arXiv subjects

Reinhard Stock

Publications and source records attributed to Reinhard Stock.

At least 19 recordsLinked to original sources

arXiv2023

Anisotropy of magnetized quark matter

Strong transient magnetic fields are generated in non-central relativistic heavy-ion collisions. These fields induce anisotropy within the strongly interacting medium that, in principle, can affect the thermodynamic properties of the medium. We use the Polyakov loop extended Nambu Jona-Lasinio model to study the quark matter subjected to an external magnetic field at vanishing baryon chemical potential ($\mu_{B}$). We have estimated the degree of anisotropy in the speed of sound and isothermal compressibility within the magnetized quark matter as a function of temperature ($T$) and magnetic field ($eB$). This study helps us to understand the extent of directionality generated in the initial stages of non-central collisions while giving us useful information about the system.

hep-ph↗

arXiv2021

Ambiguities in the hadro-chemical freeze-out of Au+Au collisions at SIS18 energies and how to resolve them

The thermal fit to preliminary HADES data of Au+Au collisions at $\sqrt{s_{_{NN}}}=2.4$ GeV shows two degenerate solutions at $T\approx50$ MeV and $T\approx70$ MeV. The analysis of the same particle yields in a transport simulation of the UrQMD model yields the same features, i.e. two distinct temperatures for the chemical freeze-out. While both solutions yield the same number of hadrons after resonance decays, the feeddown contribution is very different for both cases. This highlights that two systems with different chemical composition can yield the same multiplicities after resonance decays. The nature of these two minima is further investigated by studying the time-dependent particle yields and extracted thermodynamic properties of the UrQMD model. It is confirmed, that the evolution of the high temperature solution resembles cooling and expansion of a hot and dense fireball. The low temperature solution displays an unphysical evolution: heating and compression of matter with a decrease of entropy. These results imply that the thermal model analysis of systems produced in low energy nuclear collisions is ambiguous but can be interpreted by taking also the time evolution and resonance contributions into account.

hep-ph↗

arXiv2018

The QCD Phase Diagram from Statistical Model Analysis

In high multiplicity nucleus-nucleus collisions baryon-antibaryon annihilation and regeneration occur during the final hadronic expansion phase, thus distorting the initial equilibrium multiplicity ratios. We quantify the modifications employing the hybrid UrQMD transport model and apply them to the grand canonical partition functions of the Statistical Hadronization Model(SHM). We analyze minimum bias and central Pb+Pb collision data at SPS and LHC energy. We explain the Pion to Proton ratio puzzle. We also reproduce the deuteron to proton ratio at LHC energy by the SHM, and by UrQMD after attaching a phase space coalescence process. We discuss the resulting (T,$μ_{B}$) diagram.

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arXiv2017

The QCD Phase Diagram from Statistical Model Analysis

Ideally, the Statistical Hadronization Model (SHM) freeze-out curve should reveal the QCD parton-hadron phase transformation line in the ($T$,$μ_B$) plane. We discuss the effects of various final state interaction phenomena, like baryon-antibaryon annihilation, core-corona effects or QCD critical point formation, which shift or deform the SHM freezeout curve. In particular, we present a method to remove the annihilation effects by quantifying them with the microscopic hadron transport model UrQMD. We further discuss the new aspects of hadronization that could be associated with the relatively broad cross-over phase transformation as predicted by lattice-QCD theory at low $μ_B$. That opens up the possibility that various observables of hadronization, e.g. hadron formation or susceptibilities of higher order (related to grand canonical fluctuations of conserved hadronic charges) may freeze out at different characteristic temperatures. This puts into question the concept of a universal \textit{(pseudo-)critical} temperature, as does the very nature of a cross-over phase transformation.

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arXiv2015

Toward the Limits of Matter: Ultra-relativistic nuclear collisions at CERN

Strongly interacting matter as described by the thermodynamics of QCD undergoes a phase transition, from a low temperature hadronic medium to a high temperature quark-gluon plasma state. In the early universe this transition occurred during the early microsecond era. It can be investigated in the laboratory, in collisions of nuclei at relativistic energy, which create "fireballs" of sufficient energy density to cross the QCD Phase boundary. We describe 3 decades of work at CERN, devoted to the study of the QCD plasma and the phase transition. From modest beginnings at the SPS, ultra-relativistic heavy ion physics has evolved today into a central pillar of contemporary nuclear physics and forms a significant part of the LHC program.

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arXiv2014

Collective Flow of QCD Matter: a Historical Introduction

We present a historical review of the physics observables developed for relativistic nuclear collisions, that describe collective hydrodynamic flow of hadronic or partonic matter, and of the corresponding experimental progress. We begin with the early discovery phase of radial and directed flow at the Bevalac, and continue the review until the recent work at RHIC and LHC, and related theory.

