General Electromagnetic Nonminimal Couplings in the Dirac Equation

Abstract

We examine a new class of CPT-even and dimension-five nonminimal interactions between fermions and photons, deprived of higher-order derivatives, yielding electric dipole moment and magnetic dipole moment in the context of the Dirac equation. These couplings are Lorentz-violating nonminimal structures, composed of a rank-2 tensor, the electromagnetic tensor, and gamma matrices, being addressed in its axial and non-axial hermitian versions. We use the electron's anomalous magnetic and electric dipole moment measurements to reach upper bounds of 1 part in 10 11 and 10 16 GeV −1 .The Standard Model (SM) structure allows for C, P, and T violations (and combinations) as long as CPT symmetry is preserved. Among the most important tests for physics beyond the SM is the search for the electric dipole moment (EDM) of particles in connection with the strong CP problem.1,2 The EDM nonrelativistic interaction term has the form d(σ · E), with E, σ and d as the electric field, the spin operator, and the EDM modulus, respectively. This interaction violates both P and T symmetries, P (σ ·E) → −(σ ·E), T (σ·E) → −(σ·E), but preserves C and CPT symmetries. Lorentz-violating nonminimal couplings in the context of the Dirac equation that engender EDM at tree level can be stringently constrained by EDM data.3-5 Theories endowed with Lorentz violation are a possible route for physics beyond SM that has been intensively studied in the latest years, mainly in the context of the Standard-Model Extension (SME). 6,7Connections between LV theories and EDM physics have been addressed in Ref. 8. In this work, a new class of dimension-five nonminimal couplings is proposed and examined with respect to the possible generation of an EDM and magnetic dipole moment (MDM), 9 having the hermiticity as the main criterion to be observed.