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 SU(3)×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 323×64 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 βp=2.79(22)( +13−18)×10−4 fm3 and βn=2.06(26)( +15−20)×10−4 fm3, where the numbers in parentheses describe statistical and systematic uncertainties.