Geometric scaling at BNL RHIC and CERN LHC

Abstract

We present a new phenomenological model of the dipole scattering amplitude to demonstrate that the RHIC data for hadron production in $d$-$Au$ collisions for all available rapidities are compatible with geometric scaling, just like the small-$x$ inclusive deep inelastic scattering data. A detailed comparison with earlier geometric scaling violating models of the dipole scattering amplitude in terms of an anomalous dimension $\ensuremath{\gamma}$ is made. In order to establish whether the geometric scaling violations expected from small-$x$ evolution equations are present in the data a much larger range in transverse momentum and rapidity must be probed. Predictions for hadron production in $p$-$Pb$ and $p$-$p$ collisions at LHC are given. We point out that the falloff of the transverse momentum distribution at LHC is a sensitive probe of the variation of $\ensuremath{\gamma}$ in a region where $x$ is much smaller than at RHIC. In this way, the expectation for the rise of $\ensuremath{\gamma}$ from small-$x$ evolution can be tested.