NewCPT-even and Lorentz-violating nonminimal coupling in the Dirac equation

Abstract

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 .

New effects in the interaction between electromagnetic sources mediated by nonminimal Lorentz violating interactions

“…The SME constitutes a quite general framework that facilitates investigations on the breaking of Lorentz and CPT symmetries. Theoretical aspects of LV have been investigated in Maxwell electrodynamics [7][8][9][10][11], QCD [12], gravity [13,14], noncommutative theories [15], statistical mechanics [16], QED [17][18][19][20], supersymmetry [21][22][23][24], electromagnetic wave propagation [25][26][27], to name a few. Experimental tests of LV have been performed in experiments involving photons [28,29], electrons [30,31], muons [32,33], and many others [3].…”

Constraining CPT -odd nonminimal interactions in the electroweak sector

“…Such a coupling has been addressed in numerous aspects [25], including the radiative generation of CP T -odd LV terms [26], topological phases [27], [28], and generation of electric dipole moment [29]. Dimension-five CP T -even NMCs were also proposed in the context of the Dirac equation [30], [31], [32], with MDM and EDM experimental measurements being used to state upper bounds at the level of 1 part in 10 20 (eV) −1 and 10 24 (eV) −1 , respectively. A systematic investigation on NMCs of dimension five and six was recently proposed in Ref.…”

He–McKellar–Wilkens-type effect, quantum holonomies and Aharonov–Bohm-type effect for bound states from the Lorentz symmetry breaking effects

“…We show that analogues of the Anandan quantum phase [17,18] and the He-McKellar-Wilkens effect [19] can be obtained from the effects of the violation of the Lorentz symmetry. Recently, a non-minimal coupling has been introduced in the fermionic sector whose property is that a tensor governs the Lorentz symmetry violation in the CPT-even gauge sector of the Standard Model Extension [28,29]. The coupling suggested allow us to write the Dirac equation in the form:…”