Abstract
The application of a uniform background magnetic field makes standard quark operators utilising gauge-covariant Gaussian smearing inefficient at isolating the ground state nucleon at nontrivial field strengths. In the absence of QCD interactions, Landau modes govern the quark energy levels. There is evidence that residual Landau mode effects remain when the strong interaction is turned on. Here we introduce novel quark operators constructed from the two-dimensional $U(1)$ Laplacian eigenmodes that describe the Landau levels of a charged particle on a periodic finite lattice. These eigenmode-projected quark operators provide enhanced precision for calculating nucleon energy shifts in a magnetic field. Using asymmetric source and sink operators, we are able to encapsulate the predominant effects of both the QCD and QED interactions in the interpolating fields for the neutron. The neutron magnetic polarizability is calculated using these techniques on the $32^3 \times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. In conjunction with a chiral effective-field theory analysis, we obtain a neutron magnetic polarizability of $\beta^n = 2.05(25)(19) \times 10^{-4}$ fm$^3$, where the numbers in parentheses describe statistical and systematic uncertainties.
Highlights
The study of the magnetic polarizability of the neutron is an area of ongoing experimental and theoretical interest
The neutron magnetic polarizability has been calculated using a novel approach in which asymmetric operators are used at the source and sink
The use of gaugeinvariant Gaussian smearing at the source encapsulates the dominant QCD dynamics, while a gauge-fixed Uð1Þ two-dimensional eigenmode projection technique is used at the sink to encode the Landau level physics resulting from the presence of the uniform magnetic field
Summary
The study of the magnetic polarizability of the neutron is an area of ongoing experimental and theoretical interest. Baryon correlation functions suffer from a rapidly decaying signal-to-noise problem [13] This makes the extraction of the magnetic polarizability using standard nucleon interpolating fields challenging as it appears at second order in the energy expansion, as demonstrated by previous studies [7,9,10,11]. The application of three-dimensional gauge-covariant Gaussian smearing on the quark fields at the source and/or sink is highly effective at isolating the nucleon ground state in pure QCD calculations. Under a uniform magnetic field, in the absence of QCD interactions, each quark will have a Landau energy proportional to its charge. When QCD interactions are enabled, the quarks will hadronize, such that (in the confining phase) the Landau energy corresponds to that of the composite particle. Calculations are performed at multiple quark masses in order to enable a chiral extrapolation to the physical regime
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