Quantum chromodynamics (QCD) is the theory of the strong interaction between quarks, mediated by the exchange of gluons. At low energies, due to confinement, quarks are bound into hadrons and impossible to be observed free. Numerical simulations on the lattice have proven, that due to the phenomenon of asymptotic freedom of QCD at high energies, hadronic matter undertakes a phase-transition at high baryon densities and temperatures (Fig. 1). In this phase, known as quark-gluon plasma, quarks are quasi-free and the chiral symmetry is restored. This phase-transition also triggers a change of the structure of QCD vacuum, quantified in a change of value of the order parameter that characterizes QCD phases: the chiral quark condensate. Intuitively speaking the value of chiral quark condensate is related to the density of virtual quark-antiquark pairs that populate the vacuum in the hadronic-matter phase. Theoretically it has been proven, starting from effective models of QCD of the Nambu-Jona-Lasinio type, that the magnitude of the chiral quark condensate is sensitive to the density and temperature of hadronic matter (see Fig. 2). For example, in nuclei at densities close to nuclear matter saturation density, the value of the chiral quark condensate decreases with about 30% compared with its value in vacuum. Therefore, medium effects are phenomena preceding chiral symmetry restoration and the phase transition of hadronic matter into quark-gluon plasma. The precise way in which the partial restoration of chiral symmetry in nuclear matter affects the hadron properties is a current topic of debate and research. In principle, taking the explicit example of the ρ and a1 vector mesons which would form a parity dublet if chiral symmetry were not broken, the effect of chiral symmetry restoration can manifest itself either through spectral functions of equal strength at the position of ρ and a1 pole mass or through a uniform distribution over the entire mass range and hence a melting of these mesons in a chiral symmetric vacuum.
Change of hadron properties manifests through either a simple mass-shift (as in the case of the nucleon) or through the development of complex spectral functions (mesons and nucleonic resonances). For the latter case, photo-absorption on heavy-nuclei experiments have revealed increased decay widths hinting to a possible melting of these resonances in a dense nuclear medium. Complementary, heavy-ion collisions offer a unique possibility for the study of nuclear matter under extreme conditions, namely high density and temperature. In this context, the production of the light vector mesons ρ(770) and ω(782) in nucleon-nucleon collisions and photo-absorption processes is of special interest. Their decay into dilepton pairs (electron-positron and muon-antimuon) recommends them as probes of the high density and temperature nuclear medium since they leave the production region essentially undistorted due to their only electromagnetic interaction with the surrounding hadronic matter.
Theoretical models, either based on fundamental properties of QCD or effective hadronic interactions predict a change of masses and decay widths of vector mesons at high density and temperature. Brown-ρ scaling, starting from QCD scale invariance extended at the level of effective hadronic models, predicts a decrease meson masses while preserving quasi-particle properties. Hadronic models, on the other hand, favour an important increase of ρ meson's decay width and the developing of complex spectral functions, i.e. the appearance of several maxima due to excitation of nucleonic resonances. Concerning the ω meson the situation is more complicated: hadronic models predict an increase of its decays width but allow for mass shifts in either direction. QCD sum rules based models, due to dependence of in-medium meson properties on higher order chiral quark condensates, are not able to make a precise statement about in-medium mass shifts. Among the nucleonic resonances Δ(1232) has been the most studied: its in-medium properties as well as those of the π(138) meson have been exhaustively researched within the delta-hole model. Less studied have been the N*(1520) and N*(1535) resonances. For the first one, its decay widths increase can be understood theoretically within a model which allows for the coupling of π and ρ mesons to this state. In the case of the N*(1535) a strong coupling of the η meson implies only moderate medium effects, in line with the experimental results. For a profound and complete understanding of in-medium effects it is desirable that from a theoretical point a view the interactions of both mesons and nucleonic resonances with the nuclear medium to be described in a unified way.
