Physics motivation

Introduction

Chiral symmetry  

The effect of chiral symmetry restoration

The structure of Hadrons

Form Factors

Vector Meson Dominance Model

In-medium modifications of vector meson properties

Electromagnetic transition Form Factors

Characteristics of heavy ion collisions

Strange particles

DiLepton Production

Exploring the QCD phase diagram with heavy-ion collisions

Experimental conditions

Looking into the fireball

Strangeness and charm production

Maximum baryon densities

Physics Motivation

It is a great challenge to understand the processes, which led to the creation of the physical world around us. In the Big Bang theory, a singularity in time started the existence of our universe, its evolution thereafter being determined by physical processes that occur in different time scales. Baryonic genesis, the formation of baryonic matter, is believed to have formed on a time scale of 10 to 20 microseconds after the beginning. The understanding of the behavior of baryonic matter is of central importance since baryonic matter serves as a building block of all the atoms we know today. The only way of studying baryonic genesis in the laboratory is by means of high-energy heavy-ion collisions. In such collisions, nuclear matter is produced at high density and high temperature, and thus creating the physical environment necessary for the study of baryonic genesis.   

The main goals of modern nuclear physics is the investigation of hadron properties, such as effective masses, decay widths, electromagnetic form factors etc., inside nuclear matter under extreme conditions of high density and high temperature. The aim of this proposal is a better understanding of the various processes contributing to di-lepton production in hot and compressed nuclear matter, leading ultimately to a search for signals of the partial restoration of the chiral symmetry of QCD. Electron-positron pair spectroscopy of the vector meson decays is assumed to be a promising tool to investigate these properties, as leptons do not undergo strong final-state interaction with the surrounding nuclear medium. They carry information from the inside of strongly interacting matter to the outside world, and bring forth information not accessible by measuring purely hadronic final states. For such decay studies, the light short-lived vector mesons and are of particular interest since they have a direct e+e- decay branch. While the mesons ( ) mainly decay inside a nucleus or a reaction medium of comparable volume, even the longer living mesons ( ) might do so to a substantial fraction.

The new High Acceptance Di-Electron Spectrometer (HADES) [1] is set up at GSI by an international collaboration of 22 institutions from 9 European countries. The physics program for HADES can be summarized by the following broad research goals.
  1. The study of electron-positron pair emission in relativistic heavy-ion collisions.

  2. Di-lepton production in elementary reactions and experiments aimed at studying the structure of hadrons.

  3. The study of vector meson mass distributions.

  4. The study of chiral symmetry restoration to elementary properties of hadrons.

The HADES spectrometer is a second-generation experiment for high-resolution electron pair spectroscopy, produced in nucleon-nucleon and nucleus-nucleus collisions.  The key features of this experiment are an excellent mass resolution (m/m 1%) and a very large acceptance (=40%) for comprehensive studies of the behavior of , , and   mesons in the nuclear medium. Apart from this, the new instrument provides strong background rejection power, high granularity, and advanced count rate capability to cope with the heaviest collision systems (238U + 238U at E=1xA GeV), which are necessary to achieve nuclear energy densities (2-3 times normal nuclear matter density).  

presently available at GSI for all ions, from protons to uranium. The physics for the new Compressed Baryonic Matter (CBM) [2] experiment can be summarized as follows:

    The first goal is to achieve a comprehensive and quantitative understanding of all aspects of matter that are governed by the strong (nuclear) and the weak force, that critically determine the structure of matter at the microscopic level. Matter at the level of nuclei, nucleons, quarks and gluons are governed by the strong interaction and are often referred to as hadronic matter.

    The second goal addresses many-body aspects of matter. Research during the past century found that the structure of matter has an intrinsic complexity, which is more than just the linear superposition of its components. These many-body aspects govern the behavior of matter as it appears in our physical world as well as on the hadronic level.

These two broad science aspects, the structure and dynamics of hadronic matter and the complexity of the physical many-body system, transcend and determine the more specific research programs that will be pursued at the future facility. These include:

  1. The study of in-medium properties of hadrons

  2. The search for the chiral and deconfinement phase transition at high baryon densities,

  3. The study of the nuclear equation of state of baryonic matter at high densities,

  4. The search for the critical point strongly interacting matter,

  5. The search for new states of matter at highest baryon densities.

Our experimental approach is to measure simultaneously observables, which are sensitive to high-density effects and phase transitions. The key observables include:

Short-lived light vector mesons (, , ), which decay into e+e- pairs. Since the leptons are almost unaffected by the passage through the high-density matter, they provide, as a penetrating probe, almost undistorted information on the conditions in the interior of the collision zone.
Strange baryons (anti-baryons), which contain more than one strange (anti-strange) quark. Hyperons serve as a probe for high baryon densities. The phase-space distributions of baryons are expected to be sensitive to the early and dense stage of the collisions.
 Mesons containing a charm or an anti-charm quark (open charm, e.g. D mesons). An experimental investigation of charm production mesons at threshold beam energies will shed light on the in-medium production processes. 
 Macro-dynamical effects, like collective flow of nuclear matter during the expansion of the initially compressed system and critical event-by-event fluctuations. These observables contain information on the nuclear equation of state at high densities. The identification of a critical point would provide direct evidence for the existence and the character of a deconfinement phase transition in strongly interacting matter.
 Charmonium production and propagation as a probe for quark-gluon matter at high baryon densities.

