K. Nakayama, Yongseok Oh, H. Haberzettl
The production of $η$ and $η^\prime$ mesons in photon- and hadron-induced reactions are studied in a combined analysis based on an effective Lagrangian approach in order to learn about the relevant production mechanisms and the possible role of nucleon resonances in these reactions.
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I review recent insights and open questions connected with the production of eta--mesons from hadrons.
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.
A short, and definitely not a complete representation of ηproduction processes on hadrons is given. First of all, the different ways of obtaining the πN \to ηN and πN \to ηN amplitudes are presented. After that, an overview of results obtained using these amplitudes as input for calculating processes like: NN \to ηNN, pd \to η^{3}He, πd \to ηNN and ηd, η^{3}He and η^{4}He as well as η-light nuclei bond states, will be given. The experimental and theoretical results will be reviewed. The opened problems and the way how to solve them will be presented.
The production rate for η' in pp ->pp η' at rest is calculated in a covariant one boson exchange model, previously applied to study pi^0 and ηproduction in NN collisions. The transition amplitudes for the elementary BN -> eta' N processes with B being the meson exchanged (B = pi, sigma, eta, rho, omega and delta) are taken to be the sum of s and u channels with a nucleon in the intermediate states, and a delta meson pole in a t-channel. The couplings of the eta' to hadrons are a factor 0.437 weaker than the respective eta-hadron couplings, as suggested by a quark model and a singlet-octetmixin…
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 …
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 new state of matter produced at Relativistic Heavy Ion Collider reveals a strongly coupled quark-gluon plasma with an extremely small shear viscosity to entropy density ratio eta/s. We calculate the eta/s of an equilibrated hadron matter characterized by a relativistic hadron resonance gas with a Hagedorn mass spectrum that grows exponentially with the hadron mass. We find with increase in temperature of the system the eta/s value decreases due to rapid increase in the multiplicity of massive resonances. In the vicinity of the critical temperature for deconfinement transition, the minimum …
We compare results for the D13(1520) photon-decay amplitudes determined in analyses of eta- and pion-photoproduction data. The ratio of helicity amplitudes (A_3/2 / A_1/2), determined from eta-photoproduction data, is quite different from that determined in previous analyses of pion-photoproduction data. We consider how strongly the existing pion-photoproduction data constrain both this ratio and the individual photon-decay amplitudes.
The Chew-Mandelstam parameterization, which has been used extensively in the two-body hadronic sector, is generalized in this exploratory study to the electromagnetic sector by simultaneous fits to the pion- and eta-photoproduction S-wave multipole amplitudes for center-of-mass energies from the pion threshold through 1.61 GeV. We review the Chew-Mandelstam parameterization in detail to clarify the theoretical content of the SAID hadronic amplitude analysis and to place the proposed, generalized SAID electromagnetic amplitudes in the context of earlier employed parameterized forms. The paramet…
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.
A combined analysis of new eta photoproduction data for total and differential cross sections, target asymmetry and photon asymmetry is presented. Using a few reasonable assumptions we perform the first model-independent analysis of the E0+, E2- and M2- eta photoproduction multipoles. Making use of the well-known A3/2 helicity amplitude of the D13(1520) state we extract its branching ratio to the eta-N channel, Gamma(eta,N)/Gamma = (0.08 +- 0.01)%. At higher energies, we show that the photon asymmetry is extremely sensitive to small multipoles that are excited by photons in the helicity 3/2 st…
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.
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.
Photoproduction of eta mesons from nucleons can provide valuable information about the excitation spectrum of the nucleons. The angular dependence of photoproduction in the photon-induced reaction is investigated in the multi-source thermal model. The results are compared with experimental data from the decay mode. They are in good agreement with the experimental data. It is shown that the movement factor increases linearly with the photon beam energies. And, the deformation and translation of emission sources are visually given in the formalism.
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.
