Universal Transition Curve in Pseudo-Rapidity Distribution

Abstract

We show that an unambiguous way of determining the universal limiting fragmentation region is to consider the derivative ($d^2n/d\eta^2$) of the pseudo-rapidity distribution per participant pair. In addition, we find that the transition region between the fragmentation and the central plateau regions exhibits a second kind of universal behavior that is only apparent in $d^2n/d\eta^2$. The $\sqrts$ dependence of the height of the central plateau $(dn/d\eta)_{\eta=0}$ and the total charged particle multiplicity $n_{\rm total}$ critically depend on the behavior of this universal transition curve. Analyzing available RHIC data, we show that $(dn/d\eta)_{\eta=0}$ can be bounded by $\ln^2 s$ and $n_{\rm total}$ can be bounded by $\ln^3 s$. We also show that the deuteron-gold data from RHIC has the exactly same features as the gold-gold data indicating that these universal behaviors are a feature of the initial state parton-nucleus interactions and not a consequence of final state interactions. Predictions for LHC energy are also given.