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The energy dependence of the chaoticity $λ$ parameter from BEC of $π$-pairs produced in $pp$ collisions

The $\sqrt{s_{pp}}$ behavior of the chaoticity parameter $λ$, derived from Bose - Einstein Correlations (BEC) of pion-pairs produced in $pp$ collisions, is investigated. Considered are the one and three dimensions (1D, 3D) of the BEC analyzed in terms of a Gaussian and/or Exponential distributions. A marked difference is observed between the $λ$ dependence on energy in the 1D and the 3D analyzes. The experimental data are examined in terms of the relation between the pion cluster of sources and the BEC dimension R which in turn are deduced from the charged outgoing particle multiplicity. While in this approach the general decrease with energy of the 1D $λ$ is accounted for it fails to represent the few 3D $λ$ data which are seen to remain constant with energy above $\sim$200 GeV.