A quantitative criterion for the anisotropic dynamical fluctuation in high energy collisions

The Levy-stability of self-affine random cascading model is investigated in some detail. It is found that the Levy-stability indices of cascading process depend upon not only the dynamical fluctuation parameter a but also the way of shrinking phase space when calculating scaled factorial moments, which propose a quantitative criterion to determine whether the dynamical fluctuation is anisotropic. Besides, the puzzle of Levy-stability violation of NA22 data is comprehensively solved under the hypothesis of anisotropic dynamical fluctuation.