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

Abstract

Geometric scaling is well confirmed for transverse momentum distributions observed in proton-proton collisions at 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 $W^{\ast }$ to distinguish it from $W$) and associate the energy-dependent saturation momentum $Q_{\mathrm{sat}}(W^{\ast })$ with particle number density. By using $Q_{\mathrm{sat}}(W^{\ast })$ for a scaling variable $\tau$, 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 dependences of mean transverse momentum $⟨p_{\mathrm{T}}⟩$ for LHC energies scales in terms of $Q_{\mathrm{sat}}(W^{\ast })$. Furthermore, our model explains a scaling property of event-by-event $p_{\mathrm{T}}$ fluctuation measure $\sqrt{C_m}/⟨p_{\mathrm{T}}⟩$ at LHC energies for pp collisions, where $C_m$ is two-particle transverse momentum correlator. Our analysis of the $p_{\mathrm{T}}$ fluctuation makes possible to evaluate a non-perturbative coefficient of the gluon correlation function.

2.nd version: 9 pages 8 figures