Studying multiplicity and rapidity dependence of K$^{*}$ production and probing initial conditions of high energy collisions with ALICE at the LHC energies

Quantum chromodynamics (QCD) is the theory of strong interaction that describes the basic building blocks of nature. The QCD predicts a new state of strongly interacting matter at a very high temperature and/or density known as Quark-Gluon-Plasma (QGP), in which quarks and gluons are in a free state. It is believed that such a state of matter was present in the microsecond after the Big-Bang. To recreate such a primordial state of QCD matter in the laboratory and study its properties, ultra-relativistic heavy-ion collisions are carried out at Large Hadron Collider (LHC) facility and the data recorded using the ALICE detector. The present study aims to understand the properties of QCD matter and the different stages formed in ultra-relativistic high-energy collisions through hadronic resonance production. Hadronic resonances are short-lived (a few fm/c) in nature and decay via the strong interaction. These resonances are sensitive probes of the hadronic phase and the particle production mechanism. The yield, mass, and width of resonances are expected to be modified due to their decay daughters interaction within the hadronic phase via rescattering and regeneration processes. K$^{*0,\pm}$ is suitable for this purpose because of its very short lifetime ($\sim$ 4 fm/$c$), which is comparable to the hadronic phase lifetime. We have measured the K$^{*0,\pm}$ production in the rapidity interval --0.5 $<$ $y$ $<$ 0 for proton-nucleus (p--Pb) collisions at $\sqrt{s_{NN}}$ = 5.02 and 8.16 TeV for various multiplicity classes. The $p_{T}$ spectra, $p_{T}$-integrated yield, $\langle p_{T} \rangle$ $x_\mathrm{T}$-scaling, resonance to stable particle yield ratio, and nuclear modification factor ($R_\mathrm{pPb}$) are discussed. The p--Pb is an asymmetric and intermediate collision system compared to the pp and Pb-Pb collisions. It plays a vital role in disentangling initial cold nuclear matter effects from final state effects of hot dense matter produced in heavy-ion collisions. In the p-Pb collisions, one expects the mechanism of particle production to be different in forward (p-going) and backward (Pb-going) rapidities. The partons from the p-going side are expected to undergo multiple scattering while traversing the Pb-nucleus. Those on the Pb-side are likely to be affected by the properties of the nucleus. Thus, the rapidity dependence measurement of K$^{*0}$ production in p--Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV is interesting. We have measured the K$^{*0}$, production in the rapidity interval --1.2 $<$ $y$ $<$ 0.3 for p--Pb at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV for four multiplicity classes. The $p_{T}$ spectra, $p_{T}$-integrated yield,$\langle p_{T} \rangle$ , rapidity yield asymmetry ($Y_\mathrm{asym}$), and nuclear modification factor ($Q_\mathrm{CP}$) are presented. The high $p_{T}$ region of K$^{*0}$ production obeys an interesting $x_\mathrm{T}$-scaling behaviour for the LHC energies. K$^{*0}$/K ratio decreases with increasing event multiplicity which suggests that the rescattering effect dominates over regeneration. No significant energy dependence in $R_\mathrm{pPb}$ is observed, and values are consistent with unity within the uncertainties for K$^{*0}$ and other light flavor hadrons at $p_{T}$$>$8 GeV/$c$, confirming the absence of QGP-like effects in p--Pb collisions. The rapidity asymmetry has been observed at low $p_{T}$ and Cronin-like enhancement seen in the $Q_\mathrm{CP}$ at the intermediate $p_{T}$ suggests that nuclear effects play an important role in p--Pb collisions. In non-central relativistic heavy-ion collisions, where two nuclei collide with a nonzero impact parameter, a large orbital angular momentum ($\vec{L}$) of O(10$^{6-7}$ $\hbar$), and magnetic field ($|\vec{B}|$) of O(10$^{18}$ Gauss) are expected to be created. In the presence of large initial angular momentum, vector mesons (spin = 1) can be polarized due to the spin-orbital interaction of the QCD. The spin-orbit coupling could lead to a polarization of quarks that is followed by a net-polarization of vector mesons along the direction of angular momentum. Recently, the spin alignment of vector mesons at LHC energy was found to be surprisingly large compared to the polarisation measured for hyperons at RHIC and LHC energies. Theoretical studies have suggested that the local polarisation (where polarisation axes are chosen as a beam direction or along the momentum of vector meson) can also lead to the spin alignment of vector mesons and hyperons. It is exciting and challenging to extend such type of measurements to understand the contribution coming from global and local polarization. We have presented new measurements of spin alignment of vector mesons (K$^{*0,\pm}$, and $\phi$) using different polarisation axes in Pb--Pb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV with high statistics Run-2 data. The spin alignment of vector mesons is observed at low $p_{T}$ for mid-central collisions, whereas no spin alignment at high $p_{T}$ . No significant energy dependence is observed. K$^{*0}$ and K$^{*\pm}$ show similar spin alignment.