Freeze-out Curve Research Articles

Cumulants of the chiral order parameter in a nonequilibrium Bjorken expansion with a QCD critical point

To understand experimentally obtained net-proton number cumulants in the search for the QCD critical point, we study a dynamical model based on an effective quark-meson Lagrangian with chiral symmetry. We investigate the evolution of the expanding medium created in a heavy-ion collision using a spatially homogeneous fluid and a time-dependent order parameter, the sigma field evolved by a Langevin equation. We extract cumulants of the sigma field along a parametrized freeze-out curve and match the obtained freeze-out points to corresponding beam energies. These cumulants can be related to cumulants of the net-proton number through the sigma-proton coupling to provide a qualitative comparison to experimental data from STAR’s beam energy scan program. We demonstrate that the presence of the spinodal or mixed phase region around the first-order chiral phase transition allows for a wide interval of cumulants at the lowest beam energies.

Neutron irradiation induced defects in oxides and their impact on the oxide properties

Understanding the irradiation-induced defects in oxides is of interest for a wide range of applications. ZnO is an interesting oxide with mixed ionic and covalent bonding that contains a variety of point defect structures—making it an excellent model for studying irradiation-induced defects and their impact on properties. Here, we investigate the effects of neutron irradiation on the formation of defects and on the structural, optical, and electrical properties of ZnO single crystals. We observe the formation of vacancies and voids via positron annihilation spectroscopy. Neutron irradiation led to a significant deterioration of the ZnO structure and formed a high concentration of point defects, vacancy clusters, and voids with large disparities in their structure across variable irradiation times. It also led to significant changes in the optical properties and sample color. Irradiation for 444 h induced a high concentration of Cu acceptors as well as a high concentration of Ga donors. Temperature-dependent Hall effect measurements revealed the competing production of donors and acceptors and showed an increase in the slope of the carrier freeze-out curve with increasing irradiation dose. This work demonstrates the combined effects of neutron irradiation in producing a wide range of structural defects, impurities, and dopants in oxides and their enormous impact on modifying the oxide structure and both the optical and electronic properties. It particularly emphasizes the importance of considering the production of new impurities and dopants during the neutron irradiation of oxides.

Quartic cumulant of baryon number in the presence of a QCD critical point

In the context of the ongoing search for the QCD critical point at the Relativistic Heavy-Ion Collider, we study the equation of state near the critical point in the temperature and baryon chemical potential plane. We use the parametric representation introduced in earlier literature, which maps the universal 3D Ising equation of state onto the QCD phase diagram using several non-universal parameters. We focus on the quartic cumulant of the baryon number, or baryon number susceptibility~$\chi_4^B$, which can be accessed experimentally via net-proton fluctuation kurtosis measurements. It was originally predicted, through universality arguments based on the {\em leading} singular contribution, that $\chi_4^B$ and net-proton kurtosis should show a specific non-monotonic behavior due to the critical point. In particular, when following the freeze-out curve on the phase diagram by decreasing beam energy, the kurtosis is expected to dip, and then peak, when the beam energy scan passes close to the critical point. We study the effects of the non-universal and thus far unknown parameters of the Ising-to-QCD mapping on the behavior of~$\chi_4^B$. We find that, while the peak remains a solid feature, the presence of the critical point does not necessarily cause a dip in $\chi_4^B$ on the freezeout line {\em below} the transition temperature. The critical point contribution to the dip appears only for a narrow set of mapping parameters, when subleading singular terms are sufficiently suppressed.

Exploring hot and dense QCD matter with HADES

Experiments at snn 3 GeV provide the lowest energy point of the global effort made by the heavy-ion community in order to map the QCD phase diagram. This correspond to the highest baryon chemical potential, 700-900 MeV according to the universal freeze-out curve, and temperatures of the fireball of 60-80 MeV. The formed matter can be characterized in terms of particle spectra, fluctuations and correlations. The dilepton spectrum is dominated by thermal emission from the medium and it is sensitive to in medium hadron properties. Strangeness production occurs below the free nucleon-nucleon threshold and it is a sensitive probe to test models of strangeness propagation in matter and its coupling to baryons. Data show a common scaling of measured yields as a function of number of participating nucleons independently on the strangeness content or mass of the hadron. Strangeness propagation in cold nuclear matter produced in pion induced reactions on heavy and light targets shows a significant absorption of negative kaons in heavy targets as well as a similar behaviour of ϕ indicating a strong coupling of ϕ with nucleons. Two-pion correlations, flow harmonics, fluctuations are explored as well in order to further pin down the properties of the created matter.