Introduction

The standard model of particle physics describes the current physics understanding of matter on a microscopic scale. It uses two fundamental forces: The electroweak force and the strong force. These forces can in principle describe the dynamics of matter in our world. Quantum Chromo Dynamics (QCD) is the theory of the strong force. Strongly interacting matter which constitutes more than 99% of the visible mass in our world exists in different forms:

Quarks, the elementary particles of QCD, which have not been observed so far as free particles. 
Hadrons, consisting of three quarks, which include the nucleons, the building blocks of the matter, and the mesons consisting of a quark and an antiquark. Quarks are bound together by the exchange of gluons, the mediators of the strong force.
Atomic nuclei, consisting of up to about 270 protons and neutrons. These nucleons are bound by a short-range attraction.
Neutron stars, consisting of about 1057 neutrons, which are bound by gravitation. 

 For processes at high energies, where large 4-momentum transfers are involved, the equations of QCD are perturbatively solvable. For low 4-momentum transfers a numerical solution is achieved by Lattice QCD calculations, which are strongly limited by the computing technology available today. Therefore, one needs to use effective theories for describing processes at low 4-momentum transfer. These theories are based on principle symmetries of the QCD or use model assumptions from phenomenological indications resulting in solvable equations.

QCD describes the dynamics of quarks and gluons [3] and is able to explain the properties of hadronic matter. It has the remarkable feature that the interaction between two particles, quarks or gluons, becomes weak as the separation between them is reduced. This phenomenon, called asymptotic freedom, simplifies the description of certain high-energy processes and is the main reason behind the successful account of short distance phenomena in QCD. Conversely, at large distances, comparable to the size of the nucleon, the interaction between two quarks is strong.

The characteristics of the hadrons can be found listed for example in the Particle Physics Booklet [4], where the world data is summarized. The most essential properties include the charge, the mass, the life-time, the decay channels and the spin, etc. Many of these fundamental features are well known and understood, but there are still many open questions. These properties are measured in vacuum and one expects changes when these particles are surrounded by hadronic matter. By analogy, this is similar to the effective mass of an electron moving in a crystal lattice; the surrounding potentials of the lattice result in a change of the mass used in the differential equations of their motion.

A great effort is being made for the experimental observation and theoretical interpretation of this fundamental issue, to get a better understanding of the laws of nature. A special class of hadrons is the so-called light vector mesons. These mesons have a rare electromagnetic decay channel into an electron/positron pair. One remarkable feature of this decay channel is the fact that the leptons do not interact strongly with hadronic matter and therefore penetrate hadronic matter undisturbed.

Heavy-ion collisions provide the unique possibility to create and investigate in the laboratory hadronic matter at high temperatures and high densities [5]. By colliding two nuclei at  relativistic energies in the range from 0.2 to 10 GeV, baryonic densities can reach values up to 10 times the normal nuclear matter density and temperature of 50 to about 200 MeV. This provides the opportunity to investigate the equation of state of nuclear matter, the phase transitions, and the possible restoration of chiral symmetry. The knowledge of the nuclear equation of state is essential for understanding the dynamics of supernova and the stability of neutron stars by varying the density with energy.

 One of the goals of the experimental program is to produce dense and hot fireball in a collision between two nuclei at high energies, which may serve for the study of fundamental properties of the strong interaction and its underlaying theory, Quantum Chromodynamics (QCD). Some of the most fascinating features of strong interaction physics are still not quantitatively understood: why are quarks not observed as individual particles? Why is a hadron that is composed of light quarks much heavier than the sum of the masses of its constituents? The nucleon (p=uud, n=udd), for instance, is roughly 50 times heavier than the sum of the mass of its three basic constituents (Mu = 1-5 MeV, Md = 3-9 MeV). Does mesons change their mass inside dense nuclear matter? Is this an indication of chiral symmetry restoration?

The phenomenology indicates that if QCD is to describe the real world, then the u and d quarks must have very small masses. But if these quarks have indeed very small masses, then the equations of QCD possess some additional symmetries, called chiral symmetries. These symmetries allow separate transformations among the right-handed quarks (spinning, in relation to their motion, like ordinary right handed screws) and left-handed quarks. But according to QCD theory, the interaction of a quark with gluons does not change the orientation of the quark spin relative to its momentum. The conservation of chirality is a consequence of chiral symmetry. It is strictly valid only in the limit of vanishing quark masses. So if QCD is to describe the real world, the chiral symmetry must be spontaneously broken, much like the breaking of the rotational symmetry of a ferromagnet below the Curie temperature. An important consequence of the spontaneous chiral symmetry breaking is the existence of an almost massless Goldstone boson (the meson) and the absence of parity doublets in the hadron spectrum. Chiral symmetry is expected to be restored at high baryon density even at low temperature. Many theoretical studies are addressed to this phenomenon up to now [6].  

The experimental program on heavy ion collision at CERN-SPS and RHIC has the outstanding goal of searching for the QCD phase transition. This transition from deconfined quark and gluon matter, the so-called Quark Gluon Plasma (QGP), to colourless hadrons is believed to have happened in the early universe, a few microseconds after the Big Bang. Among the many phase transitions, which occurred in the early universe, the QCD phase transition is the only one, which is experimentally reproducible today. This is because the temperatures and energy densities needed for the transition can be reached in ultra relativistic heavy ion collisions (see figure 2.1).

Figure 2.1: High temperature and high baryonic density did exist in the early universe, a few microseconds after the Big Bang, and can be created in the laboratory by means of heavy-ion collisions at relativistic and ultra-relativistic energies.

