QCD equation of state at finite density with a critical point from an alternative expansion scheme*

In Ref. [1], results for the QCD equation of state from the lattice Taylor expansion were combined with the 3D Ising model critical behavior, to build a family of equations of state which match first principle results and contain a critical point in the expected universality class for QCD. This family of equations of state was limited to baryon chemical potentials from 0  to 450MeV, due to the limitations of the Taylor expansion. In Ref.[2], an alternative expansion scheme was introduced, for extrapolating the lattice QCD equation of state to finite chemical potential. In this research, we combine these two approaches to obtain a family of equations of state in the range of baryon chemical potentials from  0 to  700 MeV and Temperature from  30 MeV to 800 MeV, that match the lattice QCD results at a small density and contain a 3D-Ising model critical point. With these new equations of state, we substantially extend the coverage of the QCD phase diagram. 

Our open-source code allows the user to choose the position and strength of the critical point. Our results provide input for hydrodynamical simulations at finite Temperature and unprecedentedly large baryon chemical potential and will help constrain the location of the critical point through a comparison with experimental data from the Second Beam Energy Scan at RHIC.

[1]  Paolo Parotto et al. “Lattice-QCD-based equation of state with a critical point”. In:arXiv preprintarXiv:1805.05249(2018)

[2]   S Borsányi et al. “Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme”. In: Physical Review Letters126.23 (2021), p. 232001