Study of CP violation in hyperon decays at super-charm-tau factories with a polarized electron beam

Abstract

Nonleptonic two-body weak decays of baryons are an important tool to probe the combined charge conjugation--parity symmetry ($CP$) violation. We explain why the decays of strange baryons provide complementary information to the decays of kaons. A model-independent parametrization of the nonleptonic decays of the $\mathrm{\ensuremath{\Lambda}}$ and $\mathrm{\ensuremath{\Xi}}$ baryons is reviewed, and the amplitudes are updated according to the latest experimental input. We demonstrate the potential of performing precision tests in strange baryon decays at the next-generation electron-positron $J/\ensuremath{\psi}$ factories with luminosity of ${10}^{35}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. The copious production of spin-entangled hyperon-antihyperon pairs via the $J/\ensuremath{\psi}$ resonance allows for a direct comparison of the baryon and antibaryon decay properties. Using analytic approximations and numerical calculations, we study the quantitative impact of spin correlations and polarization in such $CP$ tests. We show that by using a longitudinally polarized electron beam the statistical precision of the $CP$ tests can be significantly improved compared to the experiments without polarized beams. Furthermore, we map out further directions for possible improvements, like analysis of incompletely reconstructed events or a combination of the isospin related processes. Altogether, these methods are promising for the observation of a statistically significant $CP$-violation signal with a strength corresponding to the standard model predictions. Our conclusions should encourage more detailed feasibility studies, including optimization of the measurement methods and studies of systematic effects. Finally, our results call for an update of the theory predictions with increased precision.