arXiv subjects

Horst Stoecker

Publications and source records attributed to Horst Stoecker.

At least 91 records · Page 5Linked to original sources

arXiv2018

Finite resonance widths influence the thermal-model description of hadron yields

Different scenarios for modeling resonances in a thermal model description of hadron yields measured in heavy-ion collisions are explored: the zero-width approximation, the energy independent Breit-Wigner scheme, and the energy dependent Breit-Wigner (eBW) scheme. Application of the eBW scheme leads to a notable suppression in the proton yields, stemming mainly from a reduced feeddown from $Δ$ resonances because of the threshold effects. A significantly improved agreement of thermal model with hadron yields measured in Pb-Pb collisions at $\sqrt{s_{_{NN}}} = 2.76$ TeV by the ALICE collaboration is obtained in the eBW scheme at $T \simeq 155$ MeV, indicating a possible resolution of the so-called 'proton anomaly'. The results obtained show that there are significant systematic uncertainties in the thermal model due to the modeling of broad resonances.

nucl-th↗

arXiv2018

Novel physics opportunities at the HESR-Collider with PANDA at FAIR

Exciting new scientific opportunities are presented for the PANDA detector at the High Energy Storage Ring in the redefined $\bar{\text{p}} \text{p}(A)$ collider mode, HESR-C, at the Facility for Antiproton and Ion Research (FAIR) in Europe. The high luminosity, $L \sim 10^{31}$ cm$^{-2}$ s$^{-1}$, and a wide range of intermediate and high energies, $\sqrt{s_{\text{NN}}}$ up to 30 GeV for $\bar{\text{p}} \text{p}(A)$ collisions will allow to explore a wide range of exciting topics in QCD, including the study of the production of excited open charm and bottom states, nuclear bound states containing heavy (anti)quarks, the interplay of hard and soft physics in the dilepton production, and the exploration of the regime where gluons -- but not quarks -- experience strong interaction.

hep-ph↗

arXiv2018

The cumulants of the baryon number from central Au+Au collision at $E_{lab}$= 1.23 GeV$/$nucleon reveal the nuclear mean-field potentials

Fluctuations of the baryon number in relativistic heavy-ion collisions are a promising observable to explore the structure of the QCD phase diagram. The cumulant ratios in heavy ion collisions at intermediate energies ($\sqrt{s_{\textrm{NN}}} < 7$ GeV) have not been studied to date. We investigate the effects of mean field potential and clustering on the cumulant ratios of baryon and proton number distributions in Au+Au collisions at beam energy of 1.23 GeV$/$nucleon as measured by the HADES Collaboration at GSI. Ultrarelativistic Quantum Molecular Dynamics (UrQMD) and the JAM model are used to calculate the cumulants with different mean field potentials. It is found that the cumulant ratios are strongly time dependent. At the early stage, the effects of the potentials on the fluctuations of the particle multiplicity in momentum space are relatively weak. The mean fields enhance the fluctuations during the expansion stage, especially for small rapidity acceptance windows. The enhancement of cumulant ratios for free protons is strongly suppressed as compared to that for all baryons. The mean field potentials and the clustering play an important role for the measured cumulant ratios at intermediate energy.

nucl-th↗

arXiv2018

Multiplicity dependence of light nuclei production at LHC energies in the canonical statistical model

The statistical model with exact conservation of baryon number, electric charge, and strangeness - the Canonical Statistical Model (CSM) - is used to analyze the dependence of yields of light nuclei at midrapidity on charged pion multiplicity at the LHC. The CSM calculations are performed assuming baryon-symmetric matter, using the recently developed Thermal-FIST package. The light nuclei-to-proton yield ratios show a monotonic increase with charged pion multiplicity, with a saturation at the corresponding grand-canonical values in the high-multiplicity limit, in good qualitative agreement with the experimental data measured by the ALICE collaboration in pp and Pb-Pb collisions at different centralities and energies. Comparison with experimental data at low multiplicities shows that exact conservation of charges across more than one unit of rapidity and/or a chemical freeze-out temperature which decreases with the charged pion multiplicity improves agreement with the data.

