Eigenmode Projection Techniques for Magnetic Polarisabilities in Lattice QCD

Abstract

The magnetic polarisability of a selection of octet baryons and the pion are calculated using lattice QCD and the background field method. Results are from 32³ x 64 dynamical QCD gauge fields with 2 + 1 flavours provided by the PACS-CS collaboration through the International Lattice Data Grid (ILDG) . These use a clover fermion action and an Iwasaki gauge action with β = 1:9 providing a physical lattice spacing of a = 0:0907(13) fm. As the application of a uniform background magnetic field renders standard gauge covariant Gaussian smeared quark operators inefficient at isolating ground state hadron energy eigenstates at non-trivial field strengths, Landau level quark propagator projection techniques are created and utilised. First the two-dimensional U(1) Laplacian eigenmodes are considered. These describe the Landau levels of a charged particle on a finite periodic lattice. Using this eigenmode projection technique, the neutron ground state energy eigenstate is isolated and hence the magnetic polarisability of the neutron calculated. These results are used to inform a chiral effective field theory analysis to produce a prediction for the magnetic polarisability of the neutron at the physical point. The chiral analysis incorporates both finite-volume effects and sea-quark-loop contributions. Wilson-like fermion actions are exposed to additive mass renormalisations; when a background magnetic field is introduced, the Wilson term causes a field-dependent renormalisation to the quark mass. This quark mass renormalisation is studied using the neutral pion mass. Herein, the clover fermion action is investigated to determine the extent to which the O(a) removal of errors suppresses the field-dependent quark mass changes. We demonstrate how a careful treatment of the nonperturbative-improvement of the clover term is required to resolve this artefact of the Wilson term. Motivated by the success of the U(1) eigenmode-projected quarkpropagator technique, a new technique utilising eigenmodes of the SU(3) x U(1) Laplacian is considered. Here both QCD and background magnetic field effects are included in the quark propagator projection. This technique is used to calculate proton, neutron, Σ⁺ and Ξ⁰ two-point correlation functions in a background magnetic field. From these, the magnetic polarisability is calculated at several quark masses enabling a chiral effective field theory analysis. The chiral effective field theory techniques established for the neutron’s magnetic polarisability are extended to the other baryons considered herein and the results are compared. Finally, using the analysis and methods of the SU(3) x U(1) quark propagator projection technique and improved clover-fermion action, the pion sector is investigated. Results for the magnetic polarisability of both the charged and neutral pions are presented. For the first time, the relativistic energy shift is used to determine the magnetic polarisabilities.