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arXiv2013

Hadron Formation in Relativistic Nuclear Collisions and the QCD Phase Diagram

We analyze hadrochemical freeze-out in central Pb+Pb collisions at CERN SPS and LHC energies. We determine the effects of baryon and antibaryon annihilation and/or regeneration occurring during the final cascade expansion stage of the collisions by deriving "survival factors" for each hadronic species and all energies considered by employing the UrQMD hybrid model. These survival factors are shown to resemble the pattern of data deviation from the statistical equilibrium calculations with the statistical model. We apply them in the SM data analysis, obtaining new points in the $T-μ_B$ plane which follow closely the parton-hadron phase boundary predicted by lattice QCD.

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arXiv2013

Hadron Formation and the Phase Diagram of QCD Matter

We investigate hadronic species freeze-out systematics in A+A collisions at low SPS energies, corresponding to a baryochemical potential above 300 MeV, analyzing NA49 hadron production data in the framework of the statistical hadronization model, and in the UrQMD hadronic transport model. Observing no deviation from universal grand canonical hadro-chemical equilibrium freeze-out, we argue that the observed hadronic freeze-out points should universally signal the boundary line of the hadronic phase in the QCD matter phase diagram.

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arXiv2012

Net-baryon-, net-proton-, and net-charge kurtosis in heavy-ion collisions within a relativistic transport approach

We explore the potential of net-baryon, net-proton and net-charge kurtosis measurements to investigate the properties of hot and dense matter created in relativistic heavy-ion collisions. Contrary to calculations in a grand canonical ensemble we explicitly take into account exact electric and baryon charge conservation on an event-by-event basis. This drastically limits the width of baryon fluctuations. A simple model to account for this is to assume a grand-canonical distribution with a sharp cut-off at the tails. We present baseline predictions of the energy dependence of the net-baryon, net-proton and net-charge kurtosis for central ($b\leq 2.75$ fm) Pb+Pb/Au+Au collisions from $E_{lab}=2A$ GeV to $\sqrt{s_{NN}}=200$ GeV from the UrQMD model. While the net-charge kurtosis is compatible with values around zero, the net-baryon number decreases to large negative values with decreasing beam energy. The net-proton kurtosis becomes only slightly negative for low $\sqrt{s_{NN}}$.

hep-ph↗

arXiv2012

Hadronization and Hadronic Freeze-Out in Relativistic Nuclear Collisions

We analyze hadrochemical freeze-out in central Pb+Pb collisions at CERN SPS energies, employing the hybrid version of the Ultrarelativistic Quantum Molecular Dynamics model, which describes the transition from a hydrodynamic stage to hadrons by the Cooper-Frye mechanism, and matches to a final hadron-resonance cascade. We fit the results both before and after the cascade stage using the Statistical Model, to assess the effect of the cascade phase. We observe a strong effect on antibaryon yields except anti-Omega, resulting in a shift in T and mu_B of the freeze-out curve. We discuss indications of a similar effect in SPS and RHIC data, and propose a method to recover the bulk hadron freeze-out conditions.

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arXiv2009

The QCD Phase Diagram: Expectations and Challenges

A survey is given of recent QCD theory advances concerning the phase diagram, in particular the indications for a critical point and adjacent first order phase transition at high baryo-chemical potential, and the new ideas concerning a further phase at high $μ_{B}$, the quarkyonic matter phase. The latter state might finally explain the hadro-chemical equilibrium freeze-out points from A+A collisions at energies below SPS energy. We review several event-by-event fluctuation signals that promise to shed a light on the existence of a critical point, and we discuss its possible reflection in recent lattice QCD calculations.

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arXiv2009

Relativistic Nuclear Collisions

A comprehensive introduction is given to the field of relativistic nuclear collisions, and the phase diagram of strongly interacting matter. The content of this complex of reviews is shown.

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arXiv2008

Global Properties of Nucleus-Nucleus Collisions

In this lecture note, we discuss the global properties of nucleus-nucleus collisions. After a brief introduction to heavy-ion collisions, we introduce useful kinematics and then discuss the bulk hadron production in A+A collisions. At the end we discuss the hadronization and hadronic freeze-out in A+A collisions. We have tried to cover the topic from very fundamental arguments especially for the beginners in the field. We also give very useful formulae frequently used by experimentalists, from a first principle derivation.

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arXiv2008

Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram

This review will be concerned with our knowledge of extended matter under the governance of strong interaction, in short: QCD matter. Strictly speaking, the hadrons are representing the first layer of extended QCD architecture. In fact we encounter the characteristic phenomena of confinement as distances grow to the scale of 1 fm (i.e. hadron size): loss of the chiral symmetry property of the elementary QCD Lagrangian via non-perturbative generation of "massive" quark and gluon condensates, that replace the bare QCD vacuum. However, given such first experiences of transition from short range perturbative QCD phenomena (jet physics etc.), toward extended, non perturbative QCD hadron structure, we shall proceed here to systems with dimensions far exceeding the force range: matter in the interior of heavy nuclei, or in neutron stars, and primordial matter in the cosmological era from electro-weak decoupling (10^-12 s) to hadron formation (0.5 10^-5 s). This primordial matter, prior to hadronization, should be deconfined in its QCD sector, forming a plasma (i.e. color conducting) state of quarks and gluons: the Quark Gluon Plasma (QGP).

