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1. QCD critical point, Lee-Yang edge singularities, and Padé resummations

   https://doi.org/10.1103/PhysRevC.110.015203  

   Başar, Gökçe (July 2024, Physical Review C)

   I analyze the trajectory of the Lee-Yang edge singularities of the QCD equation of state in the complex baryon chemical potential ( ${\mu }_B$) plane for different values of the temperature by using the recent lattice results for the Taylor expansion coefficients up to eighth order in ${\mu }_B$and various resummation techniques that blend in Padé expansions and conformal maps. By extrapolating from this information, I estimate for the location of the QCD critical point: $T_c\approx 100$MeV, ${\mu }_c\approx 580$MeV. I also estimate the crossover slope at the critical point to be ${\alpha }_1\approx 9^{\circ }$and further constrain the nonuniversal mapping parameters between the three-dimensional Ising model and QCD equations of state. Published by the American Physical Society2024 

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2. QCD equation of state with improved precision from lattice simulations

   https://doi.org/10.1051/epjconf/202429614007  

   Parotto, Paolo; Borsányi, Szabolcs; Fodor, Zoltan; Guenther, Jana N; Kara, Ruben; Pásztor, Attila; Ratti, Claudia; Szabó, Kalman K (January 2024, EPJ Web of Conferences)

   Bellwied, R; Geurts, F; Rapp, R; Ratti, C; Timmins, A; Vitev, I (Ed.)

   The equation of state of Quantum Chromodynamics has been in recent years the focus of intense effort from first principle methods, mostly lattice simulations, with particular interest to the finite baryon density regime. Because of the sign problem, various extrapolation methods have been used to reconstruct bulk properties of the theory up to as far asμ_B=T≃ 3:5. However, said efforts rely on the equation of state at vanishing baryon density as an integration constant, which up toμ_B=T≃ 2 - 2:5 proves to be the dominant source of uncertainty at the level of precision currently available. In this contribution we present the update of our equation of state at zero net baryon density from 2014, performing a continuum limit from lattices with Nτ = 8; 10; 12; 16. We show how the improved precision is translated in a lower uncertainty on the extrapolated equation of state at finite chemical potential. 

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3. Lattice-QCD-based equations of state at finite temperature and density

   https://doi.org/10.31349/SuplRevMexFis.3.040907  

   Karthein, Jamie M.; Mroczek, Debora; Nava Acuña, Angel R.; Noronha-Hostler, Jacquelyn; Parotto, Paolo; Price, Damien R.; Ratti, Claudia (December 2022, Suplemento de la Revista Mexicana de Física)

   The equation of state (EoS) of QCD is a crucial input for the modeling of heavy-ion-collision (HIC) and neutron-star-merger systems. Calculations of the fundamental theory of QCD, which could yield the true EoS, are hindered by the infamous Fermi sign problem which only allows direct simulations at zero or imaginary baryonic chemical potential. As a direct consequence, the current coverage of the QCD phase diagram by lattice simulations is limited. In these proceedings, two different equations of state based on first-principle lattice QCD (LQCD) calculations are discussed. The first is solely informed by the fundamental theory by utilizing all available diagonal and non-diagonal susceptibilities up to O(µ 4 B) in order to reconstruct a full EoS at finite baryon number, electric charge and strangeness chemical potentials. For the second, we go beyond information from the lattice in order to explore the conjectured phase structure, not yet determined by LQCD methods, to assist the experimental HIC community in their search for the critical point. We incorporate critical behavior into this EoS by relying on the principle of universality classes, of which QCD belongs to the 3D Ising Model. This allows one to study the effects of a singularity on the thermodynamical quantities that make up the equation of state used for hydrodynamical simulations of HICs. Additionally, we ensure that these EoSs are valid for applications to HICs by enforcing conditions of strangeness neutrality and fixed charge-to-baryonnumber ratio. 

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4. 4D-TExS: A new 4D lattice-QCD equation of state with extended density coverage

   https://doi.org/10.1051/epjconf/202531606002  

   Jahan, Johannes; Abuali, Ahmed; Borsányi, Szabolcs; Kahangirwe, Micheal; Parotto, Paolo; Pásztor, Attila; Ratti, Claudia; Shah, Hitansh; Trabulsi, Seth A (January 2025, EPJ Web of Conferences)

   Cheshkov, C; Guernane, R; Maire, A (Ed.)

   Although calculations of QCD thermodynamics from first-principle lattice simulations are limited to zero net-density due to the fermion sign problem, several methods have been developed to extend the equation of state (EoS) to finite values of theB,Q,Schemical potentials. Taylor expansion aroundµ_i=0 (i = B,Q,S) enables to cover with confidence the region up toµ_i/T< 2.5. Recently, a new method has been developed to compute a 2D EoS in the (T,µ_B) plane. It was constructed through aT-expansion scheme (TExS), based on a resummation of the Taylor expansion, and is trusted up to densities aroundµ_B/T= 3.5. We present here the new 4D-TExS EoS, a generalization of the TExS to all 3 chemical potentials, expected to offer a larger coverage than the 4D Taylor expansion EoS. After explaining the basics of theT-Expansion Scheme and how it is generalized to multiple dimensions, we will present results for thermodynamic observables as functions of temperature and both finite baryon and strangeness chemical potentials. 

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5. Calculating QCD Phase Diagram Trajectories of Nuclear Collisions using a Semi-analytical Model

   https://doi.org/10.1051/epjconf/202327601012  

   Mendenhall, Todd; Lin, Zi-Wei (January 2023, EPJ Web of Conferences)

   Kim, Y.; Moon, D.H. (Ed.)

   At low to moderate collision energies where the parton formation time τ F is not small compared to the nuclear crossing time, the finite nuclear thickness significantly affects the energy density ϵ( t ) and net conserved-charge densities such as the net-baryon density n B ( t ) produced in heavy ion collisions. As a result, at low to moderate energies the trajectory in the QCD phase diagram is also affected by the finite nuclear thickness. Here, we first discuss our semi-analytical model and its results on ϵ( f ), n R ( t ), n Q ( t ), and n s ( t ) in central Au+Au collisions. We then compare the T ( t ), μ B ( t ), μ Q ( t ), and μ S ( t ) extracted with the ideal gas equation of state (EoS) with quantum statistics to those extracted with a lattice QCD-based EoS. We also compare the T -μ B trajectories with the RHIC chemical freezeout data. Finally, we discuss the effect of transverse flow on the trajectories. 

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