Testing of $P$ and $CP$ Symmetries with $e^+e^- \to J/\psi \to \Lambda\bar \Lambda$

TL;DR

This paper proposes a method to test $P$ and $CP$ symmetries in the process $e^+e^- o J/\psi o \Lambdaar \\Lambda$, deriving angular distributions and observables to distinguish symmetry violations, with estimations indicating current experiments can probe these effects.

Contribution

The paper introduces a novel set of observables for testing $P$ and $CP$ violations in $J/\psi$ decays, providing a framework for high-precision symmetry tests at future colliders.

Findings

BESIII can currently probe $P$-violation effects due to $Z$ exchange.

Proposed super-tau-charm factory can test SM predictions with higher precision.

Sensitivity to $CP$ violation related to the $\\Lambda$ electric dipole moment can be significantly improved.

Abstract

We propose to test $P$- and $CP$-symmetries with the process $e^+e^- \to J/\psi \to \Lambda\bar \Lambda$. The general form of the angular distribution of the process is derived and several observables for the proposed test are introduced. With these observables one can distinguish the effects of $P$-violations in the production of $J/\psi$ from its decay into a pair of $\Lambda \bar \Lambda$. Numerical estimations for proposed asymmetries of $P$-violation due to $Z$ exchange in SM are given. Our results show that BESIII has reached the sensitivity to probe these effects. At the proposed super-tau-charm factory with much enhanced luminosity it will be able to test the SM predictions with high precision. $CP$ violating effect in $J/\psi \to \Lambda \bar \Lambda$ can also be tested. In particular, BESIII data already reached the sensitivity to prove $CP$ violating effect due to current upper limit of electric dipole moment of $\Lambda$. At the proposed super-tau-charm factory the upper limit can be improved by an order of magnitude.