R. Vertesi, T. Csorgo, J. Sziklai
PHENIX and STAR data on the intercept parameter of the two-pion Bose-Einstein correlation functions in $\sqrt{s_{NN}}= 200$ GeV Au+Au collisions were analysed in terms of various models of hadronic abundances. To describe these data, an in-medium $η^\prime$ mass decrease of at least 200 MeV was needed in each case.
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The pp -> pp eta' reaction is investigated within a relativistic meson-exchange model of hadronic interactions. We explore the role of nucleonic and mesonic, as well as the N* resonance currents, in producing eta' mesons. In order to learn more about the production mechanisms, new measurements in the energy region far from the threshold are required.
I review recent insights and open questions connected with the production of eta--mesons from hadrons.
A microscopic few-body description of near-threshold coherent photoproduction of the eta meson on tritium and 3He targets is given. The photoproduction cross-section is calculated using the Finite Rank Approximation (FRA) of the nuclear Hamiltonian. The results indicate a strong final state interaction of the eta meson with the residual nucleus. Sensitivity of the results to the choice of the eta N T-matrix is investigated.
The scattering lengths of eta-meson collisions with light nuclei d,t,3He, and 4He are calculated on the basis of few-body equations in coherent approximation. It is found that the eta-nucleus scattering length depends strongly on the number of nucleons and the potential-range parameter. By taking into account the off-shell behavior of the eta-N amplitude, the eta-4He scattering length increases considerably.
A microscopic few-body description of near-threshold coherent photoproduction of the eta-meson on tritium and He3 targets is given. The photoproduction cross-section is calculated using the Finite Rank Approximation (FRA) of the nuclear Hamiltonian. The results indicate a strong final state interaction of the eta-meson with the residual nucleus. Sensitivity of the results to the choice of the eta-N T-matrix is investigated. The importance of obeying the two-body unitarity condition in the eta-N system is demonstrated.
The isobar models eta-MAID and eta'-MAID have been used to analyze new data on quasi-free eta photoproduction on the deuteron from Bonn and recent eta' data on the proton from Jlab. In eta photoproduction on the neutron a bump around W=1700 MeV was observed which could possibly arise from a narrow P11 state that is discussed as a non-strange member of the Theta^+ anti-decuplett. In eta' photoproduction on the proton resonance contributions are found that can be attributed to missing resonances in the energy region around W=1900 MeV.
The decoupling of the eta meson from the nucleon, as recently deduced from analyzing \bar p p collisions and eta photoproduction off the proton at threshold, is shown to provide an argument against the octet Goldstone boson nature of the eta meson. This argument concerns the structure of the strong isoscalar axial vector current. A vanishing eta-N coupling means a vanishing contribution of the eta-pole term to the hypercharge nucleon axial vector current. Therefore, no partial conservation of the latter can be achieved. This new situation invalidates the octet Goldberger--Treiman relation for …
The two-step model with pi-, rho- and omega- exchanges taken into account is applied to investigate the reactions pn -> d eta and pn -> d eta-prime. The existing experimental data on the reaction pn -> d eta are analysed and predictions for the cross section of the reaction pn -> d eta-prime are presented. It is found that pi- as well as rho exchange yield significant contributions in both reactions. The effect of the final state interaction is also studied.
The position and movement of poles of the amplitude for elastic eta-meson scattering off the light nuclei d, t, ^3He, and ^4He are studied. It is found that, within the existing uncertainties for the elementary eta-N interaction, all these nuclei can support a quasi-bound state. The values of the eta-nucleus scattering lengths corresponding to the critical eta-N interaction which produces a quasi--bound state are given.
An analysis of incoherent photoproduction of $η$ mesons off the deuteron for photon energies from threshold to 800 MeV is presented. The dominant contribution, the $γ$N-$η$N amplitude, is described within an isobar model. Effects of the final state interactions in the $NN$ as well as the $ηN$ systems are included employing models derived within the meson-exchange approach. It is found that their consideration is important. Specifically, due to an interference effect the influence of the $ηN$ final state interaction is enhanced in the reaction $γd \to np η$ close to threshold.
