Project A02: From QCD transport to particle yields

Project Leaders: Silvia Masciocchi, Jan Pawlowski

Summary: This project aims to determine the transport properties of the quark-gluon plasma produced in heavy-ion collisions, combining first-principle calculations and the constraints obtained from experimental data through phenomenological studies. During the first two funding periods, we established robust methods for the first- principle computation of QCD transport coefficients and already moved from the description of light particle production to the one of charm hadrons. Building on our successful developments, we plan to address further properties of the hot QCD matter, such as heavy-quark diffusion (with its mass and temperature dependence), electrical conductivity, baryon number transport and more. The current fluid-dynamic simulations of heavy-ion collisions are rather successful in describing experimental data, however they are largely relying on empirical modelling and parameters. The combined approach with first-principles transport coefficients and the very flexible and efficient fluid-dynamic code (FLUIDuM, developed in C06) set-up in A02, plus the novel develop- ments of hydrodynamic attractor solutions, allows for a comprehensive analysis of the experimental data with AI-based methods developed in C06. This allows us to pin down the fundamental QCD transport properties in a model-independent way.

A02-1 Spectral functions and transport coefficients.

Single particle spectral functions will be computed within a twofold approach: On the one hand we use precision data for imaginary time correlation functions and spectral functions are extracted with advanced spectral reconstruction schemes developed in A02. On the other hand we use direct computations of real-time QCD correlation functions at finite temperature and chemical potential within functional approaches developed in A02. In combination this allows for a precision determination of spectral functions with a small systematic error. The spectral functions constitute the pivotal input for the direct real-time computation of transport coefficients via the computation of the respective correlation functions within the diagrammatic functional QCD approach. As for the single particle spectral functions, the twofold approach explained above also allows for a systematic error control and further improvements here: the imaginary time correlators allow for the reconstruction of transport coefficients, that obeys the tight constraints from the direct diagrammatic computation. We will compute in particular the heavy-quark spatial diffusion coefficient and relaxation time, the baryon number diffusion coefficient and relaxation time, as well as the electrical conductivity of the quark-gluon plasma. These will be directly fed to the hydrodynamic model for the description of the quark- gluon plasma and heavy-quark diffusion (A02-2) for pinning down the fundamental QCD transport properties.

A02-2 Hydrodynamic description of heavy quarks.

The extension of the fluid-dynamic description of the quark- gluon plasma to the diffusion of the charm quarks has been successfully achieved during the second fund- ing period. Recent lattice QCD calculations and exploratory studies carried out within C05(E) suggest that beauty quarks undergo a partial thermalisation within the QGP lifetime. Therefore, a fluid-dynamic approach to beauty-quark diffusion will be implemented. The heavy-quark spatial diffusion coefficient, its dependence on temperature and quark mass, and its relaxation times will be provided by A02-1. They will be implemented in the QGP evolution description provided by FLUIDuM (C06). Using the neural-network based Bayesian infer- ence framework developed in C06, we will use experimental data on charm- and beauty-hadron momentum distributions and flow coefficients, to rigorously constrain the QCD parameters. The heavy-flavour description will be extended to consider the influence of strong electromagnetic fields (C06), gaining sensitivity to the QGP electric conductivity (A02-1). Further constraints on the heavy-quark initial conditions will be gained through the developments on attractors in A02-3. Other methods for global optimisation developed in C06 will be adopted, in particular the application of persistent homology to heavy-ion collision data, in collaboration with B03.

A02-3 Pre-equilibrium and hydrodynamic attractors for the heavy-quark current.

Heavy quarks are produced via hard scatterings happening at the very beginning of the collision. Hence, they are initially produced very far from local kinetic equilibrium. Nevertheless, an out-of-equilibrium hydrodynamic regime for charm quarks seems to be established at a time-scale compatible with the formation time of the quark-gluon plasma. There- fore, the existence of pre-equilibrium attractors for the charm quark current will be investigated. This study is important to understand to what extent the initial conditions of the heavy-quark spatial distribution matter in the thermalisation process and their influence on final observables, such as charm-hadron directed flow, studied in A02-2. Furthermore, we plan to search for hydrodynamic attractors of charm-quark variables, such as density and diffusion current, aiming at shedding light on the approach of heavy quarks to local kinetic equilibrium within the expanding plasma. This analysis will profit from the calculations of QCD correlation functions in the scaling regime provided by A02-1.