hep-ph↗

arXiv2018

Critical point of nuclear matter and beam energy dependence of net proton number fluctuations

The beam energy dependence of net baryon number susceptibilities is studied in the framework of the hadron resonance gas model with the attractive and repulsive van der Waals interactions between baryons. The collision energy dependences for the skewness $Sσ$ and kurtosis $κσ^2$ deviate significantly from the Poisson baseline and demonstrate the existence of rich structures at moderate collision energies. This behavior may result from the critical end point of the nuclear liquid-gas first order phase transition. In particular, $κσ^2$ shows a non-monotonic energy dependence, and, in contrast to the standard scenario for the QCD critical point, it does not decrease at low collision energies. It is also found that the measurable net proton fluctuations differ significantly from the net baryon fluctuations when interactions between baryons cannot be neglected. The results are compared with the experimental net proton number fluctuations measured by the STAR collaboration.

nucl-th↗

arXiv2018

Cluster Expansion Model for QCD Baryon Number Fluctuations: No Phase Transition at $μ_B / T < π$

A Cluster Expansion Model (CEM), representing a relativistic extension of Mayer's cluster expansion, is constructed to study baryon number fluctuations in QCD. The temperature dependent first two coefficients, corresponding to the partial pressures in the baryon number $B = 1$ and $B = 2$ sectors, are the only model input, which we fix by recent lattice data at imaginary baryochemical potential. All other coefficients are constructed in terms of the first two and required to match the Stefan-Boltzmann limit at $T \to \infty$. The CEM allows calculations of the baryon number susceptibilities $χ_k^B$ to arbitrary order. We obtain excellent agreement with available lattice data for the baryon fluctuation measures $χ_2^B$, $χ_4^B$, $χ_6^B$ and predict higher order susceptibilities, that are not yet available from Lattice QCD. The calculated susceptibilities are then used to extract the radius of convergence of the Taylor expansion of the pressure. The commonly used ratio test fails due to the non-trivial asymptotic behavior of the Taylor coefficients. At the same time, a more elaborate estimator provides finite convergence radii at all temperatures and in agreement with the singularities of Padé approximants. The associated singularities lie in the complex $μ_B/T$-plane and appear smoothly connected to the Roberge-Weiss transition at high temperatures and imaginary chemical potential. No evidence for a phase transition at $μ_B / T \lesssim π$ is found.

hep-ph↗

arXiv2018

Nuclear interactions and net-proton number fluctuations in heavy ion collisions at the SIS18 accelerator

The effect of nuclear interactions on measurable net-proton number fluctuations in heavy ion collisions at the SIS18/GSI accelerator is investigated. The state of the art UrQMD model including interaction potentials is employed. It is found that the nuclear forces enhance the baryon number cumulants, as predicted from grand canonical thermodynamical models. The effect however is smeared out for proton number fluctuations due to iso-spin randomization and global baryon number conservation, which decreases the cumulant ratios. For a rapidity acceptance window larger than $Δy> 0.4$ the effects of global baryon number conservation dominate and all cumulant ratios are significantly smaller than 1.

nucl-th↗

arXiv2018

Beth-Uhlenbeck approach for repulsive interactions between baryons in a hadron gas

The quantum mechanical Beth-Uhlenbeck (BU) approach for repulsive hard-core interactions between baryons is applied to the thermodynamics of a hadron gas. The second virial coefficient $a_2$ -- the "excluded volume" parameter -- calculated within the BU approach is found to be temperature dependent, and it differs dramatically from the classical excluded volume (EV) model result. At temperatures $T =100-200$ MeV, the widely used classical EV model underestimates the EV parameter for nucleons at a given value of the nucleon hard-core radius by large factors of 3-4. Previous studies, which employed the hard-core radii of hadrons as an input into the classical EV model, have to be re-evaluated using the appropriately rescaled EV parameters. The BU approach is used to model the repulsive baryonic interactions in the hadron resonance gas (HRG) model. Lattice data for the second and fourth order net baryon susceptibilities are described fairly well when the temperature dependent BU baryonic excluded volume parameter corresponds to nucleon hard-core radii of $r_c = 0.25-0.3$ fm. Role of the attractive baryonic interactions is also considered. It is argued that HRG model with a constant baryon-baryon EV parameter $v_{NN} \simeq 1$ fm$^3$ provides a simple yet efficient description of baryon-baryon interaction in the crossover temperature region.