Eta meson production in both proton-proton and proton-neutron collisions is investigated within a relativistic meson exchange model of hadronic interactions. It is found that the available cross section data can be described equally well by either the vector or pseudoscalar meson exchange mechanism for exciting the S_{11}(1535) resonance. It is shown that the analyzing power data can potentially be very useful in distinguishing these two scenarios for the excitaion of the S_{11}(1535) resonance.
A microscopic calculation of near-threshold eta-meson production in the reaction NN -> NNeta is presented. It is assumed that the eta meson is produced via direct emission and via elementary rescattering processes MN -> etaN of various mesons M = pi, rho, etc. As a novel feature the amplitudes for the latter production mechanism are taken from a multi-channel meson-exchange model of the pi N system developed by the Juelich group which contains explicitly the channels pi N, rho N, eta N, sigma N, and pi Delta. Furthermore, effects of the NN interaction in the final as well as in the initial sta…
We study eta meson properties in the infinite nuclear matter and in atomic nuclei with an emphasis on effects of the eta coupling to N*(1535)--nucleon-hole modes. The N*(1535) resonance, which dominates the low-energy eta-nucleon scattering, can be seen as a chiral partner of the nucleon. The change of the chiral mass gap between the N* and the nucleon in a nuclear medium has an impact on the properties of the eta-nucleus system. If the N*-nucleon mass gap decreases with a density increase (chiral symmetry restoration) the calculations show the existence of the resonance state at the energy ab…
Very recent data for the reaction gamma{d} --> eta{np} are analyzed within a model that includes contributions from the impulse approximation and next order corrections due to the np and eta{N} interactions in the final state. Comparison between the calculations and data indicate sizable contributions from the np and eta{N} final state interactions close to threshold.
We present a unitary and gauge-invariant model with coupled channels, which provides a consistent description of pion photoproduction off nucleons in the E$_{0+}$ channel and eta-meson photoproduction off protons and deuterons. An effective field theory with hadrons and photons is constructed, which includes non-resonant Born terms as well as the S$_{11}$(1535) and S$_{11}$(1650) baryon resonances. Due to the coupling between the channels, the production of eta-mesons is strongly affected by the S$_{11}$(1650) although its direct coupling to the $η$N channel is negligible. The rho- and omega-m…
Data on the total cross sections for the pp -> pp eta, pn -> pn eta, and pn -> d eta reactions and the pp -> pp eta differential cross section near threshold are analysed in a one-meson-exchange model. After including initial and final-state nucleon-nucleon distortion, the magnitude and most of the energy dependence are well reproduced. It is found that the contribution of rho-exchange is larger than that of pi-exchange. With destructive rho/pi interference in the pp case, the model explains quantitatively the pp -> pp eta/pn -> pn eta cross section ratio and the slope of the pp -> pp eta diff…
The pp -> pp eta and pp -> pLambda K^+ reactions near threshold are dominated by the first and second S_11 resonance respectively. It is shown that a one-pion-exchange model exciting these isobars reproduces well the ratio of the production cross sections. The consequences for this and other channels are discussed.
We have investigated the 6Li(gamma,d) reaction theoretically for the formation of the eta'(958) mesic nucleus close to the recoilless kinematics. We have developed the theoretical formula and reported the quantitative results of the formation spectra for various cases in this article. We have found that the formation cross sections are reduced by the effects of the fragile deuteron form factor.
Back in the mid eighties, a new branch of investigation which was related to the interaction of eta mesons with nuclei came into existence. It started with the theoretical prediction of possible exotic states of eta mesons and nuclei bound by the strong interaction and later developed into an extensive experimental program to search for such unstable states as well as understand the underlying interaction via eta meson producing reactions. The vast literature of experimental as well as theoretical works which studied various aspects of eta producing reactions such as the $π^+$ $n$ $\to ηp$, $p…
Eta meson production in the proton-proton scattering is dominated by the low-mass meson exchange. We present a brief study on how the type of the exchanged mesons within coupled-channel and multi-resonance model influences the scattering observables. We show under which circumstances the eta exchange may explain the shape of the observed cross sections, and present a few selected results: total cross section in the full energy range, and the proton-proton energy distribution at 15.5 MeV.
