Quark mass dependence of the vacuum electric conductivity induced by the magnetic field in SU(2) lattice gluodynamics

We study the electric conductivity induced by the magnetic field B in quenched SU(2) lattice gauge theory at a finite temperature below the deconfinement phase transition as a function of the bare quark mass m(q) in the range m(q) = 55MeV ... 540 MeV. At fixed quark mass, the conductivity grows linearly with the magnetic field strength vertical bar B vertical bar. The proportionality coefficient in this dependence increases towards smaller quark masses and seems to saturate at some finite value in the zero-mass limit. The nonanalytic dependence on the field strength might result from the mixing between vector mesons and pions in an external magnetic field. We discuss the implications of our results for dilepton angular distributions in heavy-ion collisions.