nucl-th↗

arXiv2017

van der Waals Interactions and Hadron Resonance Gas: Role of resonance widths modeling on conserved charges fluctuations

The quantum van der Waals (QvdW) extension of the ideal hadron resonance gas (HRG) model which includes the attractive and repulsive interactions between baryons -- the QvdW-HRG model -- is applied to study the behavior of the baryon number related susceptibilities in the crossover temperature region. Inclusion of the QvdW interactions leads to a qualitatively different behavior of susceptibilities, in many cases resembling lattice QCD simulations. It is shown that for some observables, in particular for $χ_{11}^{BQ} / χ_2^B$, effects of the QvdW interactions essentially cancel out. It is found that the inclusion of the finite resonance widths leads to an improved description of $χ_2^B$, but it also leads to a worse description of $χ_{11}^{BQ} / χ_2^B$, as compared to the lattice data. On the other hand, inclusion of the extra, unconfirmed baryons into the hadron list leads to a simultaneous improvement in the description of both observables.

nucl-th↗

arXiv2017

Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential

The first principle lattice QCD methods allow to calculate the thermodynamic observables at finite temperature and imaginary chemical potential. These can be compared to the predictions of various phenomenological models. We argue that Fourier coefficients with respect to imaginary baryochemical potential are sensitive to modeling of baryonic interactions. As a first application of this sensitivity, we consider the hadron resonance gas (HRG) model with repulsive baryonic interactions, which are modeled by means of the excluded volume correction. The Fourier coefficients of the imaginary part of the net-baryon density at imaginary baryochemical potential -- corresponding to the fugacity or virial expansion at real chemical potential -- are calculated within this model, and compared with the $N_t = 12$ lattice data. The lattice QCD behavior of the first four Fourier coefficients up to $T \simeq 185$ MeV is described fairly well by an interacting HRG with a single baryon-baryon eigenvolume interaction parameter $b \simeq 1$ fm$^3$, while the available lattice data on the difference $χ_2^B - χ_4^B$ of baryon number susceptibilities is reproduced up to $T \simeq 175$ MeV.

hep-ph↗

arXiv2017

Multicomponent van der Waals equation of state: Applications in nuclear and hadronic physics

A generalization of the quantum van der Waals equation of state for a multi-component system in the grand canonical ensemble is proposed. The model includes quantum statistical effects and allows to specify the parameters characterizing repulsive and attractive forces for each pair of particle species. The model can be straightforwardly applied to the description of asymmetric nuclear matter and also for mixtures of interacting nucleons and nuclei. Applications of the model to the equation of state of an interacting hadron resonance gas are discussed.

nucl-th↗

arXiv2017

Modeling baryonic interactions with the Clausius-type equation of state

The quantum statistical Clausius-based equation of state is used to describe the system of interacting nucleons. The interaction parameters $a$, $b$, and $c$ of the model are fixed by the empirically known nuclear ground state properties and nuclear incompressibility modulus. The model is generalized to describe the baryon-baryon interactions in the hadron resonance gas (HRG). The predictions of such a Clausius-HRG model are confronted with the lattice QCD data at zero and at small chemical potentials, and are also contrasted with the standard van der Waals approach. It is found that the behavior of the lattice QCD observables in a high-temperature hadron gas is sensitive to the nuclear matter properties. An improved description of the nuclear incompressibility factor correlates with an improved description of the lattice QCD data in the crossover transition region.

nucl-th↗

arXiv2017

Enhancement of elliptic flow can signal a first order phase transition in high energy heavy ion collisions

