11], and are used to extract the magnetic moments and polarizabilities of the respective systems. For the m π ∼ 450 MeV ensemble, the ratios behave in a qualitatively similar manner and the signals are of comparable quality.…”