Universal transition curve in pseudorapidity distribution

Abstract

We show that an unambiguous way of determining the universal limiting fragmentation region is to consider the derivative $({d}^{2}n∕d{\ensuremath{\eta}}^{2})$ of the pseudorapidity 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 ${d}^{2}n∕d{\ensuremath{\eta}}^{2}$. The $\sqrt{s}$ dependence of the height of the central plateau ${(dn∕d\ensuremath{\eta})}_{\ensuremath{\eta}=0}$ and the total charged particle multiplicity ${n}_{\text{total}}$ critically depend on the behavior of this universal transition curve. Analyzing available Relativistic Heavy-Ion Collider (RHIC) data, we show that ${(dn∕d\ensuremath{\eta})}_{\ensuremath{\eta}=0}$ can be bounded by ${\mathrm{ln}}^{2}s$ and ${n}_{\text{total}}$ can be bounded by ${\mathrm{ln}}^{3}s$. We also show that the deuteron-gold data from RHIC has exactly the 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.