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…
The near-term objectives of the research program at the Data Analysis Center are established within the context of the existing partial wave analyses available through the online suite of analysis and database codes accessible through SAID, the Scattering Analysis Interactive Database. This presentation reviews the efforts to determine a model independent method to obtain sets of partial wave amplitudes for strong and electromagnetic reactions, the interpretation of the amplitudes in terms of the excited states of the nucleon, the role of new precision unpolarized and polarized data, and new d…
The recently discovered enhancement of eta photoproduction on the quasi-free neutron at energies around sqrt(s)~1.67 GeV is addressed within a SU(3) coupled channel model. The quasi-free cross sections on proton and neutron, sigma_n and sigma_p, can be quantitatively explained. In this study, the main source for the peak in sigma_n/sigma_p is a coupled channel effect in S-wave that explains the dip-bump structure in gamma n --> eta n. In particular, the photon coupling to the intermediate meson-baryon states is important. The stability of the result is extensively tested and consistency with s…
Coherent eta photoproduction on the deuteron is studied in the $S_{11}$ resonance region neglecting eta rescattering and two-body processes. For the elementary reaction on the nucleon, we have considered the dominant $S_{11}(1535)$ resonance and as background the nucleon pole terms as well as $ρ$ and $ω$ meson exchange. We have studied the influence of different choices for the neutron resonance amplitude, different prescriptions for fixing the invariant mass of the resonance amplitude and different methods for deriving the elementary production amplitude for an arbitrary reference frame.
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.
We present a combined analysis of the new eta photoproduction data for total and differential cross sections, target asymmetry and photon asymmetry. Using basic assumptions, this allows a model-independent extraction of the $E_{2-}$ and $M_{2-}$ multipoles as well as resonance parameters of the $D_{13}(1520)$ state. At higher energy, we show that the photon asymmetry is extremely sensitive to small multipoles that are excited by photons in the helicity 3/2 state. These could be, e.g., the $F_{15}(1680)$, the $F_{17}(1990)$, or the $G_{17}(2190)$ resonances.
Low-energy eta photoproduction on the nucleon is studied in an effective Lagrangian approach that contains Born terms, vector meson and nucleon resonance contributions. The resonance sector includes the $S_{11}(1535)$, $P_{11}(1440)$ and $D_{13}(1520)$ states whose couplings are fixed by independent electromagnetic and hadronic data. The available $(γ,η)$ data are employed to discuss the difference between pseudoscalar and pseudovector Born terms and to determine the magnitude of the $ηNN$ coupling constant. We present multipoles that are most sensitive to the various model ingredients and dem…
We develop a relativistic model for incoherent eta-photoproduction on nuclei. The elementary process is described using an effective Lagrangian containing photons, nucleons, the S11(1535) and D13(1520) nucleon resonances, and rho, omega, and eta mesons. The nucleon and eta wavefunctions are obtained from relativistic wave equations. Final-state interactions of the outgoing particles are included via optical potentials. The effects of these interactions are found to be large and lead to reduced cross sections.The incoherent cross sections for isovector transitions are much larger than those for…
The $η$ production in the nucleon resonance energy region is studied within the unitary coupled-channels effective Lagrangian approach of the Giessen model. We demonstrate that the second peak recently observed in the cross section of $η$ photoproduction on the neutron at $\sqrt{s}$=1.66 GeV can be explained in terms of coupled-channel effects due to $S_{11}(1650)$ and $P_{11}(1710)$ resonance excitations.
We discuss the eta and eta prime photo- and electroproduction as a way to probe the nucleon resonance structure.
The in-medium mass of the $η^{\prime}$ meson is discussed in a context of partial restoration of chiral symmetry in nuclear medium. The $η^{\prime}$ mass is expected to be reduced by order of 100 MeV at the saturation density. The reduction is a consequence of the suppression of the anomaly effect on the $η^{\prime}$ mass induced by partial restoration of chiral symmetry. This strong attraction in $η^{\prime}$ nuclear systems does not accompany large absorption of $η^{\prime}$ into nuclear matter. This leads to the possibility of so narrow bound states of the $η^{\prime}$ meson in nuclei to be…
We investigate eta electroproduction on nuclei for Q^2=2.4 and 3.6 GeV^2 in the framework of a coupled-channel BUU transport model. We analyze the importance of final state interactions and side feeding and compare with findings drawn from eta photoproduction. It is shown that in contrast to photoproduction the influence of etas stemming from secondary processes becomes important at high Q^2.
