Susceptibility of the QCD Vacuum to CP-Odd Electromagnetic Background Fields

We investigate two flavor quantum chromodynamics (QCD) in the presence of CP-odd electromagnetic background fields and determine, by means of lattice QCD simulations, the induced effective theta term to first order in (E) over right arrow . (B) over right arrow. We employ a rooted staggered discretization and study lattice spacings down to 0.1 fm and Goldstone pion masses around 480 MeV. In order to deal with a positive measure, we consider purely imaginary electric fields and real magnetic fields, and then exploit the analytic continuation. Our results are relevant to a description of the effective pseudoscalar quantum electrodynamics-QCD interactions. DOI: 10.1103/PhysRevLett.110.082002