In collaboration with scientists from all over the world, GSI plays a leading role in the field of relativistic heavy ion collisions. In particular, a rich experience exists in the investigation of dense nuclear matter as created in central collisions between two heavy nuclei at beam energies of up to 2xA GeV. Data on strange meson production and the collective flow of nucleons obtained with the KaoS and FOPI detectors at GSI provide information on the nuclear matter equation of state up to about three times the saturation density. Experimental results indicate that the properties of strange mesons are modified in dense nuclear matter. The modification of in-medium properties of vector mesons, which is expected to occur if chiral symmetry is restored, is experimentally studied with the Dilepton Spectrometer HADES at GSI. The HADES detector can measure hadrons and electrons emitted in heavy ion collisions also at higher beam energies up to about 7xA GeV and, hence, will be part of the experimental equipment at the new accelerator facility of GSI.

A direct implication of such experiments is that they provide the possibility of obtaining information on the nuclear equation of state at high baryon densities and on the properties of hadrons in dense nuclear matter. The equation of state of nuclear matter plays an important role in the dynamics of a supernova explosion and the stability of neutron stars. In neutron stars or during the collapse of very heavy stars that have burned their nuclear fuel, much higher densities can be achieved. That is because the gravitational force of such massive objects compresses the nuclear matter. Nuclear collisions are the only way that one can compress nuclear matter in the laboratory and learn what the relationship is between the density of nuclear matter and the pressure needed to compress it. The information obtained from collision experiments can help us understand why neutrons stars do not collapse into black holes and help us predict some of the properties of the interiors of neutron stars, the densest objects observed in the universe so far. 

Chiral symmetry

The theory of Quantum Chromo Dynamics (QCD) is expected to represent the additional fundamental theory of the strong interaction and so far is well tested in its short distance or large momentum transfer range. However, its dynamical properties at large distances or low momentum transfers are not well understood since standard perturbation theory is not applicable in this case. On the other hand the low energy excitation of QCD are well known experimentally in the vacuum in terms of hadron spectra or spectral functions, respectively. The question thus arises, how the low energy QCD spectrum will change when heating the vacuum or filling it with valence quarks. Since this question addresses the non-perturbative regime of QCD, combined theoretical and experimental efforts are necessary to shed some light on this issue.

Symmetries always imply conservation laws, for example invariance of the Lagrangian under translations in space and time results in momentum and energy conservation. The QCD Lagrangian for massless quarks shows a symmetry under a vector and axial transformation. This symmetry is called Chiral Symmetry. The symmetry of vector transformations leads to the conservation of the Isospin, which is well known for hadrons [7]. For the axial transformation the symmetry implies the same mass for the chiral partners, e.g. and 1. This is obviously not the case (m = 770 MeV/c2 and m1 = 1260 MeV/c2).

 

Figure 2.2: Classical mechanics potential model illustrating chiral symmetry breaking. The potential in a) is symmetric. In b) the potential is still symmetric, but the symmetry of the ground state is spontaneously broken as the ball rolls to a certain point in the potential and selects a direction, which breaks the symmetry. However, a rotation (moving the ball in the valley) does not cost energy [7].

This large discrepancy cannot be explained by the explicit symmetry breaking of the Lagrangian due to the finite current quark masses. As the masses of the light quarks are about 5 - 10 MeV/c2 and the relevant energy scales of QCD of about 200 MeV is much larger, one can speak of an approximate symmetry. The solution to this is that the vector-axial symmetry is spontaneously broken, which means that the symmetry of the Lagrangian is not realized in the ground state. This can be illustrated in a mechanical analog shown in figure 2.2 [7]. In (a) the ground state is right in the middle, and the potential plus ground state are still invariant under rotations. In (b), on the other hand, the ground state is at a finite distance away from the center. The point at the center is a local maximum of the potential and thus unstable. If we put a little ball in the middle, it will roll down somewhere and find its ground state some place in the valley, which represents the true minimum of the potential. By picking one point in this valley (i.e picking the ground state), the rotational symmetry is obviously broken. Potential plus ground state are not symmetric anymore. The symmetry has been broken spontaneously by choosing a certain direction to be the ground state. However, effects of the symmetry are still present. Moving the ball around in the valley (rotational excitations) does not cost any energy, whereas radial excitations do cost energy.

In order to understand what the spontaneous breakdown of the axial-vector symmetry of the strong interaction means. Assume, that the effective QCD Hamiltonian at zero temperature has a form similar to depicted in figure 2.2, where (x,y) coordinates are replaced by -fields. Since the ground state is not in the center but some finite distance away from it, one of the fields will have a finite expectation value. In the quark language, this means the spontaneous symmetry breaking is related to a non-vanishing scalar quark condensate  [8]. In this picture, pionic excitation corresponds to small rotation away from the ground state along the valley, which do not cost any energy. Consequently the mass of the pion should be zero. In other words, due to spontaneous breakdown of chiral symmetry, one predict a vanishing pion mass. Excitations in the -direction correspond to radial excitation and therefore are massive

The implications of this symmetry breaking are a massless Goldstone boson and massive . The is obviously not massless, however its mass is much smaller compared to all other hadrons. In the classical mechanics analogy, the corresponds to a mode where the ball moves in the valley and the corresponds to radial motion. The mass difference of the chiral partners and 1 is also explained with this model.

 One expects that at high temperatures and/or densities the finite expectation value of the scalar quark-condensate is vanishing and that, as a consequence chiral symmetry will be restored. In this phase, the chiral partners / and /1 would be degenerate and the would become massive.