Feeddown contributions from unstable nuclei in relativistic heavy-ion collisions

We estimate the feeddown contributions from decays of unstable A=4 and A=5 nuclei to the final yields of protons, deuterons, tritons, 3He, and 4He produced in relativistic heavy-ion collisions at sNN>2.4 GeV, using the statistical model. The feeddown contribution effects do not exceed 5% at LHC and top RHIC energies due to the large penalty factors involved, but are substantial at intermediate collision energies. We observe large feeddown contributions for tritons, 3He, and 4He at sNN≲10 GeV, where they may account for as much as 70% of the final yield at the lower end of the collision energies considered. Sizable (>10%) effects for deuteron yields are observed at sNN≲4 GeV. The results suggest that the excited nuclei feeddown cannot be neglected in the ongoing and future analysis of light nuclei production at intermediate collision energies, including HADES and CBM experiments at FAIR, NICA at JINR, RHIC beam energy scan and fixed-target programmes, and NA61/SHINE at CERN. We further show that the freeze-out curve in the T-μB plane itself is affected significantly by the light nuclei at high baryochemical potential.

Exploring the hadron resonance gas phase on the QCD phase diagram

Lattice computations of strongly interacting matter at finite temperature T and baryon chemical potential μB suggest that the QCD thermodynamics deep in the hadronic phase can be adequately modeled by an ideal hadron resonance gas (I-HRG). However, it is not clear where on the (μB, T) plane this description breaks down, making it essential to account for hadronic interactions and change in the nature of the degrees of freedom. We have studied several thermodynamic functions within the I-HRG model and try to identify the region of the QCD phase diagram where it becomes essential to include non-ideal effects into the I-HRG model. We work with only those thermodynamic quantities that show a monotonic rise with T and μB in I-HRG. Their high temperature limiting values where QCD becomes simply a Stefan–Boltzmann (SB) gas of massless quarks and gluons is known. The rise of these quantities in I-HRG beyond the corresponding SB limit values indicate the need to include interactions into I-HRG to study QCD thermodynamics. This works as a guiding principle on the QCD phase diagram where interacting HRGs can take over from I-HRG. For μB/T ≤ 2, shoots the SB limit at the smallest T, while for higher values of μB/T, takes over. We further comment on the relative positions between the freeze-out curve obtained by thermal fits to the measured hadron yields and the obtained line where the I-HRG overshoots the SB limit.

Effect of inverse magnetic catalysis on conserved-charge fluctuations in a hadron resonance gas model

The effect of inverse magnetic catalysis (IMC) has been observed on the conserved charge fluctuations and the correlations along the chemical freeze-out curve in a hadron resonance gas model. The fluctuations and the correlations have been compared with and without charge conservations. The charge conservation plays an important role in the calculation of the fluctuations at nonzero magnetic field and for the fluctuations in the strange charge at zero magnetic field. The charge conservation diminishes the correlations $\chi_{BS}$ and $\chi_{QB}$, but enhances the correlation $\chi_{QS}$. The baryonic fluctuations (2nd order) at $B = 0.25$ ${GeV}^2$ increases more than two times compared to $B = 0$ at higher $\mu_{B}$. The fluctuations have been compared at nonzero magnetic field along the freeze-out curve i.e along fitted parameters of the chemical freeze-out temperature and chemical potentials, with the fluctuations at nonzero magnetic field along the freeze-out curve with the IMC effect, and the results are very different with the IMC effect. This is clearly seen in the products of different moments ${{\sigma}^2}/{M}$ and $S\sigma$ of net-kaon distribution.

Unruh thermal hadronization and the cosmological constant

We use black holes with a negative cosmological constant to investigate aspects of the freeze-out temperature for hadron production in high energy heavy-ion collisions. The two black hole solutions present in the anti-de Sitter geometry have different mass and are compared to the data showing that the small black hole solution is in good agreement. This is a new feature in the literature since the small black hole in general relativity has different thermodynamic behavior from that of the large black hole solution. We find that the inclusion of the cosmological constant (which can be interpreted as the plasma pressure) leads to a lowering of the temperature of the freeze-out curve as a function of the baryochemical potential, improving the description previously suggested by Castorina, Kharzeev, and Satz.

Strangeness at high μB: Recent data from FOPI and HADES

Strangeness production in heavy-ion reactions at incident energies at or below the threshold in NN collisions gives access to the characteristics of bulk nuclear matter and the properties of strange particles inside the hot and dense nuclear medium, like potentials and interaction cross sections. At these energies strangeness is produced in multi-step processes potentially via excitation of intermediate heavy resonances. The amount of experimental data on strangeness production at these energies has increased substantially during the last years due to the FOPI and the HADES experiments at SIS18 at GSI. Experimental data on K+ and K0 production support the assumption that particles with an s quark feel a moderate repulsive potential in the nuclear medium. The situation is not that clear in the case of K-. Here, spectra and flow of K- mesons is influenced by the contribution of ø mesons which are decaying into K+K- pairs with a branching ratio of 48.9 %. Depending on incident energy upto 30 % of all K- mesons measured in heavyion collisions are originating from ø-decays. Strangeness production yields - except the yield of Ξ- are described by thermal hadronisation models. Experimental data not only measured for heavy-ion collisions but also in proton induced reactions are described with sets of temperature T and baryon chemical potential μb which are close to a universal freeze-out curve which is fitting also experimental data obtained at lower baryon chemical potential. Despite the good description of most particle production yields, the question how this is achieved is still not settled and should be the focus of further investigations.

