QCD Phase Transition in the Chiral Limit

**Principal Investigator:**

Frithjof Karsch

**Affiliation:**

Universität Bielefeld, Faculty of Physics

**Local Project ID:**

chbi08

**HPC Platform used:**

JUWELS and JUQUEEN of JSC

**Date published:**

The quantum theory of quarks and gluons is called Quantum Chromodynamics (QCD). Almost since its inception in the 1960’s physicists speculated on its phase diagram. At low temperatures and net-quark densities quarks can be observed only in bound states called hadrons (quark confinement). At sufficiently high temperatures and densities the quarks are liberated and start to exist as quasi-free particles (de-confinement). Together with the gluons, which mediate the interaction between quarks, they form a new state of matter, the Quark Gluon Plasma (QGP).

Along with the liberation of the new quark degrees of freedom, an important symmetry between left- and right-handed quarks is restored. This so-called chiral symmetry is manifest in the QCD Lagrangian of massless quarks. However, the ground state of the theory, the QCD vacuum, does not respect this symmetry, we say that the symmetry is spontaneously broken. The massless version of QCD thus exhibits a true continuous phase transition between a chirally broken and confined phase to a chirally restored and de-confined phase. This is to be seen in contrast to QCD with massive quarks as they are found in nature, where the transition is only a rapid crossover. The true chiral phase transition in the massless case is interesting as universal critical behavior is expected and can be predicted by the symmetry of QCD.

In a series of scientific studies using various HPC systems around the world the HotQCD Collaboration investigated the transition temperature in QCD. For massive quarks we determined the precise pseudo-critical transition temperature: *T*_{pc}*=156.5 MeV*. We also investigated how the temperature changes with the introduction of a small but non-vanishing net-quark density. The latest piece of the puzzle, which was leveraged also due to the vast computing power of the JUWELS system of JSC, is now the determination of the critical transition temperature in the massless limit of QCD:

This result is not only of academic interest but has also important phenomenological consequences. Firstly, remnants of the massless phase transition point might be observed in event-by-event fluctuations of conserved charges measured at the ALICE experiment at CERN. Secondly, *T*_{c} can be seen as an upper bound for the long discussed and searched for critical point in the QCD phase diagram at non-vanishing net-quark densities.

For the determination of *T*_{c} a series of calculations with smaller and smaller quark masses was performed [1-3]. In Figure 2, we show the variance of the order parameter, which signals the transition from the chirally broken to the chirally symmetric phase. A standard estimator for the transition temperature is the peak position of this quantity. It approaches *T*_{c} from above, with decreasing quark masses. We invented and considered also two further improved estimators, which exhibit much reduced quark mass dependence. One of them is based on the point where the variance takes 60% of the peak height and is indicated by the black symbols. We summarize all systematic uncertainties from continuum (lattice spacing *a*), thermodynamic (Volume *V*) and chiral (mass *m*) extrapolations in Figure 3.

For all these extrapolations several Ansätze and data ranges are considered. Our final result for the critical temperature is (as already stated above):

**References**

[1] H. Ding, P. Hegde, O. Kaczmarek, F. Karsch, A. Lahiri, S. Li, S. Mukherjee, H. Ohno, P. Petreczky, C. Schmidt, P. Steinbrecher and O. Kaczmarek, “*Chiral Phase Transition Temperature in ( 2+1 )-Flavor QCD,*” Phys. Rev. Lett. **123**, no.6, 062002 (2019) [arXiv:1903.04801 [hep-lat]].

[2] H. Ding, P. Hegde, F. Karsch, A. Lahiri, S. Li, S. Mukherjee and P. Petreczky, “*Chiral phase transition of (2+1)-flavor QCD*,” Nucl. Phys. A **982,** 211-214 (2019) [arXiv:1807.05727 [hep-lat]].

[3] O. Kaczmarek, F. Karsch, A. Lahiri, L. Mazur and C. Schmidt, “*QCD phase transition in the chiral limit,*” Published in the NIC Series volume 50, page 193 (2020); ISBN: 978-3-95806-443-0, [arXiv:2003.07920 [hep-lat]].

**Scientific Contact**

Prof. Dr. Frithjof Karsch

University of Bielefeld

Faculty of Physics

Postfach 100131, D-33501 Bielefeld (Germany)

e-mail: karsch@physik.uni-bielefeld.de

*JSC project ID: chbi18*

*July 2020*