We study the scattering lengths of charmonia (J/psi and eta_c) with light hadrons (pi, rho and N) by the quenched lattice QCD simulations on 24x24x24x48, 32x32x32x48 and 48x48x48x48 lattices with the lattice spacing a = 0.068 fm. The scattering length is extracted by using the Luscher's phase-shift formula together with the measurement of the energy shift Delta E of two hadrons on the lattice. We find that there exist attractive interactions in all channels, J/psi(eta_c)-pi, J/psi(eta_c)-rho and J/psi(eta_c)-N: The s-wave J/psi-pi (eta_c-pi) scattering length is determined as 0.0119+-0.0039 fm…
Photo- and electroproduction of eta, eta-prime mesons on protons are investigated within a relativistic chiral unitary approach based on coupled channels. The s wave potentials for electroproduction and meson-baryon scattering are derived from a chiral effective Lagrangian which includes the eta-prime as an explicit degree of freedom and incorporates important features of the underlying QCD Lagrangian such as the axial U(1) anomaly. The effective potentials are iterated in a Bethe-Salpeter equation and cross sections for eta, eta-prime photo- and electroproduction from protons are obtained. Th…
Using the (2+1)-dimensional viscous hydrodynamic code VISH2+1 with a temperature dependent specific shear viscosity (eta/s)(T), we present a detailed study of the influence of a large hadronic shear viscosity and its corresponding relaxation time tau_pi on the transverse momentum spectra and elliptic flow of hadrons produced in 200 A GeV Au+Au collisions. Although theory, in principle, predicts a well-defined relation T*tau_pi = kappa(T)*(eta/s)(T), the precise form of kappa(T) for the matter created in relativistic heavy-ion collisions is not known. For the popular choice kappa=3 the hadron s…
The photo- and electroproduction of eta, eta-prime mesons on nucleons are investigated within a relativistic chiral unitary approach based on coupled channels. The s-wave potentials for electroproduction and meson-baryon scattering are derived from a chiral effective Lagrangian which includes the eta-prime as an explicit degree of freedom and incorporates important features of the underlying QCD Lagrangian such as the axial U(1) anomaly. The effective potentials are iterated in a Bethe-Salpeter equation and cross sections for eta, eta-prime photo- and electroproduction from nucleons are obtain…
We investigate the decays of pi^0, eta and eta-prime into two photons in an effective U(3) chiral Lagrangian approach without employing large N_c arguments. Tree level and one-loop contributions from the anomalous Wess-Zumino-Witten Lagrangian are calculated and the importance of eta--eta-prime mixing is discussed. Unitarity corrections beyond one-loop play an important role for the decays with off-shell photons and are included by employing a coupled channel Bethe-Salpeter equation which satisfies unitarity constraints and generates vector-mesons from composed states of two pseudoscalar meson…
K*-charmonium dissociation reactions in hadronic matter are studied in the Born approximation, in the quark-interchange mechanism, and with a temperature-dependent quark potential. We obtain the temperature dependence of unpolarized cross sections for K*-charmonium dissociation reactions which produce charmed mesons and charmed strange mesons. We use the cross sections for charmonium dissociation in collisions with pion, rho meson, kaon, vector kaon, and eta meson to calculate dissociation rates of charmonium with the five types of mesons. Because of the temperature dependence of the meson mas…
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 isobar model EtaMAID has been updated with new and high precision data for eta and etaprime photoproduction on protons and neutrons from MAMI, ELSA, GRAAL and CLAS. The background is described in a recently developed Regge-cut model, and for the resonance part the whole list of nucleon resonances has been investigated with 21 N* states contributing to eta photoproduction and 12 N* states contributing to etaprime photoproduction. A new approach is discussed to avoid double counting in the overlap region of Regge and resonances. A comparison is done among four newly updated partial waves ana…
The pseudorapidity behaviour of the azimuthal anisotropy parameters v_1 and v_2 of inclusive charged hadrons and their dependence on the centrality has been studied in Au+Au collisions at full RHIC energy of sqrt(s) = 200 GeV within the microscopic quark-gluon string model. The QGSM simulation results for the directed flow v_1 show antiflow alignment within the pseudorapidity range |eta| < 2 in a fair agreement with the experimental v_1(eta) data, but cannot reproduce the further development of the antiflow up to |eta| around 3.5. The eta dependence of the elliptic flow v_2 extracted from the …
Using the (2+1)-dimensional viscous hydrodynamic code VISH2+1, we present systematic studies of the dependence of pion and proton transverse momentum spectra and their elliptic flow in 200 A GeV Au+Au collisions on the parameters of the hydrodynamic model (thermalization time, initial entropy density distribution, decoupling temperature, equation of state, and specific shear viscosity eta/s). We identify a tension between the slope of the proton spectra, which (within hydrodynamic simulations that assume a constant shear viscosity to entropy density ratio) prefer larger eta/s values, and the s…
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 newly developed hybrid model VISHNU which connects viscous hydrodynamics with a hadron cascade model, we study the differential and integrated elliptic flow v_2 at different centrality bins for 200 A GeV Au+Au collisions and 2.76 A TeV Pb+Pb collisions. We find that the average Quark Gluon Plasma (QGP) specific shear viscosity eta/s slightly increases from Relativistic Heavy Ion Collider (RHIC) to Large Hadron Collider (LHC) energies. However, a further study assuming different temperature dependencies for (eta/s)_QGP shows that one cannot uniquely constrain the form of (eta/s)_QGP(T…
Recently obtained polarized target and photon asymmetry data in eta photoproduction are shown to be very powerful, in conjunction with the differential cross-section data, in yielding model-insensitive constraints on the electrostrong parameters for the excitation and decay of the $N^{*}(1520)$ resonance. The extracted ratio of its electromagnetic helicity amplitudes, $A_{3/2}/A_{1/2}$, provides a critical test for the QCD-inspired hadron models.
