Possible Effect of Mixed Phase and Deconfinement upon Spin Correlations in the \(\Lambda \bar{\Lambda }\) Pairs Generated in Relativistic Heavy-Ion Collisions

Abstract

Spin correlations for the ΛΛ and ΛΛ pairs, generated in relativistic heavy-ion collisions, and related angular correlations at the joint registration of space-parity nonconserving hadronic decays of two hyperons are theoretically analyzed. The correlation tensor components can be derived from the double angular distribution of products of two decays by the method of "moments" . The properties of the "trace" T of the correlation tensor ( a sum of three diagonal components ), determining the angular correlations as well as the relative fractions of the triplet states and singlet state of respective pairs, are discussed. Spin correlations for two identical particles (ΛΛ) and two non-identical particles (ΛΛ) are considered from the viewpoint of the conventional model of one-particle sources. Within this model, correlations vanish at sufficiently large relative momenta. However, under these conditions, for two nonidentical particles (ΛΛ) a noticeable role is played by two-particle annihilation sourcestwo-quark ( i.e. quark-antiquark ) and two-gluon ones, which lead to the difference of the correlation tensor from zero. In particular, such a situation may arise, when the system passes through the "mixed phase" and -due to the multiple production of free quarks and gluons in the process of deconfinement -the number of two-particle sources strongly increases.KEYWORDS: spin correlations, ΛΛ and ΛΛ pairs, angular correlations, P -odd hadronic decays, correlation tensor, heavy-ion collisions, two-quark and two-gluon sources, "mixed phase" General structure of the spin density matrix of the pairs ΛΛ and ΛΛSpin correlations for ΛΛ and ΛΛ pairs, produced in relativistic heavy-ion collisions, and related angular correlations at the joint registration of space-parity nonconserving hadronic decays of two hyperons provide important information on the character of multiple processes.The spin density matrix of the ΛΛ and ΛΛ pairs, just as the spin density matrix of two spin-1/2 particles in general, can be presented in the following form [1][2][3]:in doing so, tr (1,2)ρ (1,2) = 1. HereÎ is the two-row unit matrix,σ = (σ x ,σ y ,σ z ) is the vector Pauli operator ( x, y, z → 1, 2, 3 ), P 1 and P 2 are the polarization vectors of the first and second particle ( P 1 = ⟨σ (1) ⟩, P 2 = ⟨σ (2) ⟩ ), T ik = ⟨σ (1) i ⊗σ (2) k ⟩ are the correlation tensor components. In the general case T ik ̸ = P 1i P 2k . The tensor with components C ik = T ik − P 1i P 2k describes the spin correlations of two particles.