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

TL;DR

This paper explores the theoretical framework of Wigner degenerate multiplets in quantum field theory, revealing novel symmetry properties and potential CPT violation, with implications for dark matter and physics beyond the Standard Model.

Contribution

It systematically develops the QFT of Wigner degenerate multiplets, analyzing their symmetries, interactions, and conditions for CPT conservation, especially for massive spin-1/2 particles.

Findings

Wigner degeneracy introduces an emergent U(2) symmetry.

Interactions can break CPT symmetry under certain conditions.

Potential implications for dark sector physics and beyond Standard Model 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.