Eta photo- and electroproduction on the nucleon is studied using an isobar model. The model contains Born terms, and contributions from vector meson exchanges and nucleon resonances. Our results are compared with recent eta photoproduction data for differential and total cross sections, beam asymmetry, and target asymmetry, as well as electroproduction data. Besides the dominant S11(1535) resonance, we show that the second S11 resonance, S11(1650), is also necessary to be included in order to extract S11(1535) resonance parameters properly. In addition, the beam asymmetry data allow us to extr…
We analyze the available data on eta photo- and electroproduction, around W~1535 MeV, in the framework of the effective Lagrangian approach, and extract, in a nearly model-independent fashion, the electrostrong amplitude for the gamma+N--> N*(1535)--> N+eta processes. Quark model approaches are shown to be quite inadequate to explain this property at all Q^2. In particular, at high Q^2, the extracted amplitude falls much slower than the predictions of the quark model, as a function of Q^2, a situation similar to the electroexcitation and decay of Delta(1232). A QCD explanation of these observa…
The eta-photon transition form factor is evaluated in a formalism based on a phenomenological description at low values of the photon virtuality, and a QCD-based description at high photon virtualities, matching at a scale $Q_{0}^{2}$. The high photon virtuality description makes use of a Distribution Amplitude calculated in the Nambu-Jona-Lasinio model with Pauli-Villars regularization at the matching scale $Q_{0}^{2}$, and QCD evolution from $Q_{0}^{2}$ to higher values of $Q^{2}$. A good description of the available data is obtained. The analysis indicates that the recent data from the BaBa…
Using the recent precise measurements of eta photopro- duction in proton and deuteron targets, we extract the ratio of the helicity amplitudes A^n_1/2 / A^p_1/2, for the excitation of N^*(1535), in the effective Lagrangian approach, It is fairly model-independent, free from the final-state interaction effects, and negative as predicted by the quark models. We stress the importance of polarization observables in further elucidation of the N^*(1520) photoexcitation amplitudes.
The $ηN$ final state is isospin-selective and thus provides access to the spectrum of excited nucleons without being affected by excited $Δ$ states. To this end, the world database on eta photoproduction off the proton up to a center-of-mass energy of $E\sim 2.3$ GeV is analyzed, including data on differential cross sections, and single and double polarization observables. The resonance spectrum and its properties are determined in a combined analysis of eta and pion photoproduction off the proton together with the reactions $πN\to πN$, $ηN$, $KΛ$ and $KΣ$. For the analysis, the so-called Jüli…
The production of eta' mesons in photon- and hadron-induced reactions has been revisited in view of the recent additions of high-precision data to the world data base. Based on an effective Lagrangian approach, we have performed a combined analysis of the free and quasi-free gamma N -> eta' N, N N -> N N eta', and pi N -> eta' N reactions. Considering spin-1/2 and -3/2 resonances, we found that a set of above-threshold resonances {S_{11}, P_{11}, P_{13}}, with fitted mass values of about M_R=1925, 2130, and 2050 MeV, respectively, and the four-star sub-threshold P_{13}(1720) resonance reproduc…
The in-medium Eta-N interaction near and below threshold is constructed from a free-space chirally-inspired meson-baryon coupled-channel model that captures the physics of the N(1535) baryon resonance. Nucleon Pauli blocking and hadron self-energies are accounted for. The resulting energy dependent in-medium interaction is used in self-consistent dynamical calculations of Eta nuclear bound states. Narrow states of width about or less than 2 MeV are found across the periodic table, beginning with A=10, for this in-medium coupled-channel interaction model. The binding energy of the 1s-Eta state …
We analyse photoproduction of eta mesons off the proton in a gauge-invariant chiral unitary framework. The interaction kernel for meson-baryon scattering is derived from the leading order chiral effective Lagrangian and iterated in a Bethe-Salpeter equation. The recent precise threshold data from the Crystal Ball at MAMI can be described rather well and the complex pole corresponding to the S11(1535) is extracted. An extension of the kernel is also discussed.
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