According to quantum chromodynamics (QCD), the interaction among quarks and gluons becomes smaller at high-temperature and the quark-gluon plasma (QGP) is formed. The high-energy heavy-ion collision experiments are performed to generate QGP and to investigate the properties of them. One of the major discoveries at the Relativistic Heavy Ion Collider (RHIC) is the large magnitude of the elliptic flow. The elliptic flow measured in experiments was consistent with the results from the relativistic hydrodynamic models. For further understanding of the collective flow, the correlation of them has been measured through the factorization ratio. To reproduce the factorization ratio measured in experiments, event-by-event fluctuations play an important role. In my study, I focus on the initial fluctuations and the hydrodynamic fluctuations to explain the factorization ratio. In this seminar, I talk about the space-time evolution of high-energy heavy-ion collisions and the relativistic hydrodynamic model. Then I show the analysis of the effect of the initial fluctuations and the hydrodynamic fluctuations on factorization ratio. This talk is based on the paper: Phys. Lett. B 829 (2022) 137053
The TMD soft function can be obtained by formulating the Wilson line in terms of auxiliary 1-dimensional fermion fields on the lattice. In this formulation, the directional vector of the auxiliary field in Euclidean space has the form $\tilde n = (in^0, \vec 0_\perp, n^3)$, where the time component is purely imaginary. The components of these complex directional vectors in the Euclidean space can be mapped directly to the rapidities of the Minkowski space soft function. I present the results of a one-loop analysis of the soft function in Euclidean space, and show that the computation is valid for values of $\tilde n$ that obey: $|r| = |n^0/n^3| > 1$. This result corresponds to a computation in Minkowski space with space-like directed Wilson lines. Finally, I show that a lattice calculable object can be constructed that has the desired properties of the soft function.
Determining the phase structure of nuclear and quark matter in external magnetic fields is not only of theoretical interest, but also experimentally motivated by the large magnetic fields found in heavy-ion collisions and compact star physics. Including the effects of the chiral anomaly within Chiral Perturbation theory, at finite baryon chemical potential, neutral pions form an inhomogeneous phase dubbed the "Chiral Soliton Lattice" (CSL) above a certain critical magnetic field. Above a second, even higher critical field, the CSL becomes unstable to fluctuations of charged pions, implying they condense.
I will point out the similarity of this second critical field to the upper critical magnetic field in conventional type-II superconductors, leading to the possibility of an inhomogeneous, superconducting charged pion phase existing above this point. Applying similar methods originally used by Abrikosov, I will present results where we've constructed such a phase and show the region where it is preferred in the baryon chemical potential-magnetic field phase diagram at zero temperature. Its local effect on the baryon number density, which is non-zero and periodic like in the CSL, will also be briefly discussed.