Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields

We investigate two flavor QCD in presence of CP-odd electromagnetic background fields and determine, by means of lattice QCD simulations, the induced effective theta term to the first order in the scalar product of E and B. 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, then exploiting analytic continuation. Our results are relevant to a description of the effective pseudoscalar QED-QCD interactions.