Spin correlations of the final leptons in the high-energy two-photon processes $\gamma \gamma \rightarrow e^+ e^-, \mu^+ \mu^-, \tau^+ \tau^-$

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Pre-published on:
2019 August 19

Published on:
2019 August 23

Abstract

The theoretical study of spin structure for the processes of lepton pair production by pairs of photons (which, in particular, may be emitted in relativistic heavy-ion and hadron-nucleus collisions) is performed. For the two-photon process $\gamma \gamma \rightarrow e^+ e^-$, it is shown that in the case of unpolarized photons the final electron and positron remain unpolarized as well, but their spins prove to be strongly correlated. Explicit expressions for the components of the correlation tensor and for the relative fractions of singlet and triplet states of the final $(e^+ e^-)$ system are derived. It is established that in the process $\gamma \gamma \rightarrow e^+ e^-$ at least one of the "classical" incoherence inequalities of the Bell type for the correlation tensor components is always violated ( i.e. there is always at least one case when the modulus of sum of two diagonal components exceeds unity ), and, thus, spin correlations of the electron and positron in this process have the strongly pronounced quantum character.

Analogous analysis can be wholly applied also to the

two-photon processes with the generation of a muon pair

and a tau-lepton pair ( $\gamma \gamma \rightarrow

\mu^+ \mu^-, \gamma \gamma \rightarrow \tau^+ \tau^-$ ),

which become possible at considerably higher energies.

The theoretical study of spin structure for the processes of lepton pair production by pairs of photons (which, in particular, may be emitted in relativistic heavy-ion and hadron-nucleus collisions) is performed. For the two-photon process $\gamma \gamma \rightarrow e^+ e^-$, it is shown that in the case of unpolarized photons the final electron and positron remain unpolarized as well, but their spins prove to be strongly correlated. Explicit expressions for the components of the correlation tensor and for the relative fractions of singlet and triplet states of the final $(e^+ e^-)$ system are derived. It is established that in the process $\gamma \gamma \rightarrow e^+ e^-$ at least one of the "classical" incoherence inequalities of the Bell type for the correlation tensor components is always violated ( i.e. there is always at least one case when the modulus of sum of two diagonal components exceeds unity ), and, thus, spin correlations of the electron and positron in this process have the strongly pronounced quantum character.

Analogous analysis can be wholly applied also to the

two-photon processes with the generation of a muon pair

and a tau-lepton pair ( $\gamma \gamma \rightarrow

\mu^+ \mu^-, \gamma \gamma \rightarrow \tau^+ \tau^-$ ),

which become possible at considerably higher energies.

DOI: https://doi.org/10.22323/1.346.0188

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