## Partonic collectivity in large and small systems at the LHC

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**Abstract**

Under extreme conditions, such as high temperature and density, quarks and gluons can be deconfined. The deconfined matter, quark-gluon plasma (QGP), that existed within the first microsecond after the Big Bang, can be recreated in ultra-relativistic heavy-ion collisions at particle accelerators. One way to investigate the initial conditions and the dynamic evolution of such a collectively expanding medium is by studying the anisotropic flow, quantified by flow coefficients $v_n$. Experimental measurements of the QGP from various flow observables show remarkable agreement with the hydrodynamic calculations, suggesting the QGP behaves like a nearly ideal fluid. The collective behaviour associated with the presence of QGP is also observed in small collision systems at very high multiplicities with significantly more produced particles than in an average small system collision. Based on the existing studies, it is known that the anisotropic flow in small systems is mainly driven by the initial geometry of the system. However, the development of flow from the initial geometry through the dynamic evolution is still under discussion. In this thesis, the anisotropic flow is studied using different observables and across different collision systems. A new generic algorithm is developed to formulate multi-particle cumulants of arbitrary order in Pb--Pb collisions at $\sqrt{s_{\rm{NN}}} = 5.02$ TeV. The measurements of multi-particle cumulants of single and mixed harmonics are reported. \linebreak Mixed harmonic cumulants $MHC(v_m^k,v_n^l)$ have a unique sensitivity to the initial conditions. Thus, the results are compared to the calculations from hydrodynamical models in order to constrain initial conditions and transport properties of the QGP. The flow coefficients $v_2(p_{\rm T})$ are calculated using the two- and four-particle cumulants method. With these observables, it is possible to study the first two moments of the probability density function of elliptic flow, the mean $\langle v_2 \rangle$ and variance $\sigma_{v_{2}}$, and the relative flow fluctuations of identified particles for the first time in heavy-ion collisions. Moreover, the elliptic flow $v_2(p_{\rm T})$ with various identified particle species is studied in Pb--Pb collisions to further probe the initial conditions and properties of QGP, in particular, the particle production mechanisms, e.g., quark coalescence. The flow measurements of identified particles in heavy-ion collisions bring a unique insight into initial conditions and the properties of QGP. Therefore, such a study in small collision systems can contribute to understanding the role of initial conditions and the state of the recreated matter. However, the study of flow coefficients in small systems is more challenging due to significant non-flow contamination. The measurement is performed in p--Pb and pp collisions at $\sqrt{s_{\rm{NN}}} = 5.02$ and 13 TeV, respectively. Thanks to the unique pseudorapidity coverage of ALICE, the flow coefficients with sufficient non-flow suppression are obtained using ultra-long-range two-particle correlations and the template fit method. Many similarities are observed in flow in large and small systems. The measured $v_2(p_{\rm T})$ coefficients exhibit mass ordering in the low transverse momentum region. Such a phenomenon originates from the radial expansion of the system. The baryon-meson grouping at the intermediate transverse momentum, which in Pb--Pb is typically associated with partonic collectivity and quark coalescence, is also reported in p--Pb and pp collisions. These observations are discussed in the context of models with and without the contribution of quark coalescence. The similarities between large and small systems show strong evidence that a droplet of QGP is created in small collision systems at high multiplicities.

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