CERN Accelerating science

The Quark$-$Gluon Plasma (QGP) is a new matter state composited by deconfined quarks and gluons which exist at extremely high temperature and energy density. This formation of matter, predicted by Quantum Chromodynamics (QCD) in the Standard Model, shows great importance as a phenomenon to test QCD theories with its phase transitions, where the properties of matter can be investigated in ultra$-$relativistic heavy$-$ion collision experiments. At the Large Hadron Collider (LHC), the produced experiments data of heavy ion collisions create possibility for QGP researches, with phenomena such as jet quenching, where high transverse momentum partons undergo energy loss interacting with de$-$confined medium via elastic processes or induced gluon radiations, and collective motions, where the expansion of bulk matter exhibits different patterns such as isotropic and anisotropic components which are physically driven by pressure gradients. Heavy quarks, are powerful probes of QGP due to their shorter formation timescale, and they are to mostly go through the full evolution of the collision system in space$-$time. $\\$ In this thesis, the measurements of non$-$prompt $\mathrm{D}^{0}$ production in pp collisions at $\sqrt{s}=5.02~\mathrm{TeV}$ and in Pb$-$Pb collisions at $\sqrt{{s_\mathrm{NN}}}=5.02~\mathrm{TeV}$ with ALICE detectors are reported. The measurements of non$-$prompt $\mathrm{D}^{0}$, which are produced in beauty$-$hadron decays, can provide valuable information in beauty sector. The measurement of production in pp collisions is important to test perturbative QCD calculations, and provide a reference for Pb$-$Pb collisions. While in latter, the non$-$prompt $\mathrm{D}^{0}$ measurement can help to study the microscopic beauty$-$medium interactions. At high $p_{\mathrm{T}}$, it allows to investigate the colour charge and mass dependence of in$-$medium energy loss. At low $p_{\mathrm{T}}$, the participation of system collective expansion and diffusion process for beauty quarks can be investigated. $\\$ In pp collisions, the $p_{\mathrm{T}}

$$-$differential production cross section of non$-$prompt $\mathrm{D}^{0}$ is measured at midrapidity ($|y|<0.5$). The $\mathrm{D}^{0}$ meson candidates are reconstructed via the hadronic decay channel $\mathrm{D}^{0}\rightarrow\mathrm{K^{-}\pi^{+}}$. Then specific selections based on Boosted Decision Trees (BDT), a machine learning model trained with pseudo$-$data from Monte Carlo simulations and background sample in data, are applied to the candidates. The application of BDT reduces the combinatorial background, and also to enhance the non--prompt fraction of $\mathrm{D}^{0}$ from around 30$\%$ to 90$\%$ in signals. Afterwards, the signals are extracted via the invariant$-$mass analysis, and the non$-$prompt fractions are estimated with a data$-$driven minimizing$-$$ \chi^2$ approach. The measured $p_{\mathrm{T}} $$-$differential cross section is within the transverse momentum range $1 \lt p_{\mathrm{T}} \lt 24~\mathrm{GeV}/c$. With an extrapolating method, the $p_{\mathrm{T}}$$ -$integrated cross section is estimated at high precision. The results are well described by perturbative QCD (pQCD) calculations. The results are in good agreement with central prediction with FONLL calculated beauty hadron cross section and PYTHIA8 decay kinematics, while another prediction with GM$-$VFNS with two different transition approaches from beauty to non$-$prompt meson underestimated the measurement. Moreover, the total $\mathrm{b\bar{b}}$ production cross section is also determined from the measurements together with non$-$prompt $\mathrm{D}^{0}$, $\mathrm{D}^{+}$, and $\mathrm{D^+_s}$ mesons, which is compatible with previous measurements of di--electron production at the same centre$-$of$-$mass energy as well as the cross section predicted by pQCD calculations such as FONLL and NNLO. The measured production in pp collisions also provide a reference for the same measurement in heavy$-$ion collisions. $\\$ While in Pb$-$Pb collisions, a similar measurement is performed at same per$-$nucleon$-$pair centre$-$of$-$mass energy. The nuclear modification factor ($R_{\mathrm{AA}}$) of non$-$prompt $\mathrm{D}^{0}$ was measured for the first time down to $p_{\mathrm{T}}=1~\mathrm{GeV}/c$ in $0-10\%$ and $30-50\%$ centrality classes. A suppression in $R_{\mathrm{AA}}$ of factor about 3 (2) is observed for $p_\mathrm{T}\gt5~\mathrm{GeV}/c$ in $0-10\%$ ($30-50\%$) centrality, while at lower $p_{\mathrm{T}}$, $R_{\mathrm{AA}}$ increases with decreasing $p_{\mathrm{T}}$, and compatible with unity in $1 \lt p_{\mathrm{T}} \lt 3~\mathrm{GeV}/c$. The data are described by models that include both collisional and radiative processes in calculating beauty$-$quark energy loss in QGP, and quark recombination in addition to fragmentation as hadronization mechanism. The $R_{\mathrm{AA}}$ ratios of non$-$prompt to prompt $\mathrm{D}^{0}$$-$meson are reported significantly larger than unity at intermediate $p_{\mathrm{T}}$ in $0-10\%$ centrality, as predicted by transportation models in which the energy loss for beauty quarks are less than charm quarks due to their larger mass. $\\$