A new CPT-even and Lorentz-Violating nonminimal coupling in the Dirac   equation
  In this work, we propose a CPT-even and Lorentz-violating dimension-five nonminimal coupling between fermionic and gauge fields, involving the CTP-even and Lorentz-violating gauge tensor of the SME. This nonminimal coupling modifies the Dirac equation, whose nonrelativistic regime is governed by a Hamiltonian which induces new effects, such as an electric-Zeeman-like spectrum splitting and an anomalous-like contribution to the electron magnetic moment, between others. Some of these new effects allows to constrain the magnitude of this nonminimal coupling in 1 part in 10^16. 
R. Casana, M. M. Ferreira Jr, E. O. Silva, E. Passos, F. E. P. dos   Santos
hep-th