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

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.

Comments: 10 pages, no figure, published version