Magnetic polarizability of the nucleon using a Laplacian mode projection

Abstract

Conventional hadron interpolating fields, which utilize gauge-covariant Gaussian smearing, are ineffective in isolating ground state nucleons in a uniform background magnetic field. There is evidence that residual Landau-mode physics remains at the quark level, even when QCD interactions are present. In this work, quark-level projection operators are constructed from the $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ eigenmodes of the two-dimensional lattice Laplacian operator associated with Landau modes. These quark-level modes are formed from a periodic finite lattice where both the background field and strong interactions are present. Using these eigenmodes, quark-propagator projection operators provide the enhanced hadronic energy-eigenstate isolation necessary for calculation of nucleon energy shifts in a magnetic field. The magnetic polarizability of both the proton and neutron is calculated using this method on the ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ dynamical QCD lattices provided by the PACS-CS Collaboration. A chiral effective-field theory analysis is used to connect the lattice QCD results to the physical regime, obtaining magnetic polarizabilities of ${\ensuremath{\beta}}^{p}=2.79(22)({\text{ }}_{\ensuremath{-}18}^{+13})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{fm}}^{3}$ and ${\ensuremath{\beta}}^{n}=2.06(26)({\text{ }}_{\ensuremath{-}20}^{+15})\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}{10}^{\ensuremath{-}4}\text{ }\text{ }{\mathrm{fm}}^{3}$, where the numbers in parentheses describe statistical and systematic uncertainties.

Topics & Concepts