On the spin correlations of final leptons produced in the annihilation processes $e^+ e^- \rightarrow \mu^+\mu^-, e^+ e^- \rightarrow \tau^+ \tau^-$
The electromagnetic processes of annihilation of $(e^+ e^-)$ pairs, generated in various high-energy reactions and decays, into heavy flavor lepton pairs are theoretically studied in the one-photon approximation, applying the technique of helicity amplitudes . For the process $e^+e^- \rightarrow \mu^+\mu^-$, it is shown that -- in the case of the unpolarized electron and positron -- the final muons are also unpolarized but their spins are strongly correlated. For the final $(\mu^+ \mu^-)$ system, the structure of triplet states is analyzed and explicit expressions for the components of the spin density matrix and
correlation tensor are derived; besides, the formula for angular correlation at the decays of final muons $\mu^+$ and $\mu^-$ is obtained.
It is demonstrated that here the spin correlations of muons have the purely quantum character, since one of the Bell-type
incoherence inequalities for the correlation tensor components is always violated ( i.e. there is always one case when the modulus of sum of two diagonal components exceeds unity ). Besides, the additional contribution of the weak interaction of lepton neutral currents through the virtual $Z^0$ boson is considered in detail, and it is established that, when involving the weak interaction contribution, the qualitative character of the muon spin correlations does not change.
Analogous analysis can be wholly applied as well to the annihilation process with the formation of a tau-lepton pair ($e^+ e^- \rightarrow \tau^+ \tau^-$), which becomes possible at considerably higher energies.
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