Periodic Reporting for period 1 - RelSpinHydro (Relativistic Spin Hydrodynamics: Theory and Applications)
Okres sprawozdawczy: 2023-10-01 do 2025-09-30
One of the main challenges in nuclear physics is understanding the emergent phenomena of strongly interacting matter governed by quantum chromodynamics (QCD). Heavy-ion collisions conducted at the Large Hadron Collider at CERN and the Relativistic Heavy Ion Collider at BNL create a unique and puzzling state of matter known as quark-gluon plasma (QGP), where quarks and gluons are deconfined. The QGP behaves like a nearly perfect liquid, which is modeled using relativistic hydrodynamics. Recent experiments have shown that the QGP exhibits spin-polarization phenomena, such as the global polarization of Lambda baryons and the spin alignment of vector mesons.
While existing theoretical models, based on the assumption of local thermodynamic equilibrium of spin degrees of freedom, successfully describe the global polarization, they fail to explain other observables, such as the spin alignment. These discrepancies highlight the need to extend conventional hydrodynamic models to include spin effects. This has motivated the development of what is now called relativistic spin hydrodynamics. Developing relativistic spin hydrodynamics is essential for a deeper understanding of the QGP and hadron polarization in heavy-ion collisions. The main objectives of this proposal are (i) the formulation of causal and stable theories of relativistic spin hydrodynamics, (ii) their extensions to the far-from-equilibrium regime, and (iii) Applications of spin hydrodynamics to QGP physics.
While existing theoretical models, based on the assumption of local thermodynamic equilibrium of spin degrees of freedom, successfully describe the global polarization, they fail to explain other observables, such as the spin alignment. These discrepancies highlight the need to extend conventional hydrodynamic models to include spin effects. This has motivated the development of what is now called relativistic spin hydrodynamics. Developing relativistic spin hydrodynamics is essential for a deeper understanding of the QGP and hadron polarization in heavy-ion collisions. The main objectives of this proposal are (i) the formulation of causal and stable theories of relativistic spin hydrodynamics, (ii) their extensions to the far-from-equilibrium regime, and (iii) Applications of spin hydrodynamics to QGP physics.
Although the early termination of the grant prevented us from reaching all final objectives, the project has successfully accomplished several key milestones, which include:
1) We developed an information current for first-order hydrodynamics. This constitutes the first step towards a covariantly stable and causal formulation of first-order fluctuating hydrodynamics based on thermodynamic principles. We considered applications in chiral hydrodynamics—the theory that incorporates the effects of quantum anomalies and promotes chirality as additional degrees of freedom. This work paves the way for constructing an information current for first-order spin hydrodynamics.
2) We introduced a new formulation of relativistic ideal spin hydrodynamics based on a divergence-type theory structure. This formulation is stable, non-linearly causal, and symmetric-hyperbolic, making it suitable for numerical simulations of the QGP.
3) We derived the necessary and sufficient conditions under which a broad class of relativistic magnetohydrodynamic theories is causal and strongly hyperbolic. The theoretical techniques employed in this study may be generalized to study causality and stability in relativistic spin hydrodynamics.
4) We proposed a novel polarization phenomenon in the QGP, which is induced by the spin of the nucleons within the colliding nuclei. This initial-state spin effect can be observed using spin correlations of hyperons in the final state and can shed light on the evolution of spin dynamics in the QGP.
1) We developed an information current for first-order hydrodynamics. This constitutes the first step towards a covariantly stable and causal formulation of first-order fluctuating hydrodynamics based on thermodynamic principles. We considered applications in chiral hydrodynamics—the theory that incorporates the effects of quantum anomalies and promotes chirality as additional degrees of freedom. This work paves the way for constructing an information current for first-order spin hydrodynamics.
2) We introduced a new formulation of relativistic ideal spin hydrodynamics based on a divergence-type theory structure. This formulation is stable, non-linearly causal, and symmetric-hyperbolic, making it suitable for numerical simulations of the QGP.
3) We derived the necessary and sufficient conditions under which a broad class of relativistic magnetohydrodynamic theories is causal and strongly hyperbolic. The theoretical techniques employed in this study may be generalized to study causality and stability in relativistic spin hydrodynamics.
4) We proposed a novel polarization phenomenon in the QGP, which is induced by the spin of the nucleons within the colliding nuclei. This initial-state spin effect can be observed using spin correlations of hyperons in the final state and can shed light on the evolution of spin dynamics in the QGP.
This project has advanced our theoretical understanding of relativistic spin hydrodynamics and spin physics of the QGP by developing novel frameworks that go significantly beyond the current state of the art. Importantly, the formulation of a causal and stable theory of ideal relativistic spin hydrodynamics and the construction of an information current for first-order hydrodynamics represent critical steps toward a consistent treatment of spin in relativistic fluid dynamics. Additionally, the work on spin correlations in the QGP has profound implications not only for our understanding of spin dynamics in heavy-ion collisions but also for nuclear structure. Together, these contributions open the door to more accurate and comprehensive modeling of spin-related effects in heavy-ion collisions.