Hadrons in hot and dense matter

I discuss our current understanding of the properties of hot and dense hadronic matter in equilibrium and its excitation spectrum. The latter allows for an experimental study of matter under extreme conditions through ‘in-medium spectroscopy’.     

Formation of charmonium states in heavy-ion collisions and thermalization of charm

We examine the possibility to utilize in-medium charmonium formation in heavy-ion interactions at collider energy as a probe of the properties of the medium. This is possible because the formation process involves recombination of charm quarks which imprints a signal on the resulting normalized transverse momentum distribution containing information about the momentum distribution of the quarks. We have contrasted the transverse momentum spectra of J/ψ, characterized by 〈p _T ²〉, which result from the formation process in which the charm quark distributions are taken at opposite limits with regard to thermalization in the medium. The first uses charm quark distributions unchanged from their initial production in a pQCD process, appropriate if their interaction with the medium is negligible. The second uses charm quark distributions which are in complete thermal equilibrium with the transversely expanding medium, appropriate if a very strong interaction between charm quarks and medium exists. We find that the resulting 〈p _T ²〉 of the formed J/ψ should allow one to differentiate between these extremes, and that this differentiation is not sensitive to variations in the detailed dynamics of in-medium formation. We include a comparison of predictions of this model with preliminary PHENIX measurements, which indicates compatibility with a substantial fraction of in-medium formation.     

Hypernuclei and in-medium chiral dynamics

A recently introduced relativistic nuclear energy density functional, constrained by features of low-energy QCD, is extended to describe the structure of hypernuclei. The density-dependent mean field and the spin-orbit potential of a Λ-hyperon in a nucleus, are consistently calculated using the SU(3) extension of in-medium chiral perturbation theory. The leading long-range ΛN interaction arises from kaon-exchange and 2π-exchange with a Σ-hyperon in the intermediate state. Scalar and vector mean fields, originating from in-medium changes of the quark condensates, produce a sizeable short-range spin-orbit interaction. The model, when applied to oxygen as a test case, provides a natural explanation for the smallness of the effective Λ spin-orbit potential: an almost complete cancellation between the background contributions (scalar and vector) and the long-range terms generated by two-pion exchange.     

Model independent constraints from vacuum and in-medium QCD Sum Rules

We discuss QCD sum rule constraints based on moments of vector meson spectral distributions in the vacuum and in a nuclear medium. Sum rules for the two lowest moments of these spectral distributions do not suffer from uncertainties related to QCD condensates of dimension higher than four. We exemplify these relations for the case of the ω meson and discuss the issue of in-medium mass shifts from this viewpoint. Received: 22 December 1998 / Revised version: 13 January 1999     

Pulsed laser photothermal annealing and ablation of plasmonic nanoparticles

Within a transport code simulation for heavy-ion collisions at bombarding energies around 1 AGeV, we demonstrate that double-differential di-electron spectra with suitable kinematical cuts are useful to isolate (i) the ρ meson peak even in case of strong broadening, and (ii) the in-medium ω decay contribution. The expected in-medium modifications of the vector meson spectral densities can thus be probed in this energy range via the di-electron channel.     

Vector mesons in strongly interacting matter

Properties of hadrons in strongly interacting matter provide a link between quantum chromodynamics in the strong coupling regime and experimental observables. QCD sum rules show that changes in chiral and higher-order condensates, partially associated with a restoration of chiral symmetry in the nuclear medium, will lead to significant changes in the low-energy spectrum of hadrons. Heavy-ion collisions and reactions with elementary probes have been used to extract experimental information on in-medium properties of hadrons. Results on the light vector mesons ρ, ω, and ϕ, are summarized and compared. Almost all experiments report a softening of the spectral functions with increases in width depending on the density and temperature of the hadronic environment. No evidence for mass shifts is found in majority of the experiments. Remaining inconsistencies among experimental results demonstrate the need for further measurements with higher statistics and inrceased acceptance in particular for low-momentum vector mesons.     

What does the ρ-meson do? In-medium mass shift scenarios versus hadronic model calculations

The NA60 experiment has studied low-mass muon pair production in In–In collisions at 158 A GeV with unprecedented precision. With these results there is hope that the in-medium modifications of the vector meson spectral function can be constrained more thoroughly than before. We investigate in particular what can be learned about collisional broadening by a hot and dense medium and what constraints the experimental results put on in-medium mass shift scenarios. The data show a clear indication of considerable in-medium broadening effects but disfavor mass shift scenarios where the ρ-meson mass scales with the square root of the chiral condensate. Scaling scenarios which predict at finite density a dropping of the ρ-meson mass that is stronger than that of the quark condensate are clearly ruled out since they are also accompanied by a sharpening of the spectral function. PACS 25.75.-q     

Nuclear matter equation of state and σ-meson parameters

We try to determine phenomenologically the extent of in-medium modification of σ-meson parameters so that the saturation observables of the nuclear matter equation of state (EOS) are reproduced. To calculate the EOS we have used Brueckner-Bethe-Goldstone formalism with Bonn potential as two-body interaction. We find that it is possible to understand all the saturation observables, namely, saturation density, energy per nucleon and incompressibility, by incorporating in-medium modification of σ-meson-nucleon coupling constant and σ-meson mass by a few per cent.     

