Spin correlations and consequences of quantum-mechanical coherence

Abstract

The difference in the properties of the spin correlation tensor for factorizable and nonfactorizable two-particle states is analyzed. The inequalities for linear combinations of the components of this tensor are obtained for the case of incoherent mixtures of factorizable two-particle spin states. They include the well known Bell inequalities and can be violated for coherent superpositions of two-particle spin states. The possibility to verify the consequences of the quantum-mechanical coherence is discussed using the angular correlations in the asymmetric (parity violating) decays of the pairs of spin-1/2 particles (muons, top-quarks or Λ-hyperons), the coherence arising either from the production dynamics or due to the effect of quantum statistics.

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]:…”

“…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…”

“…Correlations at the joint registration of the decays Λ → p + π − and Λ →p + π + Due to CP invariance, the coefficients of P -odd angular asymmetry for the decays Λ → p + π − andΛ →p + π + have equal absolute values and opposite signs: αΛ = −α Λ = −0.642. The double angular distribution for this case is as follows [2,3] ( here −α Λ = +αΛ and −α 2 Λ = +α Λ αΛ ):…”