QCD thermodynamics with isospin density and magnetic fields
Final Report Abstract
In this Emmy Noether project we have investigated QCD thermodynamics in the presence of phenomenologically relevant parameters: isospin-asymmetry, background magnetic fields and baryon densities. This involved both the adaptation of established methods to explore the yet uncharted regions of the QCD phase diagram as well as the development of novel techniques to describe and discuss new phenomena. All of the investigations at nonzero isospin-asymmetry made use of simulations with an auxiliary pion source parameter, which needs to be extrapolated to zero for physical results. This extrapolation, when performed in a naive way, is a source of large systematic errors. An improvement scheme was therefore developed that overcomes the problems of this extrapolation and enables the precision and reliability that we have been aiming for in the proposal. The most important result of the project is the determination of the QCD phase diagram in the temperature–isospin-asymmetry plane for physical quark masses in the continuum limit. This rich phase diagram was found to exhibit an interplay of several interesting phenomena including chiral symmetry breaking, deconfinement and Bose-Einstein condensation as well as signatures for a BCS-type superconducting phase. In addition, a detailed comparison to a routinely employed approximation to QCD (Taylor expansion in the chemical potential) was performed and the systematics of this approximation quantified. Another milestone result is the determination of the equation of state of this system throughout the phase diagram. Beyond the original plans of the proposal, this enabled us to determine the cosmic trajectory in the case that nonzero lepton asymmetries were present in the early Universe and assess, for the first time, the impact of pion condensation on primordial gravitational waves. We also discussed various novel aspects of the phase diagram for nonzero magnetic fields, including the interpretation of the deconfinement transition as a percolation phenomenon, the factorization of QCD observables into Landau levels and the pion mass-dependence of the inverse magnetic catalysis phenomenon. A new method has been worked out that relates the equation of state in the presence of low magnetic fields (i.e. the magnetic susceptibility) to the anomalous magnetic moment of the muon. Finally, first results for the investigation of the low baryon density region of the QCD phase diagram using novel methods were presented. The research goals of the proposal have been extended in various directions, including the lattice determination of masses and decay constants of magnetized hadrons, the impact of magnetic fields on hydrodynamic simulations of heavy-ion collisions or the interpretation of the equation of state via the AdS/CFT correspondence. Besides our efforts in research, the group has been active in teaching and supervision, as well as establishing external collaborations. Regarding our scientific output, the group members have published 21 articles and 19 conference proceedings since the start of the project. Moreover, members of our group have presented the results on isospin-asymmetry and/or magnetic fields altogether on 63 occasions – 59 talks and 4 posters.
Publications
- “Landau levels in QCD,” Phys. Rev. D96 no. 7, (2017) 074506
F. Bruckmann, G. Endrödi, M. Giordano, S. D. Katz, T. G. Kovács, F. Pittler, and J. Wellnhofer
(See online at https://doi.org/10.1103/PhysRevD.96.074506) - “New class of compact stars: Pion stars,” Phys. Rev. D 98 no. 9, (2018) 094510
B. B. Brandt, G. Endrödi, E. S. Fraga, M. Hippert, J. Schaffner-Bielich, and S. Schmalzbauer
(See online at https://doi.org/10.1103/PhysRevD.98.094510) - “QCD phase diagram for nonzero isospin-asymmetry,” Phys. Rev. D97 no. 5, (2018) 054514
B. B. Brandt, G. Endrödi, and S. Schmalzbauer
(See online at https://doi.org/10.1103/PhysRevD.97.054514) - “Universal Magnetoresponse in QCD and N = 4 SYM,” JHEP 09 (2018) 070
G. Endrödi, M. Kaminski, A. Schäfer, J. Wu, and L. Yaffe
(See online at https://doi.org/10.1007/JHEP09(2018)070) - “Weak decay of magnetized pions,” Phys. Rev. Lett. 121 no. 7, (2018) 072001
G. S. Bali, B. B. Brandt, G. Endrödi, and B. Gläßle
(See online at https://doi.org/10.1103/PhysRevLett.121.072001) - “Magnetic catalysis and inverse catalysis for heavy pions,” JHEP 07 (2019) 007
G. Endrödi, M. Giordano, S. D. Katz, T. G. Kovács, and F. Pittler
(See online at https://doi.org/10.1007/JHEP07(2019)007) - “Magnetized baryons and the QCD phase diagram: NJL model meets the lattice,” JHEP 08 (2019) 036
G. Endrödi and G. Markó
(See online at https://doi.org/10.1007/JHEP08(2019)036) - “Reliability of Taylor expansions in QCD,” Phys. Rev. D 99 no. 1, (2019) 014518
B. B. Brandt and G. Endrödi
(See online at https://doi.org/10.1103/PhysRevD.99.014518) - “Magnetic susceptibility of QCD matter and its decomposition from the lattice,” JHEP 07 (2020) 183
G. S. Bali, G. Endrödi, and S. Piemonte
(See online at https://doi.org/10.1007/JHEP07(2020)183) - “Pion Condensation in the Early Universe at Nonvanishing Lepton Flavor Asymmetry and Its Gravitational Wave Signatures,” Phys. Rev. Lett. 126 no. 1, (2021) 012701
V. Vovchenko, B. B. Brandt, F. Cuteri, G. Endrödi, F. Hajkarim, and J. Schaffner-Bielich
(See online at https://doi.org/10.1103/PhysRevLett.126.012701)