Two-pion production in photon-induced reactions

Differences in the photoproduction of mesons on the free proton and on nuclei are expected to reveal changes in the properties of hadrons. Inclusive studies of nuclear photoabsorption have provided evidence of medium modifications. However, the results have not been explained in a model independent way. A deeper understanding of the situation is anticipated from a detailed experimental study of meson photoproduction from nuclei in exclusive reactions. In the energy regime above the Δ(1232) resonance, the dominant double pion production channels are of particular interest. Double pion photoproduction from nuclei is also used to investigate the in-medium modification of meson-meson interactions     

In-medium properties of the ω meson in photon induced nuclear reactions

We discuss the possibility to study the in-medium changes of the properties of the ω meson in reactions on ordinary nuclei with elementary electromagnetic probes. We present a tree-level calculation of the elementary γp→ωp process which is extended to describe also the photoproduction of medium-modified ω mesons in nuclear matter. Using a semi-classical transport approach we obtain results for e⁺e_? and π ⁰γ photoproduction off heavy nuclei in the invariant mass range of the ρ and ω mesons. Both reactions are also studied experimentally and are presently being analyzed at accelerator facilities in Bonn and at Jefferson Lab. We show that the in-medium signals expected can be as large as those obtained in heavy-ion reactions.     

Photoproduction of η -mesons off nuclei for Eγ ? 2.2 GeV

The photoproduction of η -mesons off ¹²C , ⁴⁰Ca , ⁹³Nb , and ^nat Pb nuclei has been measured with a tagged photon beam with energies between 0.6 and 2.2GeV. The experiment was performed at the Bonn ELSA accelerator with the combined setup of the Crystal Barrel and TAPS calorimeters. It aimed at the in-medium properties of the S ₁₁(1535) nucleon resonance and the study of the absorption properties of nuclear matter for η -mesons. Careful consideration was given to contributions from ηπ final states and secondary production mechanisms of η -mesons, e.g. from inelastic πN reactions of intermediate pions. The analysis of the mass number scaling shows that the nuclear absorption cross-section for η -mesons is constant over a wide range of the η momentum. The comparison of the excitation functions to data off the deuteron and to calculations in the framework of a BUU model show no unexplained in-medium modifications of the S ₁₁(1535) .     

Subthreshold ϕ-meson production and medium effects in proton-nucleus reactions

Within the spectral function approach, we study the direct production and decay via the dikaon (dimuon) channel of ϕ mesons in the interactions of 2.4-and 2.7-GeV protons with light and medium target nuclei. It is shown that the K ⁺ K ⁻ (μ⁺ μ⁻) invariant-mass distribution consists of the two components, which correspond to the ϕ decay “outside” and “inside” the target nucleus. The first (narrow) component has the free ϕ width, while the second (broad) component is distorted by the nuclear matter owing to resonance-nucleon scattering and a possible in-medium modification of the kaons and ρ meson at finite baryon density. The relative strength of the “inside” and “outside” components is analyzed in different scenarios for the ϕ width and momentum cut. It is demonstrated that the width of the resulting dimuon invariant-mass distribution on medium nuclei is larger than the free ϕ width by a factor of about 2 if the total ϕ in-medium width is used and the respective cutoff for the ϕ three-momentum is applied, whereas the resulting dikaon invariant-mass distribution has an insignificant sensitivity to the ϕ in-medium properties owing to the strong absorption of the K ⁻ in the surrounding nuclear matter. On the other hand, because of the distortion of the K ⁺ and K ⁻ on their way out of the target nucleus mainly due to the hadronic kaon potentials, the latter distribution is broadened and shifted to higher invariant masses, which means that the measurement of such broadening would give additional evidence for the modification of the kaon and antikaon properties in the nuclear medium. The text was submitted by the author in English.     

Study of in-medium <Emphasis Type="Italic">ω</Emphasis>-meson properties in <Emphasis Type="Italic">Ap</Emphasis> and <Emphasis Type="Italic">pA</Emphasis> collisions

The possibility to investigate the in-medium properties of the vector ω mesons at normal nuclear density is considered. The folding model and simulations with the RQMD generator have been used for studying of the ω-resonance production in Ap and pA reactions and its ω → π ⁰ γ → 3γ decay. We show that measurements in the inverse Ap kinematics is an effective way to get information about the ω-meson mass modification especially in not yet explored range of small meson momenta relative to the projectile nuclei where the strength of the effect is expected to be most strong. The traditional pA kinematics appears to be more preferable for the investigation of the in-medium ω-meson width. Using of compact electromagnetic calorimeter provides the possibility to collect large statistics and study the momentum dependencies of both the ω-meson mass and width at the density of normal nuclei.     

