Is there a paradox in CP asymmetries of tau to K_{L,S} pi nu decays?

Abstract

Based on the description of unstable $K_{L,S}$ particles in quantum field theory (QFT), we compute the time-dependent probabilities for transitions between asymptotic states in $\tau^{\pm} \to [\pi^+\pi^-]_K\pi^{\pm}\nu$ decays, where the pair $[\pi^+\pi^-]_K$ is the product of (intermediate state) neutral kaon decays. Then we propose a definition of $\tau$ decays into $K_L$ and $K_S$ states, which reflects into the cancellation between their CP rate asymmetries, thus solving in a natural way the paradox pointed out previously in litterature. Since our definition of $K_{L,S}$ final states in $\tau$ decays is motivated on experimental grounds, our predictions for the integrated CP rate asymmetries can be tested in a dedicated experiment.