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Collectivity in small, srongly interacting systems

Periodic Reporting for period 2 - collectiveQCD (Collectivity in small, srongly interacting systems)

Reporting period: 2020-08-01 to 2022-01-31

Curiosity is deeply rooted in the nature of human beings. It is curiosity that lets us do research "So that I may perceive whatever holds The world together in its inmost folds" (Johann Wolfgang von Goethe: "Faust - Der Tragödie erster Teil", translation by George Madison Priest from To our current understanding the answer to this fundamental question is 'the strong force'. The strong force holds atomic nuclei together. And it rules over quarks and gluons, that make up protons and neutrons (the building blocks of atomic nuclei).

The strong force has a peculiar property called 'asymptotic freedom' that sets it apart from all other forces. What that means is that the force between quarks and gluons gets stronger when the particles move further apart. An important consequence of that is that quarks and gluons cannot exist alone, but are always bound into composite particles like protons and neutrons. However, when such particles are compressed and/or heated enough, the interaction becomes weak and the particles 'melt' to form a new state of matter known as the Quark-Gluon Plasma (QGP). Powerful accelerators like the Large Hadron Collider LHC at CERN in Geneva can collide heavy atomic nuclei at energies that are high enough to form a QGP for a very short time. Experiments have found out that the QGP behaves like a liquid, which came as a surprise since most scientists had expected it would behave like a gas. The really big surprise, however, came when the experiments found that sometimes collisions of protons at the LHC look a bit as if a QGP was formed there too. This was thought to be impossible because proton-proton collisions are much smaller in size and not nearly as dense as colliding heavy nuclei.

The main goal of this project is to better understand from the theory side how the QGP is formed and how its properties come about. In particular, why it behaves like a liquid, and why proton-proton and nucleus-nucleus collisions sometimes look alike.

To this end two new theoretical models will be developed and implemented as simulation tools that allow for a direct comparison of the theoretical calculations to the experimental data. Both models describe all relevant aspects of all collision systems (i.e. proton-proton, proton-nucleus, and nucleus-nucleus). One is inspired by the traditional view on nucleus-nucleus collisions, and the other one by the traditional view on proton-proton collisions.
So far most of the work has gone into setting up a computer simulation of the Quark-Gluon Plasma based on a successful effective kinetic theory by Arnold, Moore and Yaffe. In kinetic theory the evolution of a system of particles scattering off each other is described. It is a very powerful framework, but some caution is needed as it cannot be applied in all situations. In this case the scattering processes include normal elastic scattering (like scattering of billard balls), but also processes where a quark (or a gluon) splits into a quark (or a gluon) and another gluon, or absorbs a gluon. The implementation (in the form of a computer program) of elastic scattering is ready, as is most of the splitting processes. The gluon absorption is still missing. An important problem was solved on the way: the scattering probability depends not only on the properties of the scattering particles, but also on the particles in the surroundings (even though they do not participate in the scattering). We managed to calculate the scattering probabilities knowing only the particles in the system and nothing else. This had not been achieved before.

We also studied what happens in the effective kinetic theory when there is at most one scattering during the evolution of the system by directly solving the theory for this case, i.e. without the full simulation. In this set-up the system shows a behaviour characteristic for liquids, but it does not come close to being a Quark-Gluon Plasma. We understand how this comes about in the theory, and this is important for understanding small collision systems like proton-proton. It will also help in validating the simulation, i.e. we can check that the simulation is working properly by comparing to this result.
The two models to be developed will be unique in that they in a single framework consistently describe collisions at colliders covering the entire range in system size (i.e. going from proton-proton to nucleus-nucleus collisions) and the entire range in particle energy (i.e. going from very low energy to very high energy particles). Both are set up as computer simulations whose output can be directly compared to experimental measurements. They are based on solid theory as much as possible. The underlying theory of the strong interaction is, however, far too complicated to be solved directly. In particular some effects that are crucial for a direct comparison to experimental data cannot be calculated, and have to be modeled instead.

Having these two models that describe various collisions without a priori assuming that a QGP is formed will be essential for our understanding of these collisions. They will help answering the questions like
* How is the QGP formed?
* Can it be formed in small systems such as proton-proton collisions?
* Why do proton-proton and nucleus-nucleus collisions share certain characteristics?
* What are the properties of the QGP, e.g. why does it behave like a fluid?
Answers to these questions will not only teach us something about an exotic state of matter, the QGP, which can only exist for fractions of a second in the laboratory, but will help us to better understand the strong force. The strong force has many fascinating facets: it holds atomic nucei together, generates masses for the protons and neutrons, and describes how the universe evolved very shortly after the Big Bang.

The simulation code will be published when it is ready, so that everybody can use it to check our results, or for their own research.