Saturation momentum scale extracted from semi-inclusive transverse spectra in high-energy pp collisions

Geometric scaling is well confirmed for transverse-momentum distributions observed in proton-proton collisions at Large Hadron Collider (LHC) energies. We introduced multiplicity dependence on a saturation momentum of the geometrical scaling, assuming the scaling holds for semi-inclusive distributions as well as for inclusive distributions. The saturation momentum is usually given by Bjorken's x variable, but redefinition of the scaling variable can make the saturation momentum a function of collision energy W. We treat the energy as a free parameter (denoted W* to distinguish it from W) and associate the energy-dependent saturation momentum Qsat(W*) with particle number density. By using Qsat(W*) for a scaling variable τ, we show semi-inclusive distributions can be geometrically scaled, i.e., all semi-inclusive spectra observed at W=0.90, 2.76, and 7.00 TeV overlap one universal function. The particle density dependencies of mean transverse momentum 〈pT〉 for LHC energies scales in terms of Qsat(W*). Furthermore, our model explains a scaling property of event-by-event pT fluctuation measure Cm/〈pT〉 at LHC energies for pp collisions, where Cm is a two-particle transverse-momentum correlator. Our analysis of the pT fluctuation makes possible to evaluate a nonperturbative coefficient of the gluon correlation function.