Experimental progress during the last decade has put serious constraints on the plethora of theoretical models. Dilepton measurents in ultra-relativistic heavy-ion collisions (Pb+Au) performed at CERN-SPS (CERES, HELIOS experiments) have revealed an enhancement of the dilepton spectrum below the ρ meson peak relative to the known hadronic sources. Its explanation could not discriminate between Brown-ρ dropping mass scenario and many-body hadronic models. The high resolution NA60 (also at CERN) muon experiment allowed however the extraction of the in-medium ρ spectral function, clearly favouring the more complex picture put forward by many-body hadronic models.
In the lower end of energy regime (1.0 AGeV Ca+Ca and C+C) the situation has not been as simple. The experiments performed by the DLS collaboration at BEVALAC have also revealed a theoretical underestimation of the dilepton spectrum, contrary to results extracted from elementary reactions (p+p and p+d). This disagreement could not be resoluted within either scenario (Brown-ρ vs. spectral function approaches) of in-medium effects on vector meson masses and/or decay widths. However, in this energy domain which probes the region of high density/low temperature of the hadronic matter, the situation is improving as a consequence of present and future results of the HADES collaboration at GSI. Complementary experimental efforts are in progress at CB-TAPS/ELSA and CLAS/JLAB by studying the reaction γ+N->V+N. The former collaboration has extracted a downward shift of mass and broadening of the decay width for the ω meson both of about 80 MeV. The CLAS collaboration has found no evidence for an in-medium modification of meson masses, but only a broadening of decay widths of the order of 50-70 MeV. Similarly, the dilepton mass spectrum measured in reactions p+A at KEK has revealed an excess of dileptons below the ρ meson mass peak which could not be explained within the bounds of current models describing in-medium effects.
The present projects aims at the continuation of efforts for the development of a unified model for the description of medium effects on mesons and nucleonic resonances. For a profound understanding of how nuclear medium affects properties of hadrons it is compulsory that medium effects on mesons and nucleonic resonances are implemented in a similar fashion both at the level of NRD+eVMD and of the QMD transport model. This high sophistication level is required for self-consistency and in the prospect of measuring dilepton spectra in heavy-ion collisions at an unprecedented mass resolution by the HADES (GSI) collaboration. Currently experimental data for the C+C reaction at 2.0 AGeV are available and the results of the measurements of C+C at 1.0 AGeV are being analyzed. For the future dilepton spectra in the reactions p+A and p+A together with A+A for super heavy-ions are being planned, which would allow the investigation of compressed hadronic matter up to densities 3 times the nuclear matter saturation density. From the theoretical side, the present day models will have to be extended to include medium effects in a unified way and, where possible, to consider contribution that go beyond the limit of applicability of the low-density theorem. The DLS collaboration has measured dilepton spectra in heavy ion-collisions C+C and Ca+Ca at energies of 1.04 AGeV and in p+p and p+d elementary reactions at 1.0-4.8 GeV. The dilepton spectrum in elementary reactions is well described by the NRD+eVMD model in vacuum, recommending it for the description, in its extended version to nuclear-medium, in a unified way of in-medium effects on hadrons and the emission of dileptons in heavy-ion reactions.
At present, the in-medium spectral functions of the ρ and ω vector mesons, starting from the NRD+eVMD model and including contributions due to meson Compton scattering off medium nucleons, are known. Theoretical studies having as input the Bonn nucleon-nucleon potential and the associated in-medium G matrix have shown that in nuclear matter, at densities couple of times higher than the nuclear matter saturation density, the nucleon mass suffers a sizeable downward shift which possible repercussions on medium effects of all hadrons. Returning to ρ and ω mesons, it is well known that their non-zero vacuum decay widths are generated by decays into two and respectively three p mesons. Medium effects on pions have been studied intensively notably within a resonance-hole excitation model through the coupling of pions to nucleons and Δ(1232) resonances. How medium modifications of the pion virtual cloud surrounding the mesons has been studied for the case of the ρ vector meson and proven to be quantitatively as important as contributions originating in excitation of resonances. For completeness we will include these effects in our model, this procedure serving also as an exercise for a similar calculation, only more involved, for the ω meson. In this case we will start from the assumption that the ω->3π decay is a two-step process: ω->ρπ->3π the first decay being described by the effective Gell-Mann-Sharp-Wagner model which will allow, given the in-medium ρ and pionic spectral functions, to determine the influence of the in-medium virtual pion cloud on the properties of the ρ meson. The medium effects due to a less important decay channel ω->γπ will also be investigated. A complementary study, of importance for heavy-ion collisions, concerns the finite-size effects of nuclear matter on the in-medium properties of mesons.
