Violation of Time Reversal Invariance in the Decays K_L -> pi^+ pi^- gamma and K_L -> pi^+ pi^- e^+ e^-

TL;DR

This paper investigates the CP- and T-violating asymmetries in K_L decays, linking them to photon polarization properties, and demonstrates genuine T-symmetry breaking within a CPT-invariant framework.

Contribution

It reveals the polarization-based origin of observed asymmetries and shows T-violation persists even without unitarity phases, a novel insight into symmetry breaking.

Findings

Photon polarization components S_1 and S_2 are sizable across phase space.

S_2 corresponds to circular polarization, S_1 to asymmetry in decay.

T-violation persists in the hermitian limit without unitarity phases.

Abstract

The origin of the large CP-odd and T-odd asymmetry observed in the decay K_L -> pi^+ pi^- e^+ e^- is traced to the polarization properties of the photon in the decay K_L -> pi^+ pi^- gamma. The Stokes vector of the photon S = (S_1, S_2, S_3) is studied as a function of the photon energy and found to possess CP-violating components S_1 and S_2 which are sizeable over a large part of the phase space, despite being proportional to the epsilon parameter of the K_L wave function. The component S_2 is T-even and manifests itself as a circular polarization of the photon, while S_1 is T-odd and gives rise to the asymmetry observed in K_L -> pi^+ pi^- e^+ e^-. The latter is shown to survive in the ``hermitian'' limit in which all unitarity phases are absent, and represents a genuine example of time reversal symmetry breaking in a CPT invariant theory.