An estimate of the bulk viscosity of the hadronic medium

The bulk viscosity (ζ) of the hadronic medium has been estimated within the ambit of the Hadron Resonance Gas (HRG) model including the Hagedorn density of states. The HRG thermodynamics within a grand canonical ensemble provides the mean hadron number as well as its fluctuation. The fluctuation in the chemical composition of the hadronic medium in the grand canonical ensemble can result in non-zero divergence of the hadronic fluid flow velocity, allowing us to estimate the ζ of the hadronic matter up to a relaxation time. We study the influence of the hadronic spectrum on ζ and find its correlation with the conformal symmetry breaking measure, . We estimate ζ along the contours with constant, (total entropy/net baryon number) in the plane (temperature-baryonic chemical potential) for and 300. We also assess the value of ζ on the chemical freeze-out curve for various centers of mass energy () and find that the bulk viscosity to entropy density ratio, is larger in the energy range of the beam energy scan program of RHIC, low energy SPS run, AGS, NICA and FAIR, than LHC energies.

Extended Soft-wall Model for the QCD Phase Diagram

The soft-wall model, emerging as bottom-up holographic scenario anchored in the AdS/CFT correspondence, displays the disappearance of normalisable modes referring to vector mesons at a temperature $T_{\dis}$ depending on the chemical potential $\mu$, $T_{\dis}(\mu)$. We explore options for making $T_{\dis}(\mu)$ consistent with the freeze-out curve $T_{\rm f.o.}(\mu)$ from relativistic heavy-ion collisions and the cross-over curve $T_{\rm c}(\mu)$ from QCD at small values of $\mu$.

Exploring effects of magnetic field on the hadron resonance gas

We present a study of the effects of magnetic fields on fluctuations and correlations in the hadron resonance gas model. We find significant changes in the fluctuations of net baryon number, electric charge and strangeness. This is also reflected in various fluctuation ratios along the freezeout curve.

Critical line of2+1flavor QCD: Toward the continuum limit

We determine the continuum limit of the curvature of the pseudocritical line of QCD with $n_f$=2+1 staggered fermions at nonzero temperature and quark density. We perform Monte Carlo simulations at imaginary baryon chemical potentials, adopting the HISQ/tree action discretization, as implemented in the code by the MILC collaboration. Couplings are adjusted so as to move on a line of constant physics, as determined in Ref.~\cite{Bazavov:2011nk}, with the strange quark mass $m_s$ fixed at its physical value and a light-to-strange mass ratio $m_l/m_s=1/20$. The chemical potential is set at the same value for the three quark species, $\mu_l=\mu_s\equiv \mu$. We attempt an extrapolation to the continuum using the results on lattices with temporal size up to $L_t=12$. Our estimate for the continuum value of the curvature $\kappa$ at zero baryon density, $\kappa=0.020(4)$, is compared with recent lattice results and with experimental determinations of the freeze-out curve.

Freeze-out, Hadronization and Statistical Model

The comparison of the statistical hadronization model with experimental data and lattice QCD results is not always straightforward. Indeed, the interpretation of the ϕ meson production, of the proton to pion multiplicity ratio at LHC and the agreement of the freeze-out curve with the lattice critical line in the T — µB plane, require further analyses. Moreover the dynamics of the hadronization has to be compatible with: 1) the statitical behavior also observed in elementary high energy collisions; 2) a universal hadronization temperature for all high energy collisions; 3) the freeze-out criteria. In these lecture notes the SHM is recalled and some explanations of the puzzling aspects of its comparison with data are discussed.

Determination of freeze-out conditions from fluctuations in the Hadron Resonance Gas model

Fluctuations of conserved charges measured in Heavy-Ion Collisions (HICs) received increasing attention in recent years, because they are good candidates to explore the phase diagram of QCD matter. During the last year, net-electric charge and net-proton moments of multiplicities measured at RHIC have been published by the STAR collaboration, for a range of collision energies which spans a region of the phase diagram at finite chemical potential. Here we present a new freeze-out curve obtained using the Hadron Resonance Gas (HRG) model approach to fit these experimental data. The HRG model is modified in order to have a realistic description of the HICs: kinematic cuts, resonance feed-down and resonance regeneration are taken into account. Our result is in agreement with preliminary studies by the ALICE collaboration, and is supported by a recent lattice analysis of the same quantities.

