Phase transitions and critical behavior in hadronic transport with a relativistic density functional equation of state

Sorensen, Agnieszka; Koch, Volker

doi:10.1103/physrevc.104.034904

Cited by 35 publications

(28 citation statements)

References 62 publications

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“…1. More details on the expected behaviors of these quantities in both models can be found in [13]. Here, comparing the exact results to the approximations, we see that Eq.…”

Section: Validationmentioning

confidence: 60%

“…To our best knowledge, only a few attempts have been made to estimate 𝑐 𝑠 in matter created in heavy-ion collisions [11,12]. In our study [13], we suggest a novel way of measuring 𝑐 𝑠 using wellknown heavy-ion collision observables: the cumulants of the baryon number distribution, which are central observables in studies devoted to the QCD phase diagram due to their characteristic behavior near the CP [14,15]. This qualitatively distinct behavior of the cumulants near the CP follows directly from their dependence on the derivatives of pressure 𝑃 with respect to 𝜇 𝐵 .…”

Section: Introductionmentioning

confidence: 89%

“…First of them is the well-known Walecka model [16], which utilizes interactions of scalar and vector type and describes the ordinary nuclear liquid-gas phase transition. The other model is the relativistic vector density functional (VDF) model with two phase transitions [13], which utilizes vector-type interaction terms and describes two phase transitions: the nuclear liquid-gas phase transition and a conjectured highdensity, high-temperature phase transition modeling the QGP phase transition. The position of the critical point and the width of the spinodal region associated with this "QGP-like" phase transition can be freely chosen within the VDF model; in this work, the QGP-like phase transition is chosen to exhibit a CP at 𝑇 𝑐 = 100 MeV and 𝑛 𝑐 = 3𝑛 0 , with the 𝑇 = 0 boundaries of the spinodal region in the 𝑇-𝑛 𝐵 plane given by 𝑛 𝐵,left spinodal (𝑇 = 0) ≡ 𝜂 𝐿 = 2.5𝑛 0 and 𝑛 𝐵,right spinodal (𝑇 = 0) ≡ 𝜂 𝑅 = 3.32𝑛 0 , where 𝑛 0 = 0.160 fm −3 ; this choice is arbitrary and serves as a plausible example.…”

Section: Validationmentioning

confidence: 99%

“…The data points for the matched VDF results (shown only for collisions at low energies, where using the model is justified) are chosen to reproduce experimental values of 1 − 𝜅 3 𝜅 1 /𝜅 2 2 (see Fig.3). Figure adapted from[13].…”

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confidence: 99%

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Cumulants: It's More Than You Think

Sorensen¹,

Oliinychenko²,

Koch³

et al. 2021

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Cumulants of baryon number are given considerable attention in analyses of heavy-ion collision experiments as possible signatures of the QCD critical point. In this work, we show that the values of the lowest three cumulants can also be utilized to recover information about the isothermal speed of sound and its logarithmic derivative with respect to the baryon number density. This result provides a new method for obtaining information about fundamental properties of nuclear matter studied in heavy-ion collisions, with consequences for both the search for the QCD critical point and neutron star studies. While the approximations and the model comparison we considered apply to experiments at low energies, the approach itself can be used at any collision energy provided that measurements of cumulants of baryon number distribution as well as their temperature dependence are available.

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“…1. More details on the expected behaviors of these quantities in both models can be found in [13]. Here, comparing the exact results to the approximations, we see that Eq.…”

Section: Validationmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 89%

Section: Validationmentioning

confidence: 99%

mentioning

confidence: 99%

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Cumulants: It's More Than You Think

Sorensen¹,

Oliinychenko²,

Koch³

et al. 2021

Preprint

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“…The therewith obtained results are however only reliable for as long as the chemical potentials are small, else they are dominated by uncontrolled systematic uncertainties [79]. For larger baryon densities, it is possible to extract the equation of state, for example, from a chiral model relying on chiral symmetry restoration [80], from the PNJL model beyond the mean field approximation [81], from a quasiparticle approach [82], from the 3D Ising model universality class [83], or from the VDF model [84]. Note, that these equations of state contain a first order phase transition as well as a critical end point and are matched to a hadron resonance gas at lower temperatures and baryon densities.…”

Section: Heavy-ion Collisionsmentioning

confidence: 99%

Dynamical production of hadrons and photons in hydrodynamics + transport approaches for relativistic heavy-ion collisions

