The energy dependence of the chaoticity $\lambda$ parameter from BEC of $\pi$-pairs produced in $pp$ collisions

The $\sqrt{s_{pp}}$ behavior of the chaoticity parameter $\lambda$, 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 $\lambda$ 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 $\lambda$ is accounted for it fails to represent the few 3D $\lambda$ data which are seen to remain constant with energy above $\sim$200 GeV.