We discuss the eta and eta prime photo- and electroproduction as a way to probe the nucleon resonance structure.
The fascinating physics underlying eta and eta-prime mesons can be studied theoretically and experimentally in various contexts. In this presentation we want to turn our attention to two important uncorrelated aspects of this vivid research field which provide yet unexpected challenges or surprises. First we discuss open questions in the theoretical treatment of Coulomb-interaction in the context of reaction processes like p p --> p p eta. Then we review eta - eta-prime and sigma(600) - f_0(980) mixing in the U(3) x U(3) Linear Sigma Model and extract information on eta - eta-prime mixing and …
The resonance and bound--state poles of the amplitude describing elastic scattering of $η$-meson off the light nuclei $^2H$,\,$^3H$,\, $^3He$, and $^4He$ are calculated in the framework of a microscopic approach based on few--body equations. For each of the nuclei, the two--body parameters that enhance the $ηN$--attraction which generate quasi--bound states, are also determined.
Eta photo- and electroproduction off the nucleon is investigated in an effective lagrangian approach that contains Born terms and both vector meson and nucleon resonance contributions. In particular, we review and develop the formalism for coincidence experiments with polarization degrees of freedom. The different response functions appearing in single and double polarization experiments have been studied. We will present calculations for structure functions and kinematical conditions that are most sensitive to details of the lagrangian, in particular with regard to contributions of nucleon re…
The production of $η'$ mesons in the reactions $pp\to ppη'$ and $pn\to pnη' $ at threshold-near energies is analyzed within a covariant effective meson-nucleon theory. The description of cross section and angular distributions of the available data in this kinematical region in the $pp$ channel is accomplished by including meson currents and nucleon currents with the resonances $S_{11}(1650)$, $P_{11}(1710)$ and $P_{13}(1720)$. Predictions for the $pn$ channel are given. The di-electron production from subsequent $η'$ Dalitz decay $η' \to γγ^* \toγe^+e^-$ is also calculated and numerical resul…
The importance of Born terms and resonance exchange for eta and eta-prime photoproduction off both the proton and neutron within U(3) baryon chiral perturbation theory is investigated. Low-lying resonances such as the vector mesons and J^P= 1/2^+, 1/2^- baryon resonances are included explicitly and their contributions together with the Born terms are calculated. The coupling constants of the resonances are determined from strong and radiative decays. We obtain reasonable agreement with experimental data near threshold.
The study of light pseudoscalar quark-antiquark bound states in the Dyson-Schwinger approach with the effective QCD coupling enhanced by the interplay of the dimension 2 gluon condensate <A^2> and dimension 4 gluon condensate <F^2>, is extended to the eta-eta' complex. We include the effects of the gluon axial anomaly into the Dyson-Schwinger approach to mesons. The calculated masses, mixing and two-photon decay widths of eta and eta' mesons are in agreement with experiment. Also, in a model-independent way, we give the modification of the Gell-Mann--Okubo and Schwinger nonet relations due to …
The p + 6Li --> eta + 7Be reaction has been investigated with an emphasis on the eta meson and 7Be interaction in the final state. Considering the 6Li and 7Be nuclei to be alpha-d and alpha-3He clusters respectively, the reaction is modelled to proceed via the p + d [alpha] --> 3He [α] + eta reaction with the alpha remaining a spectator. The eta meson interacts with 7Be via multiple scatterings on the 3He and alpha clusters inside 7Be. The individual eta-3He and eta-alpha scatterings are evaluated using few body equations for the eta-3N and eta-4N systems with a coupled channel eta-N interacti…
We consider the chiral Lagrangian with a nonet of Goldstone bosons and a nonet of light vector mesons. The mixing between the pseudoscalar mesons eta and eta-prime is taken into account. A novel counting scheme is suggested that is based on hadrogenesis, which conjectures a mass gap in the meson spectrum of QCD in the limit of a large number of colors. Such a mass gap would justify to consider the vector mesons and the eta-prime meson as light degrees of freedom. The complete leading order Lagrangian is constructed and discussed. As a first application it is tested against electromagnetic tran…
