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

• Published in: arXiv.org 2019-08
• Main Authors: Osada, Takeshi, Kumaoka, Takuya
• Format: Article
• Language: English
• Subjects: Correlation analysis; Particle collisions; Particle density (concentration); Saturation; Scaling; Spectra; Transverse momentum; Variation
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1904.10823

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 \(W^*\) to distinguish it from \(W\)) and associate the energy-dependent saturation momentum \(Q_{\rm sat}(W^*)\) with particle number density. By using \(Q_{\rm sat}(W^*)\) 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 \(\langle p_{\rm T} \rangle\) for LHC energies scales in terms of \(Q_{\rm sat}(W^*)\). Furthermore, our model explains a scaling property of event-by-event \(p_{\rm T}\) fluctuation measure \(\sqrt{C_m}/\langle p_{\rm T}\rangle\) at LHC energies for pp collisions, where \(C_m\) is two-particle transverse momentum correlator. Our analysis of the \(p_{\rm T}\) fluctuation makes possible to evaluate a non-perturbative coefficient of the gluon correlation function.