Dynamics of an interacting hadron gas and Measurements of $\Upsilon \rm(nS)$ production and polarization in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV with ALICE

Ultra-relativistic heavy-ion collision programs at the Large Hadron Collider (LHC) at CERN and the Relativistic Heavy Ion Collider (RHIC) at BNL are designed to explore strongly interacting matter under extreme conditions of temperature and energy density. In these experiments, the so-called little Bang created in ultra-relativistic nuclear collisions leads to the formation of a novel state of matter known as the quark–gluon plasma (QGP), in which quarks and gluons are no longer confined within hadrons. This state of matter is believed to have existed during the first few microseconds after the Big Bang. Consequently, studying the properties of QGP not only deepens our understanding of the strong interaction at the microscopic level but also provides valuable insight into the early evolution of the universe. The short lifetime of the QGP matter does not leave any direct signature. Its properties are inferred through indirect signatures and through a detailed understanding of the system’s evolution across different stages of the space-time evolution of the created fireball.

The transport properties can play a major role in characterizing the dynamical evolution of the produced medium. Since the transport coefficients can, in principle, be derived from fundamental theory, their variation with thermodynamic parameters such as temperature and chemical potential can be useful in identifying the phase structure of QCD. Furthermore, non-central heavy-ion collisions generate intense but transient magnetic fields and huge vorticity in the medium. The combined effect of these fields can significantly influence the bulk properties of QCD matter and modify the conditions governing the transitions between different phases. This thesis investigates the transport properties of the hadronic phase using an interacting hadron resonance gas (HRG) model. The van der Waals HRG (VDWHRG) model, which incorporates attractive and repulsive interactions among hadrons, is found to provide an improved description of thermodynamic observables when compared with lattice QCD calculations and experimental data. Within this framework, we investigate key transport coefficients, including thermal and electrical conductivities, and study the role of interactions by comparing with those from the ideal HRG model. In addition, we explore the possible formation of a Bose–Einstein condensate in a high-density pion gas and analyze its influence on thermodynamic quantities and transport coefficients. The effects of global rotation on interacting hadronic matter are examined using a rotating system described by a grand canonical ensemble. We investigate whether rotation can influence the phase transition and, consequently, the corresponding liquid-gas critical point associated with VDW interactions. Moreover, we study the effect of rotation in achieving the condition for the onset of BoseEinstein condensation. By studying a rotating vector meson gas in the presence of condensation, we demonstrate an interesting interplay between different physical phenomena of condensation, rotation, and polarization. In addition, we revisit the applicability of the VDWHRG model and present a modification that incorporates temperature and chemical potential-dependent VDW parameters. We calculate the proton number cumulants in the modified VDWHRG model and compare the results with those of existing ideal HRG and VDWHRG models, as well as with experimental measurements.

The experimental analysis of the polarization measurements of $\Upsilon$(1S)  is conducted in proton-proton collisions at $\sqrt{s} = 13.6$ TeV using the ALICE detector.
The polarization measurement can further help in understanding their production. Moreover, the polarization measurements in proton-proton collisions can serve as a baseline for similar studies in heavy-ion collisions. The dimuon decay channel is used to reconstruct the $\Upsilon$(1S) using the muon spectrometer in the forward rapidity region. The polarization parameters are obtained as a function of transverse momentum by fitting the angular distribution with the corresponding function. Finally, we compare our results with those obtained in ALICE Run 2 measurements at $\sqrt{s} = 13$ TeV.