The effect of chiral symmetry restoration

Chiral symmetry, in the limit of massless quarks, is spontaneously broken in the ground state of QCD as indicated by the small mass of the pion. At high temperatures and/or densities chiral symmetry is expected to be restored. In a phase where chiral symmetry is broken,  is non-zero, while a chirally symmetric phase is vanishing. To leading order in the nucleon density, a model independent relation for the quark condensate in matter can be derived [6,9]

                     (2.1)

where  is the pion-nucleon sigma term, N is the nucleon density, 0 is the saturation density of nuclear matter,  is the pion decay constant, m is the pion mass, and  is the quark condensate in vacuum. Similarly, the leading order dependence of the quark condensate on temperature is given by [10]

                                            (2.2)

These relations show that the quark condensate decreases with increasing baryon density or temperature; i.e. there is a tendency to restore chiral symmetry in hadronic matter. However, these relations cannot be used to predict the properties of hadronic matter when approaching the critical density or temperature, since they apply only to small densities or temperature. In order to connect the high and low-density regimes in a quantitative manner and to describe for example the melting of the condensate a new approach to QCD at intermediate densities is needed. Because of the large interaction strength in this regime, progress is possible only with input from dedicated experiments.

However, some interesting questions still remain on how chiral symmetry is actually restored in hot hadronic matter and what are the signatures of the restored phase. One of the interesting features of the symmetry restored phase is the appearance of the scalar -meson which forms a chiral multiplet with the pions. At low temperatures where chiral symmetry is spontaneously broken, the -meson has very large width due to the strong decay channel into two pions. On the other hand, as the quark condensate  drops with increasing temperature, the mass difference of the -meson and pion becomes small. As a result, the decay width of scalar meson decreases because the phase space available for the outgoing pions is reduced. Close to the phase transition temperature T, the becomes an elementary excitation.

The observation of a narrow width scalar meson has been suggested as a direct signature of chiral symmetry restoration [11], but since the does not couple to any penetrating probes such as photons and dileptons this is difficult to observe in experiment.  

The structure of Hadrons

Hadrons are composite systems built up from a small number of elementary particles, quarks and gluons. Quarks as objects inside the hadrons appeared first in the classical models of constituent quarks [12, 31]. The quark model gave a comprehensive tool for classifying the hadron states.

Strong evidence for quark structure of hadrons was provided by the investigation of hard processes, such as deep inelastic scattering of high-energy electrons, muons and neutrinos on hadrons, +- production with large effective masses in hadron collisions, e+e- annihilation into hadrons.

The study of hadron properties like effective masses, decay widths, electromagnetic form factor etc. inside the nuclear medium at any density and excitation energy is of fundamental interest. From a very fundamental point of view, the partial restoration of the QCD chiral symmetry is expected to lead to a mass reduction of vector mesons with finite temperature or density of the surrounding nuclear medium. More specifically, QCD sum rules [13,14] and hadronic models [15-18] predict significant changes in mass and resonance width of vector mesons, like , and , when embedded in nuclei. Picture based on a mean field approach, the bag model, or constituent quark models [19-22] predict such changes, too.  

Form Factors   

In the case of elastic scattering from a target with a particular charge distribution, (r), the scattering amplitude is modified by a form factor:

                                         (2.3)

The Mott cross-section should be multiplied by |F(q2)|2. For a unit charge target:

                                                 (2.4)

and the form factor is equal to unity for zero momentum transfer. The differential cross-section for elastic electron-proton scattering can be calculated including form factors using current algebra. The result is know as Rosenbluth formula [23]:

            (2.5)

where  is the Mott differential cross section,  is the 4-momentum transfer , k is the anomalous magnetic moment of nucleon in unit of nuclear magnetic ( ). For proton k =1.79, for neutron k=-1.91.  is Dirac magnetic moment. F1(q2) is the charge form factor, F2(q2) is the magnetic moment form factor.

For elastic scattering q2 is negative involving only 3-momentum transfer, no energy transfer. This region is called the space-like region. For annihilation processes (like e+e- +-) q2 is positive involving only energy transfer, no 3-momentum transfer. This region is called the time-like region. The corresponding Feynman graphs are shown in figure 2.3.

Figure2.3: Feynman graphs for the space-like scattering (only 3-momentum transfer) and the time-like electron positron annihilation (only energy transfer)

Vector Meson Dominance Model

The Vector Dominance Model describes very successfully a large amount of electromagnetic form factor of mesons and hadrons. In this model, the coupling of photons to hadrons is determined by intermediate vector mesons. Since the quantum numbers of the vector mesons and the virtual photon are the same (JP=1-), the off shell photon can convert to a vector meson. The decrease at mass can be explained as an interference between the and mesons and is called the / mixing. In this picture, the coupling is finally mediated by vector mesons , or . Vector meson dominance is satisfactorily describing the electromagnetic form factor particularly for pions in the space-like region as well as in the time-like region (see figure 2.3). Some important properties of the light vector mesons in vacuum are shown in table 2.1.

Table 2.1: Properties of the light vector mesons in vacuum

Vector

Meson

Mass

[MeV/c2]

Width

[MeV/c2]

Life time

[fm/c]

Main decay

Branching

ratio to e+e-

769

150

1.3

(100%)

4.5*10-5

783

8.4

23

+-0 (89%)

7.1*10-5

1019

4.5

44

K+K-  (49%)

2.9*10-4

 

In medium modifications of vector meson properties

The time-like (q2 >0) electromagnetic form factor of the pion is well understood in terms of the VMD. It has a resonance character and reflects the properties of the meson according to VMD. The short life-time of meson  has focused interest on experiments trying to observe the meson decaying inside nuclear matter. Thus, possible effects of the hadronic environment on the vector meson properties would be observed. However, only the decay into a leptonic final state is promising since leptons do not suffer from final state interaction and thus preserve the information of the vector meson state on their way out of the reaction volume.

