Low-mass dielectron measurement in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76\ \mathrm{TeV}$ with ALICE at the LHC

In ordinary matter, quarks and gluons are confined inside hadrons by the strong interaction. At extreme conditions of temperature and energy density, a new state of matter is formed, called quark-gluon plasma (QGP). This is made of deconfined quasi-free quarks and gluons. Based on the current cosmological picture, the quark-gluon plasma was the state of our universe few $\mu$s after the Big Bang. Moreover, there is evidence that a degenerate state of matter with similar properties to the QGP exists in the inner core of neutron stars and other compact astrophysical objects.Microscopic and extremely short-lived quantities of such a nuclear plasma can be created in ultra-relativistic heavy ion collisions. Its properties can be studied through several experimental probes using dedicated detectors installed around the collision region. This interesting branch of research is part of the experimental program of the Large Hadron Collider (LHC) at CERN, where lead ion beams are accelerated to unprecedented energies.The QGP properties, in principle, can be described by Quantum-Chromo Dynamics (QCD), the theory of the strong interaction. However, a description of the system based on QCD first principles is extremely complicated due to the relatively low energy scale involved (compared to $\Lambda_{QCD}$), which does not allow a perturbative approach. Further complications arise from many-body properties of QCD which are anyhow extremely interesting to explore.The deconfined medium created in heavy-ion collisions rapidly evolves, passing through several thermodynamic stages.Photons and dileptons are unique tools to study the properties of heavy-ion collisions. These particles are continuously emitted and they cross the medium with negligible interaction, thus carrying undisturbed information on their production source.Electromagnetic probes provide complementary information to hadronic probes, allowing to constrain the theoretical models used for the description of the system in the early stages. Thermal photons and dileptons carry information on the system temperature. Moreover, in-medium modifications of low-mass vector mesons spectral functions can be studied through their dilepton decay channels. These effects have since long been proposed as signatures of chiral symmetry restoration.Dileptons are also sensitive to heavy-flavor production, which gives a significant contribution to the intermediate mass region of the dilepton spectrum ($m_{\phi} < m_{l^{+}l^{-}} < m_{J /\psi}$).In this thesis, the dielectron production in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76\ \mathrm{TeV}$ with the ALICE experiment at the LHC has been studied. ALICE is the detector at the LHC dedicated to the study of heavy-ion collisions. The ALICE excellent tracking and particle identification capabilities make this experiment well suited for dielectron measurements. The main focus of this work has been the study of the low-mass region of the dielectron invariant mass spectrum, where contributions from thermal dileptons and from modified low-mass vector mesons are expected. The fraction of virtual direct photons has been measured, and the dielectron spectrum has been compared to the expected contributions from hadron decays, thermal dileptons and in-medium $\rho^{0}$ and $\omega$, resulting in good agreement within the experimental uncertainties.The future perspectives for the dielectron measurement and the predicted scenario after the ALICE upgrade are also presented