T invariance and polarization effects in the reactions p+3He → π++4He and π++4He → p+3He

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

“…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]:…”

“…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 ( (1) i ⊗σ (2) k ⟩ are the correlation tensor components. In the general case T ik ̸ = P 1i P 2k .…”

“…So, the decay Λ → p + π − selects the projections of spin of the Λ particle onto the direction of proton momentum, and the analyzing power equals ξ = α Λ n. Now let us consider the double angular distribution of flight directions for protons formed in the decays of two Λ particles into the channel Λ → p + π − , normalized by unity ( the analyzing powers are ξ 1 = α Λ n 1 , ξ 2 = α Λ n 2 ). It is described by the following formula [2,3]:…”

“…frame of the pair ( i, k = {1, 2, 3} = {x, y, z} ). All the polarization parameters (components of the polarization vectors and the correlation tensor components) can be derived by the method of "moments" -as a result of averaging the combinations of trigonometric functions of proton ( antiproton ) flight angles over the double angular distribution of flight directions for products of two decays [2,3].…”

“…The angular correlation, integrated over all angles except the angle θ between the vectors n 1 , n 2 and described by the formula [2][3][4][5] d w(cos θ) = 1 2…”