Figure 2.4: Prediction of the chiral condensate as a function of density and temperature from a Nambu and Jona-Lassino calculation [6]. The constituent quark masses are strongly reduced even at moderate densities.

Weise and collaborators have derived a description of the chiral condensate as a function of temperature and hadron density in an effective mean field approach [6]. Figure 2.4 shows the results of Nambu and Jona-Lassino type calculation. The chiral condensate drops rapidly as a function of temperature at the critical value near  which is not accessible in the SIS energy regime. The chiral condensate decreases linearly as a function of density and drops to 10 % of the zero temperature and density value at = 5 0.   

Electromagnetic transition Form Factors

Transition form factor of vector mesons are not fully described by VMD in the cases, where the vector meson is transformed into another meson [24]. As an example, in figure 2.5 experimental data for Dalitz decay 0+- is shown in comparison to various theoretical models (the corresponding Feynman graph is shown in figure 2.6). The VMD prediction does not follow the slope of the scattered data points for the dimuon invariant mass interval depicted (2m < M+-  <mm ).

Figure 2.5: Squared form factor F(q2) of the Dalitz decay  0+- as a function of the squared four-momentum of the muon pair. The solid curve represents a fit with a pole formula, the dashed curve is the prediction of VMD [24]

Figure 2.6:Basic mechanisms contributing to the Dalitz decay 0+-: (1) direct 0-coupling (2) two-step process via 0

Neutral pseudo-scalar mesons (0, ) cannot decay directly into e+e-, due to C-parity conservation. They can decay in conversion process like the Dalitz decay A B* Be+e-. These processes are described when assuming a transition form factor. With VMD calculations the transition form factor of the decay can be described very well. The detail knowledge of these form factors is not only important for understanding the fundamental structure of hadrons, it has also an important implication in the interpretation of the dilepton spectra from heavy ion collision experiments.

Characteristics of heavy ion collisions

The properties of the fireball cannot be measured directly. This information has to be deduced from the measurement of particle production probability and their phase space distributions. It is thus mandatory to understand as well as possible the dynamics of the collisions, in order to be able to extract the static properties of nuclear matter. In this respect, the theoretical models play a major role. They allow to describe the evolution of a collision and to characterize several observables relevant for the investigation of the fireball properties.

Figure 2.7 shows the collision of two Au nuclei at 2xA GeV simulated with the IQMD (Isopspin Quantum Molecular Dynamics) mode [25]. The first phase of the collision corresponds to the interpenetration of the two nuclei, which form a hot and dense fireball. At SIS energies, the maximum density (30) is reached after 10 fm/c. In the second phase, the system starts to expand until the particles do not interact strongly anymore. At this point, called the freeze-out, the particles decoupled from each other.

Figure 2.7: IQMD simulation of a Au + Au collision at 2xA GeV

The observations deduced from the measurement of particles in the detector depend on the size of the colliding nucleus, on the beam energy and on the impact parameter, which is the distance between the centers of the two nuclei as depicted in figure 2.8. This quantity characterizes the centrality of the collision. Ideally, only the nucleons in the overlapping zone, called fireball, participate in the collision. The other nucleons are called spectators.

Figure 2.8: Definition of the impact parameter and fireball

 

Strange particles

The effective mass of strange mesons is predicted to be substantially modified in dense nuclear matter [26, 27, 28]. The production and propagation of kaons in heavy-ion collisions are expected to be sensitive to the baryonic density. Experimental evidence for strange kaon potentials in the nuclear medium has been  found by KaoS and FOPI collaborations at SIS/GSI.

The properties of strange mesons in a medium of finite baryon density are essential for our understanding of strong interaction. According to various theoretical approaches, antikaons feel strong interactive forces in the nuclear medium whereas the in medium kaon nucleon potential is expected to be slightly repulsive [28,29, 30]. Predictions have been made that the effective mass of the K- meson decreases with increasing nuclear density leading to K- condensation in neutron stars above 3 times saturation density 0. This effect is expected to influence significantly the evolution of supernova explosions: the K- condensate softens the nuclear equation of state and thus causes a core with 1.5-2 solar masses to collapse into a black hole rather than to form a neutron star.   

K+ mesons are well suited to probe the properties of the dense nuclear medium because of their long mean-free path. The propagation of K+ mesons in nuclear matter is characterized by the absence of absorption and hence kaons emerge as messenger from the dense phase of the collision. In contrast, the pions created in the high density phase of the collision are likely to be reabsorbed and most of them will leave the reaction zone in the late phase.     

Heavy-ion collisions at relativistic energies offer the possibility to study in medium properties of strange mesons. In dense nuclear matter the K- effective mass is predicted to be reduced and thus the kinematical threshold for the process NN K-K+NN will be lowered. As a consequence, the K- yield in nucleus-nucleus collisions at bombarding energies below the NN threshold (Ebeam=2.5 GeV for NN K-K+NN) is expected to be enhanced significantly as compared to the case without in-medium mass reduction. In contrast, the yield of K+ effective mass and thus the in-medium K+ production threshold is slightly increased [30,32, 33].

The K-/K+ ratio observed in nucleus-nucleus collisions at beam energies below the NN threshold is sensitive to the in-medium properties of kaons and antikaons [34]. Another observable sensitive to in-medium effects is the azimuthal angle distribution of kaon. Experimentally one has found in Au+Au collisions at 1*A GeV that K+ mesons are emitted preferentially perpendicular to the reaction plane at midrapidity [35]. Moreover, K+ mesons with low transverse momenta are emitted into the reaction plane oppositely to the nucleons in Ru+Ru and Ni+Ni collisions [36]. These observations represent an independent experimental signature for a repulsive in-medium K+N potential. Within transport calculations, both the yields and the azimuthal emission patterns of K-mesons are described consistently when taken the in-medium modification of kaons and antikaons into account [37, 38, 39].