We review the present understanding of etaprime and eta meson physics and these mesons as a probe of gluon dynamics in low-energy QCD. Recent highlights include the production mechanism of eta and etaprime mesons in proton-nucleon collisions from threshold to high-energy, the etaprime effective mass shift in the nuclear medium, searches for possible eta and etaprime bound states in nuclei as well as precision measurements of eta decays as a probe of light-quark masses. We discuss recent experimental data, theoretical interpretation of the different measurements and the open questions and chall…
The effective action of the linear meson model generates the mesonic n-point functions with all quantum effects included. Based on chiral symmetry and a systematic quark mass expansion we derive relations between meson masses and decay constants. The model ``predicts'' values for f_eta and f_eta' which are compatible with observation. This involves a large momentum dependent eta-eta' mixing angle which is different for the on--shell decays of the eta and the eta'. We also present relations for the masses of the 0^{++} octet. The parameters of the linear meson model are computed and related to …
The production of pseudo scalar, Eeta, Eta-prime, and vector, Omega, Rho, Phi, mesons in NN collisions at threshold-near energies is analyzed within a covariant effective meson-nucleon theory. It is shown that a good description of cross sections and angular distributions, for vector meson production, can be accomplished by considering meson and nucleon currents only, while for pseudo scalar production an inclusion of nucleon resonances is needed. The di-electron production from subsequent Dalitz decay of the produced mesons, $η'\to γγ^* \toγe^+e^-$ and $ω\to πγ^*\to πe^+e^-$ is also considere…
New experimental data are presented on the energy dependence of the total cross sections for the np -> d eta and quasi-two-body pp -> pp eta reactions, where the final diproton is detected at very low excitation energy. Differential cross sections of pp -> pp eta away from threshold show the influence of higher partial waves and a partial wave decomposition is attempted.
Binding energy of eta_c with ^4 He has been calculated on the basis of Yukawa type potential. Final Rank Approximation (FRA) has been used for microscopical treatment of the initial 5-body problem. The results are compared with the results of the folding model and variational calculations.
The role played by subthreshold meson-baryon dynamics is demonstrated in kaonic-atom, Kbar-nuclear and eta-nuclear bound-state calculations within in-medium models of Kbar-N and eta-N interactions. New analyses of kaonic atom data reveal appreciable multi-nucleon contributions. Calculations of eta-nuclear bound states show, in particular, that the eta-N scattering length is not a useful indicator of whether or not eta mesons bind in nuclei nor of the widths anticipated for such states.
We study kaon-charmonium and eta-charmonium dissociation reactions. The K-charmonium dissociation and the eta-charmonium dissociation include 27 reactions. Cross sections for the reactions are calculated in the Born approximation, in the quark-interchange mechanism and with a temperature-dependent quark potential. The temperature dependence of peak cross sections of endothermic reactions is linked to the temperature dependence of quark-antiquark relative-motion wave functions, meson masses and the quark potential. Although the eta meson and kaon have similar masses, the energy and temperature …
This work constitutes one part of an investigation of the low-temperature changes of the properties of the eta' meson. In turn these properties are strongly tied to the U(1)_A anomaly of Quantum Chromodynamics. The final aim is to explore the interplay of the chiral anomaly and in-medium effects. We determine the lifetime of an eta' meson being at rest in a strongly interacting medium as a function of the temperature. To have a formally well-defined low-energy limit we use in a first step Chiral Perturbation Theory for a large number of colors. We determine the pertinent scattering amplitudes …
Observed for the processes gamma+p arrow eta+p, gamma+n arrow eta+n are calculated throughout the resonance energy region using the single isobar model without a background. The connection between invariant photoexcitation amplitudes of the resonances on neutrons and protons are calculated. The results are discussed in terms of a comparison with experimental data and calculations performed by other authors.
