Bypassing spin-analyzing power dependence for quantum entanglement at colliders: a case study of Λ Λ̄

A bstract We study, as a concrete case study using the Λ (→ pπ⁻)Λ̄(→ p̄π⁺) Λ → p π − Λ ¯ → p ¯ π + system, whether quantum entanglement in fermion pairs produced at colliders can be certified solely using angular information from final-state decays, while remaining independent of the parity-violating decay parameters α Λ and αΛ̄ α Λ ¯ . Building on a general decomposition of any angular observable in terms of Wigner d-functions, we show that the expectation value must take the form O₀+O₁αΛ+O₂αΛ̄+O₃αΛαΛ̄ O 0 + O 1 α Λ + O 2 α Λ ¯ + O 3 α Λ α Λ ¯ , with coefficients 𝒪 i ( i = 0 , 1 , 2 , 3) linear in the spin-density matrix elements αk,jαm,n α k , j α m , n ∗ . We obtain the value ranges of observables over the general and separable spaces of α k,j , and demonstrate a sufficient entanglement condition for pure states, extending it to mixed states by convexity. In constructing an α Λ - and αΛ̄ α Λ ¯ -independent witness from angular observables alone, we find that there are obstacles to probe quantum entanglement via the inequality-type and ratio-type ways. In particular, for the ratio-type criterion 〈 A 〉/〈 B 〉, the presence of zeros of 〈 B 〉 in both the general and separable spaces of αk,j(k,j=± 1/2) α k , j k j = ± 1 2 </jats:in