The yield of K-mesons as measured in Au+Au and in C+C collisions at the heavy-ion synchrotron (SIS) at GSI in Darmstadt [40] constrains the nuclear matter equation of state [41 

Enhanced production of strangeness has been proposed as a signal for the transient existence of a deconfined phase of quarks and gluons in nucleus-nucleus collisions at ultra-relativistic energies [42]. The idea is that the production of strange quark pairs is energetically favored in the quark-gluon plasma as compared to hadronic matter. Up to now multi-strange hyperons have been measured only at CERN-SPS by the NA49 and WA97/NA57 collaborations [43,44]. Multi-strange hyperons may be produced in nucleus-nucleus collisions by multi-step processes like K- -0 and K- - --. These collisions are favored in large collision systems and at high densities. Moreover, thermal models reproduced the measured particle ratios including / and / assuming a chemical freeze-out temperature of about 170 MeV, a baryon chemical potential of B =270 MeV and a strangeness chemical potential of S =70 MeV [45]. Whether the required fast chemical equilibration is driven by the deconfinement phase transition or by enhanced in-medium hadronic reaction rates is still an open question.  

DiLepton Production

When nuclei collide, hadrons, real and virtual photons are produced. Hadrons strongly interact as they pass through the fireball until they escape. Therefore, one can say that these hadronic processes generally probe the late stages of the nuclear fireball. Both the virtual photon and the lepton pair from its decay interact only electromagnetically with the fireball, so that they essentially are unaffected after their production. Consequently, measurement of the virtual photon can provide a direct measurement of the interior of an A-A collision. Gale and Kapusta [46] have first studied the process of pion annihilation in hot dense matter. In a static calculation, they have shown that dilepton production is sensitive to the interior density of a nucleus-nucleus collision. Furthermore, they demonstrated that the measurement of dileptons produced by - annihilations should give information on the pion dispersion relationship in nuclear matter.

The electromagnetic decay of vector mesons give us the opportunity to probe the properties of these mesons in matter, as the leptons do not interact via strong force. If they decay inside the dense collision zone, their in-medium spectral functions are reflected in the invariant mass spectrum of the electron-positron pairs. Due to the long mean free path of the leptons, the information carried by the e+e- pair is not distorted by the surrounding medium. Dilepton of low mass and transverse momentum might also indicate the presence of disordered chiral condensates [47].   

Dielectron spectra have been measured by the DiLepton Spectrometer (DLS) at BEVELAC in the beam energy range of 1-2xA GeV [48]. It has been found within microscopic studied at BEVELAC/SIS energies [49, 50, 51, 52] that above 0.5 GeV invariant mass of the lepton pair, the dominant production channel is from +- annihilation. Figure 2.9 shows the calculated inclusive dilepton invariant mass spectra

d/dM for Ca+Ca (upper part) and C+C (lower part) at the bombarding energy of 1xA GeV in comparison with the experimental data [53]. The thin lines indicate the individual contributions from the different production channels; i.e. starting from low M: Dalitz-decay 0 e+e- (dashed line), e+e- (dotted line), Ne+e- (dashed line), 0e+e- (dot-dashed line), N* Ne+e- (dotted line), proton-neutron bremsstrahlung (dot-dashed line), N bremsstrahlung (dot-dot-dashed line); for M=0.8 GeV: e+e- (dot-dashed line), 0 e+e- (dashed line), + - e+e- (dot-dashed line). The full solid lines represent the sum of all sources. The discrepancy between the data and the calculations for Ca+Ca as well as for C+C at  is about a factor of 35.

Figure 2.9: Dilepton spectrum of the reaction Ca+Ca (upper part) and C+C (lower part) at 1xA GeV measured with the DLS spectrometer [53]. The curves represent calculated contributions from different sources indicated [8].

Exploring the QCD phase diagram with heavy-ion collisions

Hot and dense nuclear matter can be generated in a wide range of temperatures and densities by colliding atomic nuclei at high energies. The measured particle multiplicity ratio is used to calculate the thermodynamic variables such as the chemical freeze-out temperature and the baryon chemical potential. During the first few microseconds after the big bang, the universe went through a phase transition where the quarks and gluons were confined into hadrons. The chiral symmetry was spontaneously broken. This critical temperature is probably reached in Pb+Pb collisions at the CERN-SPS. CERN experiment have reported evidence for the formation of such a new state, called  'Quark-Gluon Plasma [58]. The new experiments at RHIC are expected to substantiate these findings and provide further information on this unexplored state of matter. Future experiments at the Large Hadron Collider (LHC) at CERN aim at studying the phase transition as well as the properties of the Quark Gluon Plasma at even higher temperature. In all these experiments, the phases of hadronic matter are studied at extremely high temperatures and low net baryon densities, where the number of particles and anti-particles are approximately equal.  This region of the phase diagram, which corresponds to the conditions in the early universe, is characterized by small values of the baryon chemical potential (see figure 2.10).

A calculated chemical freeze-out curve and the freeze-out points as derived from particle production data obtained at SIS, AGS, SPS and RIHC are shown in figure 2.10. The sum of baryon and antibaryon density at freeze-out (pink line) corresponds to a value of 0.75 0. The blue curve represents the phase boundary as predicted by the resent QCD lattice calculation for finite baryon chemical potential [57].