The beam energy dependence of the elliptic flow,$v_2$, is studied in mid-central Au+Au collisions in the energy range of $3\leq \sqrt{s_{NN}} \leq 30$ GeV within the microscopic transport model JAM. The results of three different modes of JAM are compared; cascade-,hadronic mean field-, and a new mode with modified equations of state, with a first order phase transition (1.O.P.T.) and with a crossover transition. The standard hadronic mean field suppresses $v_2$, while the inclusion of the effects of a 1.O.P.T. (and also of a crossover transition) does enhance $v_2$ at $\sqrt{s_{NN}}<30$ GeV. The enhancement or suppression of the scaled energy flow, dubbed "elliptic flow"is understood as being due to out of plane- flow, i.e. $v_2<0$, dubbed out of plane - "squeeze-out", which occurs predominantly in the early, compression stage. Subsequently, the in-plane flow dominates, in the expansion stage, $v_2 > 0$. The directed flow, dubbed "bounce- off", is an independent measure of the pressure, which quickly builds up the transverse momentum transfer in the reaction plane. When the spectator matter leaves the participant fireball region, where the highest compression occurs, a hard expansion leads to larger $v_2$. A combined analysis of the three transverse flow coefficients, radial $v_0$-, directed $v_1$- and elliptic $v_2$- flow, in the beam energy range of $3\leq\sqrt{s_{NN}}\leq10$ GeV, distinguishes the different compression and expansion scenarios: a characteristic dependence on the early stage equation of state is observed. The enhancement of both the elliptic and the transverse radial flow and the simultaneous collapse of the directed flow of nucleons offers a clear signature if 1.O.P.T. is realized at the highest baryon densities created in high energy heavy-ion collisions.

nucl-th↗

arXiv2017

van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD

An extension of the ideal hadron resonance gas (HRG) model is constructed which includes the attractive and repulsive van der Waals (VDW) interactions between baryons. This VDW-HRG model yields the nuclear liquid-gas transition at low temperatures and high baryon densities. The VDW parameters $a$ and $b$ are fixed by the ground state properties of nuclear matter, and the temperature dependence of various thermodynamic observables at zero chemical potential are calculated within VDW-HRG model. Compared to the ideal HRG model, the inclusion of VDW interactions between baryons leads to a qualitatively different behavior of second and higher moments of fluctuations of conserved charges, in particular in the so-called crossover region $T\sim 140 - 190$ MeV. For many observables this behavior resembles closely the results obtained from lattice QCD simulations. This hadronic model also predicts nontrivial behavior of net-baryon fluctuations in the region of phase diagram probed by heavy-ion collision experiments. These results imply that VDW interactions play a crucial role in thermodynamics of hadron gas. Thus, the commonly performed comparisons of the ideal HRG model with the lattice and heavy-ion data may lead to misconceptions and misleading conclusions.

hep-ph↗

arXiv2017

Examination of the sensitivity of the thermal fits to heavy-ion hadron yield data to the modeling of the eigenvolume interactions

The hadron-resonance gas (HRG) model with the mass-proportional eigenvolume (EV) corrections is employed to fit the hadron yield data of the NA49 collaboration for central Pb+Pb collisions at $\sqrt{s_{_{\rm NN}}} = 6.3, 7.6, 8.8, 12.3,$ and $17.3$ GeV, the hadron midrapidity yield data of the STAR collaboration for Au+Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV, and the hadron midrapidity yield data of the ALICE collaboration for Pb+Pb collisions at $\sqrt{s_{\rm NN}} = 2760$ GeV. At given bombarding energy, for a given set of radii, the EV HRG model fits do not just yield a single $T-μ_B$ pair, but a whole range of $T-μ_B$ pairs, each with similarly good fit quality. These pairs form a valley in the $T-μ_B$ plane along a line of nearly constant entropy per baryon, $S/A$, which increases nearly linearly with bombarding energy $E_{\rm lab}$. The entropy per baryon values extracted from the data at the different energies are a robust observable: it is almost independent of the details of the modeling of the eigenvolume interactions and of the specific $T-μ_B$ values obtained. These results show that the extraction of the chemical freeze-out temperature and chemical potential is extremely sensitive to the modeling of the short-range repulsion between the hadrons. This implies that the ideal point-particle HRG values are not unique. The wide range of the extracted $T$ and $μ_B$ values suggested by the eigenvolume HRG fits, as well as the approximately constant $S/A$ at freeze-out, are consistent with a non-equilibrium scenario of continuous freeze-out, where hadrons can be chemically frozen-out throughout the extended space-time regions during the evolution of the system. Even when the EV HRG fits are restricted to modest temperatures suggested by lattice QCD, the strong systematic effects of EV interactions are observed.

