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From 1310.6 × 10 6 J=ψ and 448.1 × 10 6 ψð3686Þ events collected with the BESIII experiment, we report the first observation of Σ þ andΣ − spin polarization in e þ e − → J=ψ½ψð3686Þ → Σ þΣ− decays. The relative phases of the form factors ΔΦ have been measured to be ð−15.5 AE 0.7 AE 0.5Þ°and ð21.7 AE 4.0 AE 0.8Þ°with J=ψ and ψð3686Þ data, respectively. The nonzero value of ΔΦ allows for a direct and simultaneous measurement of the decay asymmetry parameters of Σ þ → pπ 0 ðα 0 ¼ −0.998 AE 0.037 AE 0.009Þ andΣ − →pπ 0 ðᾱ 0 ¼ 0.990 AE 0.037 AE 0.011Þ, the latter value being determined for the first time. The average decay asymmetry, ðα 0 −ᾱ 0 Þ=2, is calculated to be −0.994 AE 0.004 AE 0.002. The CP asymmetry A CP;Σ ¼ ðα 0 þᾱ 0 Þ=ðα 0 −ᾱ 0 Þ ¼ −0.004 AE 0.037 AE 0.010 is extracted for the first time, and is found to be consistent with CP conservation.

Though immensely successful, the standard model of particle physics does not offer any explanation as to why our Universe contains so much more matter than antimatter. A key to a dynamically generated matter–antimatter asymmetry is the existence of processes that violate the combined charge conjugation and parity (CP) symmetry1. As such, precision tests of CP symmetry may be used to search for physics beyond the standard model. However, hadrons decay through an interplay of strong and weak processes, quantified in terms of relative phases between the amplitudes. Although previous experiments constructed CP observables that depend on both strong and weak phases, we present an approach where sequential two-body decays of entangled multi-strange baryon–antibaryon pairs provide a separation between these phases. Our method, exploiting spin entanglement between the double-strange Ξ− baryon and its antiparticle2$${\bar{{\Xi }}}^{+}$$ Ξ ¯ + , has enabled a direct determination of the weak-phase difference, (ξP − ξS) = (1.2 ± 3.4 ± 0.8) × 10−2 rad. Furthermore, three independent CP observables can be constructed from our measured parameters. The precision in the estimated parameters for a given data sample size is several orders of magnitude greater than achieved with previous methods3. Finally, we provide an independent measurement of the recently debated Λ decay parameter αΛ (refs. 4,5). The $${\Lambda }\bar{{\Lambda }}$$ Λ Λ ¯ asymmetry is in agreement with and compatible in precision to the most precise previous measurement4.