The experimental challenge is to identify observables, which are messengers from the dense fireball rather than from the dilute freeze-out configuration. Some promising diagnostic tools are:

Short-lived vector mesons, which decay into an electron-positron pair. The lepton pair is a penetrating probe because it delivers undistorted information on the conditions in the interior of the collision zone [65].
The yields of rare particles containing strangeness and charm depend on the conditions inside the early fireball [8]. To a good approximation the created flavor is conserved during the expansion. Hyperons serve as a probe for high baryon densities. 
The collective flow of nucleons is driven by the pressure gradients in the early phase of the collision [59]. The flow of pions and kaons is caused by shadowing and by in-medium potentials, respectively, and hence reflects the space-time evolution of the collision [60,61,62,63]. A very interesting observable would be the flow of probes like light vector mesons (, , ), multistrange hyperons (, ) and charmonium (J/), which has not been measured so far.

Figure 2.10: The phase diagram of strongly interacting matter plotted as a function of temperature and baryochemical potential. The solid circles represent freeze-out points obtained with a statistical model analysis of particle ratios measured in heavy collisions [54-56]. The solid line indicates the chemical freeze-out curve as a function of temperature and chemical potential. The curve labeled 'Lattice QCD' represents the phase boundary between the quark-gluon plasma and the hadronic phase as obtained with QCD lattice calculations [57] with a 'critical point´ at T = 160 3.5 MeV and m = 725 3.5 MeV (rB =3r0).

The experimental conditions and observables will be discussed in the following:

 

Experimental conditions

In order to study the high baryon density regime of the QCD phase diagram in the laboratory one would like to produce a long-lived compressed fireball at moderate temperatures. Within a certain range, these properties can be tuned experimentally via the beam energy. With increasing beam energy, the lifetime of the fireball decreases while baryon density and temperature increase.

The temperature is reflected in the number of pions produced in the heavy ion collision: the multiplicity of pions varies rapidly with temperature for Tm. Figure 2.11 shows the pion multiplicity per participating nucleon measured in nucleus-nucleus (symbols) and nucleon-nucleon collisions (solid line) as function of the available energy in the c.m. system. In heavy ion collisions at AGS energies (e.g. Au+Au collisions at 10.7xA GeV) the pion to baryon ratio is about 1 while it is about 5 in Pb+Pb collisions at the CERN-SPS energy of 158xA GeV. Therefore, the experimental observables from heavy ion collisions at 10-30xA GeV are more sensitive to baryon density than at higher beam energies where temperature effects are dominating.

Figure 2.11: Pion multiplicity per participating nucleon for various nucleus-nucleus (symbols) and nucleon-nucleon collisions (solid line) as a function of available energy in nucleon-nucleon collisions [64]

Looking into the fireball

The measurement of the short-lived vector mesons via their decay into an electron-positron pair provides the unique possibility to study the properties of hadrons in dense baryonic matter. Since the leptons are almost unaffected by the passage through the high-density matter, they provide as a penetrating probe almost undistorted information on the conditions inside the dense fireball. The invariant masses of the measured lepton pairs permit the reconstruction of the in-medium spectral function of the , and mesons. Dilepton of low mass and transverse momentum might also indicate the presence of disordered chiral condensate.

Strangeness and charm production

The baryon densities determined from particle ratios which reflect the conditions at hadrochemical freeze-out are found to be well below saturation density at all beam energies [45, 66, 67]. The challenge is to find observables, which preserve a reminiscence of the dense fireball. In principle, the yield of newly created quark flavors like strangeness and charm is such an observable, in particular for nucleus nucleus collisions at threshold beam energies. The dominant production processes must involve many particles and thus implies high densities. Then, the yield of strange and charm quarks is to a good approximation conserved throughout the expansion phase.

Maximum baryon densities

A crucial issue for the experimental study high-density phenomena is the baryon density of the fireball and the its lifetime. Estimates based on relativistic transport calculations of a central Au+Au at 20xA GeV indicate that densities exceeding five times that of ordinary nuclear matter [68] (see figure 2.12). Both density and reaction time are enhanced considerably in collisions of deformed nuclei, which are aligned along their deformation axis. The effect is somewhat reduced for semi-central collisions. Tip-on-tip events might be selected experimentally by large values of transverse energy and perfect azimuthal symmetry.

Figure 2.12: Central density as a function of time for central Au+Au collisions (dotted line) and tip-on-tip U+U collisions (solid line) at 20xA GeV as calculated with the ART transport code [68] (Upper plot). Same for semi-central collisions (b=6 fm) (lower plot).

  References

[1] http://www-hades.gsi.de

[2] http://www-new.gsi.de/zukunftsprojekt/experimente/CBM/5docu_e.html

[3] F. Wilczek, Physics Today 53 (2000) 22

[4] Particle Data Group, Review of Particle Physics, The European Physi-cal Journal C15 (2000) 1

[5] THE SEARCH FOR THE QUARK - GLUON PLASMA, J. Harris, B. Muller, Ann. Rev. Nucl. Part. Sci. 46: 71-107 (1996), hep-ph/9602235

[6] M. Lutz, S. Klimt, W. Weise, Nucl. Phys. A 542 (1992) 521

[7] V. Koch, Introduction to Chiral Symmetry , LBNL-Report 38000, 1995

[8] W. Cassing, E.L. Bratkovskaya Hadronic and electromagnetic probes of hot and dense nuclear matter, Physics reports 308 (1999) 65-233

[9] T.D. Cohen, R.J. Furnstahl and D.K Griegel, Phys. Rev. C45 (1992) 1881;

[10] D.T Son and M.A. Stephanov, Phys. Rev. D61 (2000) 074012

[11] T. Hatsuda and T. Kunihiro, Prog. Theor. Phys. Suppl. 91 (1987) 284.

