Triple product asymmetries in K, D_(s) and B_(s) decays

TL;DR

This paper analyzes true and fake triple product asymmetries in various meson decays, providing theoretical expressions, discussing conditions for non-zero asymmetries, and applying results to specific B meson decay modes.

Contribution

It extends the theoretical framework for TP asymmetries to B decays with time dependence and applies it to experimental data, highlighting conditions for observable CP violation.

Findings

TP asymmetries vanish for identical final-state particles.

Non-zero TP asymmetries can occur with non-trivial kinematic correlations.

Time-integrated true CP asymmetries are not suppressed by mixing parameters.

Abstract

One distinguishes between "true" CP violating triple product (TP) asymmetries which require no strong phases and "fake" asymmetries which are due to strong phases but require no CP violation. So far a single true TP asymmetry has been measured in $K_L\to \pi^+\pi^- e^+e^-$. A general discussion is presented for T-odd TP asymmetries in four-body decays. It is shown that TP asymmetries vanish for two identical and kinematically indistinguishable particles in the final state. Two examples are $D^0\to K^-\pi^+\pi^-\pi^+$ and $D^+\to K^-\pi^+\pi^+\pi^0$. A non-zero TP asymmetry can be expected when non-trivial kinematic correlations exist, as in the decay $K_L \to e^+ e^- e^+ e^-$. Triple product asymmetries measured in charmed particle decays indicate an interesting pattern of final-state interactions. We reiterate a discussion of TP asymmetries in $B$ meson decays to two vector mesons each decaying to a pseudoscalar pair, extending results to decays where one vector meson decays into a lepton pair. We derive expressions for time-dependent TP asymmetries for neutral B decays to flavorless states in terms of the neutral $B$ mass difference $\Delta m$ and the width-difference $\Delta\Gamma$. Time-integrated true CP violating asymmetries, measurable for untagged $B_s$ decays, are shown to be suppressed by neither $\Gamma_s/\Delta m_s$ nor $\Delta\Gamma_s/\Gamma_s$ if transversity amplitudes for CP-even and CP-odd states involve different weak phases. In contrast, fake asymmetries require flavor tagging and are suppressed by the former ratio when time-integrated. We apply our results to $B\to K^*\phi$ and $B_s\to\phi\phi$ data and suggest an application for $B_s\to J/\psi\phi$.