Spin correlations of muons in the process of electron-positron pair annihilation e+e- → μ+μ-

V. L. Lyuboshitz; V. V. Lyuboshitz

doi:10.1140/epjst/e2008-00774-y

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2024 Impact factor 2.3

Special Topics

Eur. Phys. J. Special Topics 162, 43-51 (2008)
https://doi.org/10.1140/epjst/e2008-00774-y

Spin correlations of muons in the process of electron-positron pair annihilation e⁺e^- → μ⁺μ^-

V. L. Lyuboshitz and V. V. Lyuboshitz

Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia

Corresponding author: Valery.Lyuboshitz@jinr.ru

Abstract

Using the technique of helicity amplitudes, the electromagnetic process $e^+e^- \rightarrow \mu^+\mu^-$ is theoretically investigated in the one-photon approximation. The structure of the triplet states of the final $(\mu^+\mu^-)$ system is analyzed. It is shown that in the case of unpolarized electron and positron the final muons are also unpolarized, but their spins are strongly correlated. Explicit expressions for the components of the correlation tensor of the final $(\mu^+ \mu^-)$ system are derived. The formula for the angular correlation at the decays of final muons $\mu^+$ and $\mu^-$ , produced in the process $e^+e^- \rightarrow \mu^+\mu^-$ , is obtained. It is demonstrated that spin correlations of muons in the process of electron-positron pair annihilation have the purely quantum character, since one of the incoherence inequalities for the correlation tensor components is always violated. The additional contribution of the weak interaction of lepton neutral currents through the virtual Z⁰ boson is considered; it is established that, taking into account the weak interaction, the qualitative character of the muon spin correlations does not change.