hep-ph↗

arXiv2017

Surprisingly large uncertainties in temperature extraction from thermal fits to hadron yield data at LHC

The conventional hadron-resonance gas (HRG) model with the Particle Data Group (PDG) hadron input, full chemical equilibrium, and the hadron type dependent eigenvolume interactions is employed to fit the hadron mid-rapidity yield data of ALICE Collaboration for the most central Pb+Pb collisions. For the case of point-like hadrons the well-known fit result $T = 154 \pm 2$ MeV is reproduced. However, the situation changes if hadrons have different eigenvolumes. In the case when all mesons are point-like while all baryons have an effective hard-core radius of 0.3 fm the $χ^2$ temperature dependence of the $χ^2$ has a broad minimum in the temperature range of $155-210$ MeV, with fit quality comparable to the $T \sim 155$ MeV minimum in the point-particle case. Very similar result is obtained when only baryon-baryon eigenvolume interactions are considered, with eigenvolume parameter taken from previous fit to ground state of nuclear matter. Finally, when we apply the eigenvolume corrections with mass-proportional eigenvolume $v_i \sim m_i$, fixed to particular proton hard-core radius $r_p$, we observe a second minimum in the temperature dependence of the $χ^2$, located at the significantly higher temperatures. For instance, at $r_p = 0.5$ fm the fit quality is better than in the point-particle HRG case in a very wide temperature range of $170-320$ MeV, which gives an uncertainty in the temperature determination from the fit to the data of 150 MeV. These results show that thermal fits to the heavy-ion hadron yield data are very sensitive to the modeling of the short-range repulsion eigenvolume between hadrons, and that chemical freeze-out temperature can be extracted from the LHC hadron yield data only with sizable uncertainty.

hep-ph↗

arXiv2016

Equation of state dependence of directed flow in a microscopic transport model

We study the sensitivities of the directed flow in Au+Au collisions on the equation of state (EoS), employing the transport theoretical model JAM. The EoS is modified by introducing a new collision term in order to control the pressure of a system by appropriately selecting an azimuthal angle in two-body collisions according to a given EoS. It is shown that this approach is an efficient method to modify the EoS in a transport model. The beam energy dependence of the directed flow of protons is examined with two different EoS, a first-order phase transition and crossover. It is found that our approach yields quite similar results as hydrodynamical predictions on the beam energy dependence of the directed flow; Transport theory predicts a minimum in the excitation function of the slope of proton directed flow and does indeed yield negative directed flow, if the EoS with a first-order phase transition is employed. Our result strongly suggests that the highest sensitivity for the critical point can be seen in the beam energy range of $4.7\leq\srtNN\leq11.5$ GeV.

nucl-th↗

arXiv2016

Analysis of hadron yield data within hadron resonance gas model with multi-component eigenvolume corrections

We analyze the sensitivity of thermal fits to heavy-ion hadron yield data of ALICE and NA49 collaborations to the systematic uncertainties in the hadron resonance gas (HRG) model related to the modeling of the eigenvolume interactions. We find a surprisingly large sensitivity in extraction of chemical freeze-out parameters to the assumptions regarding eigenvolumes of different hadrons. We additionally study the effect of including yields of light nuclei into the thermal fits to LHC data and find even larger sensitivity to the modeling of their eigenvolumes. The inclusion of light nuclei yields, thus, may lead to further destabilization of thermal fits. Our results show that modeling of eigenvolume interactions plays a crucial role in thermodynamics of HRG and that conclusions based on a non-interacting HRG are not unique.

nucl-th↗