On the spin correlations of final leptons produced in the high-energy annihilation and two-photon processes e+e− → μ+ μ−, τ+τ− and γγ → e+e−, μ+μ−, τ+τ−

Abstract

The electromagnetic processes of annihilation of (e+e−) pairs, into heavy flavor lepton pairs are theoretically studied in the one-photon approximation, using the technique of helicity amplitudes . For the process e+e− − μ+μ−, 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; the structure of their triplet states is analyzed and explicit expressions for the correlation tensor components are derived. On the other hand, the theoretical study of spin structure for the processes of lepton pair production by photon pairs is also performed: for the two-photon process γγ → e+e−, it is found that – quite similarly - in the case of unpolarized photons the spins of final unpolarized particles prove to be strongly correlated, and explicit expressions for the correlation tensor components and relative fractions of singlet and triplet states of the final system are obtained. It is established that in both these processes the spin correlations of final leptons have the purely quantum character, since one of the Bell-type incoherence inequalities for the correlation tensor components is always violated. Analogous analysis can be wholly applied also to the annihilation process e+e− → τ+τ− and to the two-photon processes γγ → μ+μ−, γγ → τ+τ−, becoming possible at considerably higher energies.