Using the quark-meson coupling (QMC) model, we investigate whether $ω, η, η'$ and $D^-$ mesons form meson-nucleus bound states. Our results suggest that one should expect to find $η$- and $ω$-nucleus bound states in all the nuclei considered. Furthermore, it is shown that the $D^-$ meson will form quite narrow bound states with $^{208}$Pb.
We shed light upon the eta' mass in nuclear matter in the context of partial restoration of chiral symmetry, pointing out that the U_{A}(1) anomaly effects causes the eta'-eta mass difference necessarily through the chiral symmetry breaking. As a consequence, it is expected that the eta' mass is reduced by order of 100 MeV in nuclear matter where partial restoration of chiral symmetry takes place. The discussion given here is based on Ref. [1].
The electroproduction of eta and eta' mesons on the proton and the neutron is investigated at tree level within the framework of U(3) chiral perturbation theory. In addition to the Born terms low-lying resonances such as the vector mesons and J^P= 1/2^+, 1/2^- baryon resonances are included explicitly and their contributions are calculated. Results for the separated differential cross sections are presented.
The hadronic decays eta -> pi pi pi, eta-prime -> pi pi pi and eta-prime -> eta pi pi are investigated within a U(3) chiral unitary approach. Final state interactions are included by deriving the effective s-wave potentials for meson meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Salpeter equation. With only a small set of parameters we are able to explain both rates and spectral shapes of these decays.
The hadronic decays eta, eta-prime -> 3 pi and eta-prime -> eta pi pi are investigated within the framework of U(3) chiral effective field theory in combination with a relativistic coupled-channels approach. Final state interactions are included by deriving s- and p-wave interaction kernels for meson-meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Salpeter equation. Very good overall agreement with currently available data on decay widths and spectral shapes is achieved.
Although eta-eta' mixing is qualitatively well understood as a consequence of the U(1)_A anomaly in QCD together with a broken SU(3) flavor symmetry, until recently the values of decay and mixing parameters of the eta and eta' were only approximately known, e.g. values for the octet-singlet mixing angle between -20 degrees and -10 degrees could be found in the literature. New experimental data, especially for the reactions gamma gamma* -> eta, eta' and B -> eta' K, together with new theoretical results from higher order corrections in chiral perturbation theory stimulated a phenomenological re…
The production of (eta,eta')- mesons during the decay of a CP-odd phase is studied within an evolution operator approach. We derive a quantum kinetic equation starting from the Witten-DiVecchia-Veneziano Lagrangian for pseudoscalar mesons containing a U_A(1) symmetry breaking term. The non-linear vacuum mean field for the flavour singlet pseudoscalar meson is treated as a classical, self-interacting background field with fluctuations assumed to be small. The numerical solution provides the time evolution of momentum distribution function of produced eta'- mesons after a quench at the deconfine…
Using a relativistic transport model ART1.0, we explore effects of nuclear symmetry energy on eta meson production and its rare decay to the dark U-boson in heavy-ion reactions from 0.2 to 10 GeV/nucleon available at several current and future facilities. The yield of eta mesons at sub-threshold energies is found to be very sensitive to the density dependence of nuclear symmetry energy. Above a beam energy of about 5 GeV/nucleon in Au+Au reactions, the sensitivity to symmetry energy disappears. Using the branching ratio of the rare eta decay (eta->gamma U) available in the literature, we estim…
Various decays of eta and eta-prime are investigated within the framework of U(3) chiral effective field theory in combination with a relativistic coupled-channels approach. Final state interactions are included by deriving s- and p-wave interaction kernels for meson-meson scattering from the chiral effective Lagrangian and iterating them in a Bethe-Salpeter equation. Very good agreement with experimental data is achieved.
We discuss the role of QCD symmetries in understanding the eta and etaprime mesons in nuclear media. Recent results on the etaprime mass in nuclei from the CBELSA/TAPS collaboration are very similar to the prediction of the Quark Meson Coupling model.
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