Numerical Determination of the Phase Diagram of Hadronic and Nuclear Matter

**Principal Investigator:**

Owe Philipsen

**Affiliation:**

Institute for Theoretical Physics, Goethe-Universität Frankfurt

**Local Project ID:**

hkf8

**HPC Platform used:**

JUQUEEN of JSC

**Date published:**

The fundamental theory of the strong interactions is Quantum Chromodynamics (QCD). Its elementary constituents are quarks and gluons, which cannot be observed as isolated particles. Under ordinary conditions on earth, a strong attractive force binds them to form protons and neutrons, the building blocks of the atomic nuclei observed in nature, as well as many other hadrons. On the other hand, when these particles meet at very high energies, their interaction weakens and no binding happens. Such conditions are realized at either high temperatures in the early universe, shortly after the big bang, or at high matter density, such as in very compact stars. In these cases nuclear matter "melts" into a quark gluon plasma. This state of matter is also created and studied in current and future heavy ion collision experiments at RHIC in Brookhaven/USA and FAIR in Darmstadt/Germany.

Similar to the phase diagram of water, which tells us for which combinations of pressure and temperature it is solid, liquid or gaseous, the QCD phase diagram determines the form of hadronic matter depending on temperature and matter density, Fig.1. An important question is whether there are first order phase transitions via bubble nucleation (as in boiling water) or the matter forms are smoothly connected. Unfortunately, QCD cannot be solved by analytic methods. However, a version reformulated on a discrete space time grid called "Lattice QCD" is amenable to numerical simulations.

In order to be realistic, the simulated system has to be large enough to avoid boundary effects, and the grid has to be fine enough to approximate the original continuum theory. This can only be achieved with High Performance Computing resources. For theoretical reasons, quark masses are varied away from their values in nature. For zero and infinite quark masses, QCD exhibits symmetries whose breaking as a function of temperature T causes the first order phase transitions in the lower left and upper right corner of Fig.2. The boundary lines represent phase transitions of second order. For quark masses in between, in particular their physical values, there is just a smooth crossover from hadronic matter to plasma. For quark masses smaller than physical, the simulation effort explodes, but is necessary in order to understand the massless limit and its effect on the physical situation.

A particular challenge is the description of finite matter density, which is parametrized by chemical potential µ, adding an additional axis to the diagram. Real chemical potential cannot be simulated directly, so we work at imaginary values and extrapolate to real values. The boundary lines from Fig.2 then turn into the surfaces in Fig.3. The result is that with small but increasing matter density the transition from nuclear to plasma matter is completely smooth, without bubble nucleation. This prediction is being tested in heavy ion experiments.

In the meantime we have verified the qualitative structure of Fig.2 and Fig.3 to be realised on coarse lattices. It is a long term project to repeat these simulations on finer grids, until a continuum limit can be taken, which will give the final physics answers.

**Scientific Contact:**

Prof. Dr. Owe Philipsen

Institut für Theoretische Physik / ITP

Johann Wolfgang Goethe-Universität

Max-von-Laue-Straße 1

Campus Riedberg

60438 Frankfurt am Main (Germany)

e-mail: philipsen [@] th.physik.uni-frankfurt.de

*Local project ID: hkf8*

*March 2020*