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arXiv2007

Hadronization revisited: the dynamics behind hadro-chemical equilibrium

The multiplicity of hadronic species created in elementary, and in nucleus-nucleus collisions, are known to be well reproduced by the statistical hadronization model, in its canonical and grand-canonical versions.To understand the origin of the implied equilibrium we revisit the hadronization models developed for e+e- annihilation to hadrons which imply spatial color pre-confinement clusters forming at the end of the pQCD evolution, which decays into on-shell hadrons/resonances. The classical ensemble description arises as a consequence of decoherence and phase space dominance during cluster formation, and decay.For A+A collisions we assume that hadronization occurs from similar singlet clusters which will overlap spatially owing to the extreme density. This is imaged in the transition to the grand-canonical ensemble.This transition sets in with increasing A and collision centrality. It can be described by a percolation model.

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arXiv2004

Relativistic Nucleus-Nucleus Collisions: from the BEVALAC to RHIC

I briefly describe the initial goals of relativistic nuclear collisions research, focusing on the LBL Bevatron/Bevalac facility in the 1970's. An early concept of high hadronic density fireball formation, and subsequent isentropic decay (preserving information as to the high density stage) led to an outline of physics observables that could determine the nuclear matter equation of state at several times nuclear ground state matter density. With the advent of QCD the goal of locating, and characterizing the hadron-parton deconfinement phase transformation suggested the need for higher $\sqrt{s}$, the research thus moving to the BNL AGS and CERN SPS, finally to RHIC at BNL. A set of physics observables is discussed where present data span the entire $\sqrt{s}$ domain, from Bevalac and SIS at GSI, to top RHIC energy. Referring, selectively, to data concerning bulk hadron production, the overall $\sqrt{s}$ evolution of directed and radial flow observables, and of pion pair Bose-Einstein correlation are discussed. The hadronization process is studied in the grand canonical statistical model. The resulting hadronization points in the plane T vs. $μ_B$ converge onto the parton-hadron phase boundary predicted by finite $μ_B$ lattice QCD, from top SPS to RHIC energy. At lower SPS and top AGS energy a steep strangeness maximum occurs at which the Wroblewski parameter $λ_s \approx $ 0.6; a possible connection to the QCD critical point is discussed. Finally the unique new RHIC physics is addressed: high $p_T$ hadron suppression and jet "tomography".

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arXiv2004

Study on chemical equilibrium in nucleus-nucleus collisions at relativistic energies

We present a detailed study of chemical freeze-out in nucleus-nucleus collisions at beam energies of 11.6, 30, 40, 80 and 158A GeV. By analyzing hadronic multiplicities within the statistical hadronization approach, we have studied the chemical equilibration of the system as a function of center of mass energy and of the parameters of the source. Additionally, we have tested and compared different versions of the statistical model, with special emphasis on possible explanations of the observed strangeness hadronic phase space under-saturation.

nucl-th↗

arXiv2004

Relativistic Nucleus-Nucleus Collisions: A Connection between the Strangeness-Maximum at $\sqrt{s} \approx$ 7 GeV and the QCD Critical Endpoint from Lattice Studies

A steep maximum occurs in the Wroblewski ratio between strange and non-strange quarks created in central nucleus-nucleus collisions, of about A=200, at the lower SPS energy $\sqrt{s} \approx$ 7 GeV. By analyzing hadronic multiplicities within the grand canonical statistical hadronization model this maximum is shown to occur at a baryochemical potential of about 450 MeV. In comparison, recent QCD lattice calculations at finite baryochemical potential suggest a steep maximum of the light quark susceptibility, to occur at similar $μ_B$, indicative of "critical fluctuation" expected to occur at or near the QCD critical endpoint. This endpoint hat not been firmly pinned down but should occur in the 300 MeV $ < μ_B^c<700$ MeV interval. It is argued that central collisions within the low SPS energy range should exhibit a turning point between compression/heating, and expansion/cooling at energy density, temperature and $μ_B$ close to the suspected critical point. Whereas from top SPS to RHIC energy the primordial dynamics create a turning point far above in $ε$ and T, and far below in $μ_B$. And at lower AGS energies the dynamical trajectory stays below the phase boundary. Thus, the observed sharp strangeness maximum might coincide with the critical $\sqrt{s}$ at which the dynamics settles at, or near the QCD endpoint.

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