Schäfer¹

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The main subject of this thesis is the study of hadron and photon production in relativistic heavy-ion collisions by means of hydrodynamics+transport approaches. Two different kinds of such hybrid approaches are employed in this work, the SMASH-vHLLE-hybrid and a MUSIC+SMASH hybrid. While the former is capable of simulating heavy-ion collisions covering a wide range of collision energies down to √s = 4.3 GeV, reproducing the correct baryon stopping powers, the latter provides a framework to consistently model photon production in the hadronic stage of high-energy heavy-ion collisions. The SMASH-vHLLE-hybrid is a novel state-of-the-art hybrid approach whose development constitutes a major contribution to this thesis. It couples the hadronic transport SMASH to the 3+1D viscous hydrodynamics approach vHLLE. Therein, SMASH is employed to provide the fluctuating 3D initial conditions and to model the late hadronic rescattering stage, and vHLLE for the fluid dynamical evolution of the hot and dense fireball. The initial conditions are provided on a hypersurface of constant proper time, and the macroscopic evolution of the fireball is carried out down to an energy density of ecrit = 0.5 GeV/fm3, where particlization occurs. Consistency at the interfaces is verified in view of global, on-average quantum number conservation and the SMASH-vHLLE-hybrid is validated by comparison to SMASH+CLVisc as well as UrQMD+vHLLE hybrid approaches. The establishment of the SMASH-vHLLE-hybrid to theoretically describe heavy-ion collisions at intermediate and high collision energies forms a basis for a range of extensions and future research projects. It is further made available to the heavy-ion community by virtue of being published on Github. The SMASH-vHLLE-hybrid is applied to simulate Au+Au/Pb+Pb collisions between √s = 4.3 GeV and √s = 200.0 GeV. A good agreement with the experimentally measured rapidity and transverse mass spectra is obtained. In particular the baryon stopping dynamics are well reproduced at low, intermediate, and high collision energies. Excitation functions for the mid-rapidity yield and mean transverse momentum of pions, protons and kaons are demonstrated to agree well with their experimentally measured counterpart. These results further validate the approach and provide a solid baseline for potential future studies. The importance of annihilations and regenerations of protons and anti-protons is additionally investigated in Au+Au/Pb+Pb collisions between √s = 17.3 GeV and √s = 5.02 TeV with the SMASH-vHLLE-hybrid. It is found that, regarding the p + p ̄ ↔ 5 π reaction, 20-50% (depending on the rapidity range) of the (anti-)proton yield lost to annihila- tions in the hadronic rescattering stage is restored owing to the back reaction. The back reaction thus constitutes a non-negligible contribution to the final (anti-)proton yield and should not be neglected when modelling the late rescattering stage of heavy-ion collisions. The MUSIC+SMASH hybrid is a hybrid approach ideally suited to model the production of photons in relativistic heavy-ion collisions. Therein, the macroscopic production of photons in the hadronic stage in MUSIC relies on the identical effective field theories as the photon cross sections implemented in SMASH for the microscopic production. The MUSIC+SMASH hybrid thus provides the first consistent framework to the end of hadronic photon production. It accounts for 2 → 2 scattering processes of the kind π + ρ → π + γ and pion bremsstrahlung processes π + π → π + π + γ. The MUSIC+SMASH hybrid is employed in an ideal 2D setup to systematically assess the importance of non-equliibrium dynamics in the hadronic rescattering stage on mid-rapidity transverse momentum spectra and elliptic flow of photons at RHIC/LHC energies. This is achieved by comparing the outcome of the MUSIC+SMASH hybrid, involving an out-of-equilibrium late rescattering stage, to macroscopically approximating late stage photon production by means of MUSIC, employed down to temperatures well below the switching temperature. It is found that non-equilibrium dynamics have only minor implications for photon transverse momentum spectra, but significantly enhance the photon elliptic flow. At RHIC energies, an enhancement of up to 70%, and at LHC of up to 65% is observed in the non-equilibrium afterburner as compared to its hydrodynamical counterpart. In combination with the large amount of photons produced above the particlization temperature, these differences are modest regarding the transverse momentum spectra, but a significant enhancement of the elliptic flow is observed at low transverse momenta. Below pT ≈ 1.4 GeV, the combined v2 is enhanced by up to 30% at RHIC, and up to 20% at the LHC within the non-equilibrium setup as compared to its approximation via hydrodynamics. Non-equilibrium dynamics in the hadronic rescattering stage are hence important, especially in view of momentum anisotropies at low transverse momenta. These findings thus contribute to the understanding of low-pT photons produced in heavy-ion collisions at RHIC/LHC energies and the MUSIC+SMASH hybrid employed for this study provides a baseline for additional studies regarding photon production in the future. To summarize, the approaches and frameworks presented in this thesis provide a good baseline for further extensions and studies in order to improve the understanding of hadron and photon production in relativistic heavy-ion collisions across a wide range of collision energies. More broadly, such future studies of hadrons and photons may contribute to enhance the understandig of the properties of the fundamental building blocks of matter, of which everything that surrounds us is made of.

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