# Chiral Symmetry and Topological Properties in Lattice QCD With Wilson Twisted Mass Quarks

**Principal Investigator:** Carsten Urbach, Universität Bonn (Germany)

**HPC-Platform:** SuperMUC of LRZ

**Date Published: **October 2014

**LRZ Project ID: **pr63po

Symmetries are important concepts in all fields of physics. Interestingly, symmetries are not only important when they are fulfilled, but also when they are broken. A well known example for a broken symmetry is the magnetisation in a ferromagnet. Even though the ferromagnet is on a microscopic level rotationally invariant, a macroscopic magnetisation can be developed. This happens either when an external magnetic field is applied, which gives the system a preferred direction. But it can also happen spontaneously when the ferromagnet is below the so-called Curie temperature, with no external magnetic field involved.

Quantum Chromodynamics (QCD) represents the nowadays widely accepted theory describing the interaction of quarks and gluons. QCD exhibits a very similar phenomenon as a ferromagnet. The symmetry is called chiral symmetry, the magnetisation is called chiral condensate and the equivalent of the external field are finite quark masses. However, chiral symmetry is also thought to be broken spontaneously, and therefore, the chiral condensate is expected to be non-zero even in the limit of vanishing quark masses at low enough temperatures.

The challenge is that first the chiral condensate cannot be measured easily and second QCD cannot be solved analytically on a piece of paper. The method of choice is, therefore, computer simulations. And due to the complexity of QCD the largest available supercomputers like SuperMUC must be used to obtain any inside into QCD. The simulations are performed by discretising the space-time by a lattice spacing, which takes sub-nano meter values. This discretised world is then simulated using so-called Monte-Carlo methods. The discretisation introduces errors which have to be removed by investigating the limit of the lattice spacing going to zero. As said before, quark masses break chiral symmetry explicitly. As the scientists are interested in the chiral condensate of spontaneously broken chiral symmetry, they hence have to study the limit of zero quark masses as well.

Scientists of DESY and the Rheinische Friedrich-Wilhelms-Universität Bonn have computed the chiral condensate for QCD with up, down, strange and charm dynamical quark flavours at zero temperature and for three values of the lattice spacing [1]. The result is in shown in the figure. It is visible that the researchers control the chiral extrapolation of the re-normalised chiral condensate in the quark mass and the continuum extrapolation (shown in the inset) very well.

This is the first evaluation of the chiral condensate using dynamical up, down, strange and charm quarks. It confirms the expectation that chiral symmetry is broken spontaneously and it provides important insides into the fundamental mechanisms of how the matter surrounding us is built.

Copyright: Rheinische Friedrich-Wilhelms-Universität Bonn

**Scientific Contact:**

Prof. Dr. Carsten Urbach

Rheinische Friedrich-Wilhelms-Universität Bonn

Helmholtz Institut für Strahlen und Kernphysik (Theorie)

Nussallee 14-16, D-53115 Bonn/Germany

E-mail: urbach@hiskp.uni-bonn.de

*October 2014*