Probing the strange quark condensate by di-electrons from φ-meson decays in heavy-ion collisions at SIS energies

QCD sum rules predict that the change of the strange quark condensate 〈ˉss〉 in hadron matter at finite baryon density causes a shift of the peak position of the di-electron spectra from φ-meson decays. Due to the expansion of hadron matter in heavy-ion collisions, the φ peak suffers a smearing governed by the interval of density in the expanding fireball, which appears as an effective broadening of the di-electron spectrum in the φ region. The emerging broadening is sensitive to the in-medium change of 〈ˉss〉. This allows to probe directly in-medium modifications of 〈ˉss〉 via di-electron spectra in heavy-ion collisions at SIS energies with HADES. Received: 22 November 2002 / Accepted: 30 January 2003 / Published online: 29 April 2003     

Attenuation of Λ(1520) Hyperons in near-threshold <Emphasis Type="Italic">pA</Emphasis> reactions

In the framework of the nuclear spectral function approach for incoherent primary proton-nucleon and secondary pion-nucleon production processes we study the inclusive Λ(1520)-hyperon production in the interaction of 2.83-GeV protons with nuclei. In particular, the A and momentum dependences of the absolute and relative Λ(1520)-hyperon yields are investigated within the different scenarios for their in-medium width. Our model calculations show that the pion-nucleon production channel contributes distinctly to the “low-momentum” Λ(1520) creation both in light and heavy nuclei in the chosen kinematics and, hence, has to be taken into consideration on close examination of the dependences of the Λ(1520)-hyperon yields on the target mass number with the aim to get information on their width in the medium. They also demonstrate that both the A dependence of the relative Λ(1520)-hyperon production cross section and momentum dependence of the absolute Λ(1520)-hyperon yield at incident energy of interest are appreciably sensitive to the Λ(1520) in-medium width, which means that these observables may be an important tool to determine the above width.     

Probing meson spectral functions with double differential dilepton spectra in heavy-ion collisions

The double differential dilepton spectrum d/(d ² d _⊥ ²) at fixed transverse mass M _⊥ allows a direct access to the vector meson spectral functions. Within a fireball model the sensitivity of d/(d ² d _⊥ ²) against variations of both the in-medium properties of mesons and the dynamics of the fireball is investigated. In contrast to the integrated invariant-mass spectrum d/d ², in the spectrum d/(d ² d _⊥ ²) with fixed M _⊥ the ω signal is clearly seen as bump riding on the ρ background even in case of strong in-medium modifications.[3mm] Received: 16 November 2000 / Accepted: 16 January 2001     

Evaluation of QCD sum rules for light vector mesons at finite density and temperature

QCD sum rules are evaluated at finite nucleon densities and temperatures to determine the change of mass parameters for the lightest vector mesons ρ, ω and φ in a strongly interacting medium. For conditions relevant for the starting experiments at HADES we find that the in-medium mass shifts of the ρ- and ω-mesons are governed, within the Borel QCD sum rule approach, by the density and temperature dependence of the four-quark condensate. In particular, the variation of the strength of the density dependence of the four-quark condensate reflects directly the decreasing mass of the ρ-meson and can lead to a change of the sign of the ω-meson mass shift as a function of the density. In contrast, the in-medium mass of the φ-meson is directly related to the chiral strange quark condensate which seems correspondingly accessible. Received: 15 May 2002 / Accepted: 31 July 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: Kaempfer@fz.rossendorf.de Communicated by A. Sch?fer     

Investigation of in-medium ω photoproduction

Recent experimental results on the in-medium modification of the ω meson are discussed. The experiment described was performed at the ELSA accelerator facility in Bonn using the combined detector system of Crystal Barrel and TAPS. Theω-meson was identified via the reaction γ+A → ω +X → π⁰ γ +X     

QCD in the nuclear medium and effects due to Cherenkov gluons

The equations of in-medium gluodynamics are proposed. Their classical lowest-order solution is explicitly shown for a color charge moving with constant speed. For chromopermittivity larger than 1 it describes emission of Cherenkov gluons resembling results of classical electrodynamics. The values of the real and imaginary parts of the chromopermittivity are obtained from the fits to experimental data on the double-humped structure around the away-side jet obtained at RHIC. The dispersion of the chromopermittivity is predicted by comparing the RHIC, SPS, and cosmic-ray data. This is important for LHC experiments. Cherenkov gluons may be responsible for the asymmetry of dilepton mass spectra near ρ meson observed in the SPS experiment with excess in the low-mass wing of the resonance. This feature is predicted to be common for all resonances. The “color rainbow” quantum effect might appear according to higher-order terms of in-medium QCD if the chromopermittivity depends on color.     

Three- and Four-Body Correlations in Nuclear Matter

 Few-nucleon correlations in nuclear matter at finite densities and temperatures are explored. Using the Dyson-equation approach leads to effective few-body equations that include self-energy corrections and Pauli blocking factors in a systematic way. Examples given are the nucleon-deuteron in-medium reaction rates, few-body bound states including the α-particle, and α-particle condensation. Received October 17, 2001; accepted for publication November 12, 2001