Magnetic polarisability of the nucleon using a Laplacian mode projection

Abstract

Conventional hadron interpolating fields, which utilise 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 $SU(3)\times U(1)$ 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 provides the enhanced hadronic energy-eigenstate isolation necessary for calculation of nucleon energy shifts in a magnetic field. The magnetic polarisability of both the proton and neutron is calculated using this method on the $32^3\times 64$ 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 polarisabilities of ${\beta }^p=2.79(22)({}_{-18}^{+13})\times 10^{-4}$ fm${}^3$ and ${\beta }^n=2.06(26)({}_{-20}^{+15})\times 10^{-4}$ fm${}^3$, where the numbers in parantheses describe statistical and systematic uncertainties.

Comments: 16 Pages, Version published in Phys. Rev. D