Correlation Functions in QCD Matter

In the early Universe, all matter and radiation was concentrated in an extremely hot and dense fireball that expanded and cooled rapidly. During this evolution, several phenomena occurred that fundamentally shaped the world around us. In particular, during the first few microseconds, a plasma of elementary particles called quarks and gluons prevailed before converting into bound states called hadrons, which ultimately made up the atomic nuclei as we know them today. In this transition, at around two trillion degrees Kelvin, the quarks and gluons were permanently confined into hadrons, thereby generating about 98% of the visible mass in the Universe. The theoretical description of the confinement of quarks and gluons and the generation of hadronic mass remains an outstanding challenge in modern elementary-particle and nuclear physics. High-energy collisions of atomic nuclei can recreate the quark-gluon plasma (QGP) for a short moment in the laboratory, before it decays back into hadrons that can be measured in large detectors. In this project, rigorous theoretical analyses are carried out to deduce the properties of the QGP and its hadronization by analyzing the observed particle spectra. The goal of this project is to unravel microscopic mechanisms of the QGP-to-hadron transition by evaluating in-medium correlation functions. First-principle information on these is available from the theory of the strong interaction, Quantum Chromodynamics (QCD), using lattice-discretized computer simulations. However, these results are not readily applicable to experiment. This gap is bridged by utilizing the concept of spectral functions, which characterize the structure of matter. Spectral functions are calculated in both QGP and hadronic matter using quantum many-body theory, which can cope with the large interactions rates in the system. By focusing on spectral functions in the vector channel, a direct connection between lattice-QCD results (for correlation functions) and experimental data (for di-lepton spectra) is established. On the QGP side, novel techniques are developed to calculate quark-antiquark correlators at finite momentum and constrain them by lattice QCD. On the hadronic side, existing calculations of the vector spectral function are improved to incorporate mass degeneracies as predicted by QCD. A smooth matching of these calculations around the transition temperature and subsequent tests against experimental data are carried out. This project provides opportunities for students to carry out cutting-edge research, and involves outreach to high-school students. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.