Angular correlations in the decays of two unstable identical particles with close momenta

Lednický, R.; Lyuboshitz, V. V.; Lyuboshitz, V. L.

doi:10.1134/1.1577920

Cited by 27 publications

(58 citation statements)

References 5 publications

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“…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…”

Section: Spin Correlations and Angular Correlations At Joint Registramentioning

confidence: 99%

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

Lyuboshitz

2017

Proceedings of the 14th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2016)

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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.

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“…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…”

Section: Spin Correlations and Angular Correlations At Joint Registramentioning

confidence: 99%

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

Lyuboshitz

2017

Proceedings of the 14th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2016)

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“…system and ψ denotes the solutions in (130) extended to the inner region r * < d. In the case of only two open channels α and β, the leading part of the correction scaled by W P (0) is expressed through bilinear products of the amplitudes f λλ ′ in equation (44) of [48]. After a straightforward though lengthy algebra, it can be written in a more explicit form:…”

Section: Universalitymentioning

confidence: 99%

“…Since, in the cases of practical interest, the particles (pions, kaons, nucleons) in the channels α and β are members of the corresponding isotopic multiplets, one can assume the parameter matrices diagonal in the representation of the total isospin [48]. The elements of the parameter orK (K −1 ) matrices in the channel representation are then given by the corresponding isospin projections.…”

Section: Continuous Spectrum In Both Channelsmentioning

confidence: 99%

“…We will denote the channels as α = {1 + 2} and β = {3 + 4}, and the corresponding wave functions describing the scattering α → α and α → β -as ψ α and ψ β respectively. Outside the range of the strong FSI, r * > d, they can be written, for the α-and β-channel continuous spectrum, as [48]:…”

Section: Continuous Spectrum In Both Channelsmentioning

confidence: 99%

“…For the discrete levels at negative energies, the substitution k * → iκ n has to be done, particularly yielding [25,48]:…”

Section: General S-wave Solutionmentioning

confidence: 99%

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Finite-size effect on two-particle production in continuous and discrete spectrum

Lednický

2009

Phys. Part. Nuclei

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Abstract. The formalism allowing one to account for the effect of a finite spacetime extent of particle production region is given. Its applications to the lifetime measurement of hadronic atoms produced by a high-energy beam in a thin target, as well as to the femtoscopy techniques widely used to measure space-time characteristics of the production processes, are discussed. Particularly, it is found that the neglect of the finite-size effect on the pionium lifetime measurement in the experiment DIRAC at CERN could lead to the lifetime overestimation comparable with the 10% statistical error. The theoretical systematic errors arising in the calculation of the finite-size effect due to the neglect of non-equal emission times in the pair center-of-mass system, the space-time coherence and the residual charge are shown to be negligible.

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Correlation femtoscopy

Lednický¹

2006

Nuclear Physics A

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Angular correlations in the decays of two unstable identical particles with close momenta

Cited by 27 publications

References 5 publications

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

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

Finite-size effect on two-particle production in continuous and discrete spectrum

Correlation femtoscopy

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