Joint Institute for Nuclear Research Relativistic ... - Index of - JINR

PAIR CORRELATIONS OF INTERNAL QUANTUM NUMBERS AND
ENTANGLED TWO-PARTICLE STATES
V.L. Lyuboshitz and V.V. Lyuboshitz †
Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
† E-mail: Valery.Lyuboshitz@jinr.ru
The properties of nonfactorizable ( entangled ) two-particle quantum states are discussed
. The study of spin correlations of two identical particles with spin 1/2 at low
relative momenta is performed. The angular correlations of decay directions for two
unstable particles, connected with the correlations of their spin quantum numbers, are
considered. It is shown that, for nonfactorizable two-particle states, the “classical” incoherence
inequalities for the correlation tensor components [1], being analogous to the Bell
inequalities, may be violated .
Concretely, the spin correlations and angular correlations for the systems (µ + µ − ),
(τ + τ − ), produced in the reactions e + e − → µ + µ − , e + e − → τ + τ − [2], for the systems of
final leptons in the processes γγ → e + e − , µ + µ − , τ + τ − [3], and also for the ΛΛ and Λ¯Λ
systems generated in relativistic heavy-ion collisions [4], have been analyzed . It is noted
that the sharp change of the correlation tensor for the Λ¯Λ pair with the increase of energy
may testify to the passage through the “mixed phase” [4].
Some other correlations of internal quantum numbers, being analogous in structure
and having the strongly pronounced quantum character, have been also considered : spin
correlations in the (p, 3 He) system formed in the reaction π + + 4 He → p + 3 He [5],
correlations of linear and circular polarizations of two γ quanta [6], and correlations at the
registration of two neutral K mesons generated in inclusive multiparticle processes with
the strangeness conservation [7] (and also pairs of neutral charmed and beauty mesons
D 0 ¯D0 ,B 0 ¯B0 ,B 0 s ¯B 0 s [8] ) .
References
[1] R. Lednicky and V.L. Lyuboshitz, Phys. Lett. B508, 146 (2001).
[2] V.L. Lyuboshitz and V.V. Lyuboshitz, Yad. Fiz. 72, 340 (2009).
[3] V.L. Lyuboshitz and V.V. Lyuboshitz, Proc. of the DSPIN-09 Workshop
( JINR E1,2-2010-13, Dubna, 2010 ), p. 91.
[4] V.L. Lyuboshitz and V.V. Lyuboshitz, Yad. Fiz. 73, 836 (2010).
[5] V.L. Lyuboshitz and V.V. Lyuboshitz, Yad. Fiz. 63, 837 (2000).
[6] V.L. Lyuboshitz and V.V. Lyuboshitz, EChAYa, 36 (No. 7B), 123 (2005).
[7] V.L. Lyuboshitz and V.V. Lyuboshitz, Pis’ma v EChAYa, 4, 654 (2007).
[8] V.L. Lyuboshitz and V.V. Lyuboshitz, Proc. of the Helmholtz Int. School
“Heavy Quarks 2008” ( DESY-PROC-2009-07, Hamburg, 2009 ), p. 299 .
89