      H. A. Weldon, Phys. Lett. B 274(1992) 133.

     R. Pisarski, Phys. Rev. Lett. 76 (1996) 76.

[12] G. Zweig, CERN report 8419/TH 412 (1964)

[13] T. Hatsuda and S.H. Lee, Phys. Rev. C 46 (1992) R34

[14] Y. Koike and A. Hayashigaki, Prog. Theor. Phys. 98 (1997) 631

[15] F. Klingl and W.Weise, Nucl. Phys. A606 (1996) 329

[16] R. Rapp, G. Chanfray and J. Wambach, Nucl. Phys. A617 (1997) 472

[17] M. Herrmann, B. Friman and W.Nörenberg, Nucl. Phys. A560 (1993) 41

[18] R. Rapp and J. Wambach, Adv. Nucl. Phys. 25 (2000) 1

[19] G.E. Brown and M. Rho, Phys. Rev. Lett. 66 (1991) 2720

[20] K. Saito, K. Tsushima and A.W. Thomas, Nucl. Phys. A609 (1996) 339

[21] C.M. Shakin and W.-D. Sun, Phys. Rev. C49 (1994) 1185

[22] W. Schön et al., Acta Phys. Polonica B27 (1996) 2959

[23] Rosenbluth, M.N, Phys. Rev. 79 (1950) 61

[24] L.. G. Landsberg, Phys. Rep. 128,6 (1985) 301

[25] C. Hartnack, Dissertation, University of Frankfurt, German (1992).

[26] G.E. Brown et al., Phys. Rev. C 43 (1991) 1881

[27] T. Waas, N. Kaiser, W. Weise, Phys. Lett. B 379 (1996) 34

[28] M. Lutz, Phys. Lett. B 426 (1998) 12

[29] G.E Brown, C.H. Lee, M. Rho, V. Thorsson, Nucl. Phys. A 567 (1994) 937

[30] J. Schaffner-Bielich, J. Bondorf, I. Mishustin, Nucl. Phys. A 625 (1997)325

[31] R.H. Dalitz, Proceedings of the Berkeley Conference (1966)

[32] W. Cassing et al., Nucle. Phys. A 614 (1997) 415

[33] G. Q. Li, C. M. Ko, X. S. Fang, Phys. Lett. B 329 (1994)149

[34] F. Laue, C. Stum et al. Phys. Rev. Lett. 82 (1999) 1640

[35] Y. Shin et al., Phys. Rev. Lett. 81 (1998) 1576

[36] P. Crochet et al., Phys.Lett. B 486 (2000) 6

[37] W. Cassing and E. Bratkovskaya, Phys. Rep. 308 (1999) 65

[38] G. Q. Li, C.H. Lee, G. E. Brown, Phys. Rev. Lett. 79 (1997) 5214

[39] C. Fuchs et al., Phys. Rev. C56 (1997) R606

[40] C. Sturm et al., Phys. Rev. Lett. 86 (2001) 39

[41] C. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974

[42] J. Rafelski and B. Muller, Phys. Rev. Lett. 48 (1982) 1066

[43] J. Bachler et al., Nucl. Phys. A661 (1999) 45c

[44] F. Antinori et al., Nucl. Phys. A661 (1999) 130c

[45] P. Braun-Munzinger, et. al., Phys. Lett. B 465 (1999) 15

[46] C. Gale and J. Kapusta, Phys. Rev. C35, 2107 (1987).

[47] Y. Kluger, V. Koch, J. Randrup, X.N. Wang, Phys. Rev. C 57 (1998) 280

[48] R.J. Porter et al., Nucl. Phys. A661 (1999) 130c

[49] W. Cassing and U. Mosel. Prog. Part. Nucl. Phys. (1990), p.235 .

[50] Gy. Wolf, G. Batko, W. Cassing, U. Mosel, K. Niita and M. Schäfer. Nucl. Phys. A, 517 (1990), p.615.

[51] L. Xiong, Z.G. Wu, C.M. Ko and J.Q. Wu. Nucl. Phys. A512 (1990), p.772.

[52] L.A. Winckelmann, H. Sorge, H. Stöcker, W. Greiner, Phys. Rev. C 51 (1995) R9.

[53] R.J. Porter et al. Phys. Rev. Lett.79 (1997), p.1229.  

[54] P. Braun-Munzinger et al., 1999 Phys. Lett. B 465 15

[55] Cleymans J and Redlich K 1998 Phys. Rev. Lett. 81 5284

[56] Stock R 1999 Phys. Lett. B 456 277

[57] Foder Z and Katz S D 2001 Preprint hep-lat/0106002

[58] Heinz U 2001 Nucl. Phys. A 685 414c

[59] W. reisdorf and H. G. Ritter, Annu. Rev. Nucl. Part. Sci. 47 (1997) 663

[60] Y. Shin et al., Phys. Rev. Lett. 81 (1998) 1576

[61] A. Wagner et al, Phys. Rev. Lett. 85 (2000) 18

[62] Z. Wang et al., Eur. Phys. J. A 5 (1999) 275

[63] P. Chung et al., Phys. Rev. Lett. 86 (2001) 2533

[64] P. Senger and H. Ströbele, J. Phys. G: Nucl. Part. Phys. 25 (1999) R59

[65] Rapp R and Wambach J 1999 Nucl. Phys. A 661 33c

[66] R. Stock, Phys. Lett. B456 (1999) 277

[67] J. Cleymans and K. Redlich, Phys. Rev. Lett. 81 (1998) 5284