Research Projects

The recent discovery of spin polarization of final-state particles in relativistic heavy-ion collision experiments has triggered significant interest in spin-related observables. These include: (i) the spin polarization of Λ-hyperons along the direction of global angular momentum and in the transverse plane (perpendicular to the beam direction), (ii) the spin alignment of vector mesons, (iii) predictions related to the existence of magnetic field via heavy quark polarization and, (iv) connection between the spin polarization of hadrons and observation of QCD critical point. In the context of spin polarization of Λ -hyperons, these new observations prompted a growing interest in a theory of spin hydrodynamics. However, the existing formulations are plagued with ambiguities. Consequently, there is an urgent need to resolve the subtleties of spin hydrodynamics and develop reliable simulations for realistic phenomenological predictions and applications. These are the primary goals of the present proposal. The project will have several phases. One of the major shortcomings of the existing theories of spin hydrodynamics is their acausal nature. Thus, developing a first-order causal theory of spin hydrodynamics for spin-1/2 particles will be the first priority of the project. Building on this, I would like the framework will be extended for both massive and massless spin-1 particles. For the solutions to the hydrodynamic equations, initial efforts will be on highly symmetric systems, e.g., the (0+1)-D boost-invariant case. Later, less idealized approximations will be considered, followed by a full (3+1)-D hydrodynamic solution. Further extension to include the effects of external magnetic fields will provide a comprehensive framework to interpret the first three observables mentioned above. The fourth observable will require a separate framework. The search for the QCD critical point is a major goal of heavy-ion collision experiments. While various frameworks have been proposed, the problem remains challenging. Recent studies suggest that the spin polarization of hadrons may be affected by the phase transition. Moreover, in a thermal model study, the spin relaxation time was found to be sensitive to the speed of sound (c_s) of the medium. Since c_s depends on the equation of state, estimating the spin relaxation time could offer a quantitative measure of the system’s proximity to the critical point. As fluctuations become non-negligible near the critical point, developing a theory of spin hydrodynamics with fluctuations is essential. Among available approaches, I plan to use the recently developed density frame formalism, which naturally incorporates fluctuation effects. If these goals are achieved before time, I would also like to follow up on a recent study that investigates the two-particle correlators to study the influence of the initial state on the final state spin polarization.