Study of D- measure from Polyakov-Nambu-Jona-Lasinio model

We present the first case study of the net charge fluctuations in terms of D i measure within the framework of an effective model viz. Polyakov Nambu-Jona-Lasinio model. The net charge fluctuation is obtained from the charge susceptibility computed in this model. A parameterization of the freeze-out curve in heavy-ion experiments has been used to obtain D as a function of the collision energy.

The thermodynamics of heavy light hadrons at freezeout

In the discussion of hadronization at or close to the freeze-out curve statistical (hadron resonance gas) models play an important role. In particular, in the charmonium sector, regeneration models are considered which rely on the fact that charmonium states can form again already at temperatures well above the QCD transition or hadronization temperature. An important ingredient in these considerations is the regeneration or hadronization of open charm states. In this talk we report on a lattice QCD analysis of correlations of open strange and charm with other conserved quantum numbers like the net baryon number and electric charge. We analyze the temperature range in which an uncorrelated hadron resonance gas (HRG) provides an adequate description of such correlations. This limits the range of validity of HRG based thermodynamics in open flavor channels and provides an estimate for the melting temperature of heavy-light hadrons.

Fluctuations and correlations of conserved charges in an excluded-volume hadron resonance gas model

We present temperature ($T$) and baryonic chemical potential ($\mu_B$) dependence of higher order fluctuations and correlation between conserved charges in Excluded Volume Hadron Resonance Gas (EVHRG) model. Products of moments, such as ratio of variance to mean ($\sigma^2/M)$, product of skewness and standard deviation ($S\sigma$), product of kurtosis and variance ($\kappa\sigma^2$), for net-proton, net-kaon and net-charge have been evaluated on the phenomenologically determined freeze-out curve. Further, products of moments for net-proton and net-charge have been compared with the experimental data measured by STAR experiment. The dependence of the model result on the hadronic radius parameter has also been discussed.

Critical line of2+1flavor QCD

We determine the curvature of the (pseudo)critical line of QCD with ${n}_{f}\text{ }=\text{ }2\text{ }+\text{ }1$ staggered fermions at nonzero temperature and quark density by analytic continuation from imaginary chemical potentials. Monte Carlo simulations are performed by adopting the highly improved staggered quarks /tree action discretization, as implemented in the code by the MILC Collaboration, suitably modified to include a nonzero imaginary baryon chemical potential. We work on a line of constant physics, as determined in Ref. [1], adjusting the couplings so as to keep the strange quark mass ${m}_{s}$ fixed at its physical value, with a light to strange mass ratio of ${m}_{l}/{m}_{s}=1/20$. In the present investigation, we set the chemical potential at the same value for the three quark species, ${\ensuremath{\mu}}_{l}={\ensuremath{\mu}}_{s}\ensuremath{\equiv}\ensuremath{\mu}$. We explore lattices of different spatial extensions, ${16}^{3}\ifmmode\times\else\texttimes\fi{}6$ and ${24}^{3}\ifmmode\times\else\texttimes\fi{}6$, to check for finite size effects, and present results on a ${32}^{3}\ifmmode\times\else\texttimes\fi{}8$ lattice, to check for finite cutoff effects. We discuss our results for the curvature $\ensuremath{\kappa}$ of the (pseudo)critical line at $\ensuremath{\mu}=0$, which indicate $\ensuremath{\kappa}=0.018(4)$, and compare them with previous lattice determinations by alternative methods and with experimental determinations of the freeze-out curve.

Chemical freeze-out and higher order multiplicity moments

We calculate the non-normalized moments of the particle multiplicity within the framework of the hadron resonance gas (HRG) model. At finite chemical potential $\mu$, a non-monotonic behavior is observed in the thermal evolution of third order moment (skewness $S$) and the higher order ones as well. Among others, this observation likely reflects dynamical fluctuations and strong correlations. The signatures of non-monotonicity in the normalized fourth order moment (kurtosis $\kappa$) and its products get very clear. Based on these findings, we introduce a novel condition characterizing the universal freeze-out curve. The chemical freeze-out parameters $T$ and $\mu$ are described by vanishing $\kappa\, \sigma^2$ or equivalently $m_4=3\,\chi^2$, where $\sigma$, $\chi$ and $m_4$ are the standard deviation, susceptibility and fourth order moment, respectively. The fact that the HRG model is not able to release information about criticality related to the confinement and chiral dynamics should not veil the observations related to the chemical freeze-out. Recent lattice QCD studies strongly advocate the main conclusion of the present paper.