In the second stage of the project we will concentrate on the study of how the nuclear medium affects the properties of nucleonic resonances. The NRD+eVMD model describes the production of all nucleonic resonances with masses below 2 GeV through the absorption of photons or vector mesons, in total 12 N* and 13 Δ* resonances with spins ranging from 1/2 to 7/2. To properly study medium effects on resonances it is compulsory to extend the NRD model by an explicit inclusion of resonance decay processes with the emission of π or η mesons. In the spirit of NRD, effective πNR and ηNR interactions will be used with the coupling constants fixed to reproduce vacuum properties of resonances. By considering contributions of the π, η, ρ and ω mesons to the in-medium self-energies of each resonance, their properties in dense hadronic matter will be extracted. As a prerequisite, medium effects on the η meson will be studied. From the above presentation is evident that properties of mesons and resonances in nuclear matter are not independent effects. In principle, the in-medium self-energies of mesons and resonances are the solution of a coupled system of integral equations whose solving is extremely intricate from both a methodological and numerical perspective. A practical solution, which will be adopted, is to truncate the perturbation series to its first term and iterate the solution until convergence is achieved.
The third phase of the project is dedicated to the implementation of medium effects on resonances and mesons in the QMD transport model. A proper consideration of medium effects on pions is vital given their crucial effects on heavy-ion collisions dynamics. It is expected that medium effects on resonances will play a similar role. Since they mainly decay with the emission of pions, it is expected that pion related observables will be importantly affected. In this context we mention that rapidity distribution of π mesons simulated by transport models underestimated the experimental results by a factor of 2, even though the various theoretical simulations are relatively close to one another. The true test of the NRD+eVMD+QMD model will be a comparison of the simulated dilepton spectrum with the future experimental output of the HADES collaboration at GSI. This last step can only be performed in a close collaboration with our experimental colleagues, since for a meaningful comparison the HADES detector filter function will have to be applied to the theoretical spectrum.
Project Title: "Hadron Properties in Nuclear Matter and Dilepton Emission in Relativistic
Project Code: RP9
Contract Number: 07/01.10.2007
Project Director: Dr. Mircea Dan Cozma
Allocated Funds: 504500.00 LEI
Host Institution: IFIN-HH, Magurele-Bucharest, Romania (NIPNE)
Research Group: Nuclear Interactions and Hadronic Matter (NIHAM)
Progress reports, talks presented at conferences and other output material related to the project will be posted here.Progress Reports
"In-medium properties of vector mesons: nucleonic resonances effects": Talk ReportJune 2008
"Pions and vector mesons in nuclear matter: extra contributions ": TalkDecember 2008
"Effective model for the description of pions, eta and vector mesons in nuclear matter": Talk ReportPresentations at Conferences/Workshops
Hadronic Collisions at the LHC and QCD at high density, Les Houches, France: In-medium properties of vector mesons and dilepton emission in heavy-ion collisions at SIS energies
Heavy Ion Collisions from the Coulomb Barrierto the Quark Gluon Plasma, Erice, Italy: On the isospin dependence of EoS of nuclear matterPublications
M.D. Cozma, and M. Petrovici, Depedence of flow observables in heavy-ion collisions on the symmetry energy and the in-medium nucleon-nucleon interaction , to appear in Prog. Part. Nucl. Phys.
Any ideas, suggestions, criticism or questions are welcome either via email at cozma at niham dot nipne dot ro or by phone at +(4021) 404.6143. You can visit also my homepage here.