Mean transverse-momentum fluctuations from soft particles produced in pp, p$-$Pb and Pb$-$Pb collisions at the LHC

Within this thesis, data of ultra-relativistic hadron$-$hadron and heavy-ion collisions measured with ALICE at the Large Hadron Collider (LHC) at CERN are analysed. Event-by-event mean transverse-momentum fluctuations are studied in proton$-$proton (pp), proton$-$lead (p$-$Pb) and lead$-$lead (Pb$-$Pb) collisions. The pp data are covering three different centre-of-mass collision energies of $\sqrt{s}$ = 0.9, 2.76 and 7 TeV. Pb$-$Pb data are analysed at a nucleon$-$nucleon collision energy of $\sqrt{s_\mathrm{NN}}$ = 2.76 TeV and p$-$Pb data at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV. In order to quantify the non-statistical mean transverse-momentum fluctuations, the two-particle transverse-momentum correlator is studied. It is constructed such, that it vanishes in the case of purely statistical fluctuations. Any non-zero signal indicates correlations of the particles in momentum space leading to dynamical fluctuations. The analysis is performed selecting soft particles within a transverse-momentum ($p_\mathrm{T}$) range of 0.15 GeV/c < $p_\mathrm{T}$ < 2 GeV/c. The main results are presented as a function of the charged-particle multiplicity density ($\langle\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\rangle$). In pp and p$-$Pb collisions, also the inclusive values considering the full event samples are determined. In all cases, significant non-statistical mean $p_\mathrm{T}$ fluctuations are found. In pp collisions, the fluctuations do not exhibit any significant dependence on the collision energy. This invariance is also preserved in comparison to measurements by other experiments at much lower collision energies. The mean $p_\mathrm{T}$ fluctuations decrease with increasing multiplicity density in all three collision systems following a power-law behaviour. Furthermore, the results are in quantitative agreement or at least comparable in the overlapping region in multiplicity. The Pb$-$Pb data are in agreement with an extrapolation of the pp results to higher multiplicities, exhibiting a slight enhancement above this pp baseline in the region $100 \lesssim \langle\mathrm{d}N_\mathrm{ch}/\mathrm{d}\eta\rangle \lesssim 500$ and a significant reduction of the fluctuations above. Model calculations suggest, that the behaviour in Pb$-$Pb may be related to a partial thermalisation of the created system with an increasing thermalised fraction with increasing multiplicity. In pp collisions, the results can be explained by a superposition of multiple parton$-$parton collisions. Finally, in p$-$Pb collisions the fluctations are studied separately for like-sign and unlike-sign charged-particle pairs. Some differences are found, which decrease with increasing multiplicity.