Wigner multiplets in QFT: dark sector and CPT-violating scenarios

Abstract: The classification of elementary particles based on unitary irreducible representations of the Poincare group has been a cornerstone of modern Quantum Field Theory (QFT). While the Standard Model (SM) does not inherently include Dark Matter (DM), any fundamental DM candidate should still conform to this classification or its extensions. Beyond the standard representations, Wigner introduced a class of nontrivial states characterized by an additional discrete degree of freedom, known as the Wigner degeneracy. We systematically investigate the QFT of such Wigner degenerate multiplets, particularly focusing on the massive spin-1/2 case. We construct a theoretical framework where the two-fold Wigner spinor fields, $\psi_{\pm\frac{1}{2}}(x)$, form a doublet representation. We analyze their transformation properties under discrete symmetries (C, P, and T), revealing novel mixing effects due to Wigner degeneracy and an emergent accidental U(2) global symmetry. Furthermore, we explore their Yukawa and gauge interactions, demonstrating that such interactions generally break the CPT symmetry. However, we derive conditions for the CPT conservation and discuss potential phenomenological consequences beyond the SM. These results provide new insights into the possible role of Wigner-degenerate states in fundamental physics, particularly in the dark sector.