Threshold pion photoproduction in a light-cone quark model

Abstract The instantaneous and seagull graphs are calculated for pion photoproduction in a relativistic light-cone model of the nucleon. In both pseudoscalar and pseudovector coupling we find the ratios A (−) : A (0) : A (+) = 1: ( −1 2 μ):( −9 5 μ) in the nonrelativistic limit. These results correspond to the sum of seagull and Z -graph in the nonrelativistic quark model. In pseudovector coupling also the numerical results for realistic-model parameters are close to those values.

Medium energy physics with c.w. electron accelerators

A dispersion theoretical approach to the threshold amplitudes of pion photoproduction

We give predictions for the partial wave amplitudes of pion photoproduction near threshold by means of dispersion relations at fixed t. The free parameters of this approach are determined by a fit to experimental data in the energy range 160 MeV $\le E_{\gamma} \le$ 420 MeV. The observables near threshold are found to be rather sensitive to the amplitudes in the resonance region, in particular to the $\Delta$ (1232) and $N^*$ (1440). We obtain a good agreement with the existing threshold data for both charged and neutral pion production. Our predictions also agree well with the results of chiral perturbation theory, except for neutral pion production off the neutron.

Generalized polarizabilities and electroexcitation of the nucleon

Generalized nucleon polarizabilities for virtual photons can be defined in terms of electroproduction cross sections as function of the 4-momentum transfer $Q^2$. In particular, the sum of the generalized electric and magnetic polarizabilities $\Sigma=\alpha+\beta$ and the spin polarizability $\gamma$ can be expressed by virtual photon absorption cross sections integrated over the excitation energy. These quantities have been calculated within the framework of the recently developed unitary isobar model for pion photo- and electroproduction on the proton, which describes the available experimental data up to an excitation energy of about 1 GeV. Our results have been compared to the predicti…

Ground state correlations and the nuclear charge distribution

Combining a sum rule approach and the generator coordinate model we evaluate the influence of ground state correlations on the moments of the radial charge distribution. The isotopic and isotonic differences of the moments come out to be particularly sensitive to fluctuations of the ground state correlations due to changes in the low energy spectrum. A comparison with the experimental results for the isotopes of Ca, Fe, Ni and Zn shows a fair agreement and confirms the importance of the ground state correlations for isotopic and isotonic differences of radial moments.

The Gerasimov-Drell-Hearn Sum Rule and the Spin Structure of the Nucleon

The Gerasimov-Drell-Hearn sum rule is one of several dispersive sum rules that connect the Compton scattering amplitudes to the inclusive photoproduction cross sections of the target under investigation. Being based on such universal principles as causality, unitarity, and gauge invariance, these sum rules provide a unique testing ground to study the internal degrees of freedom that hold the system together. The present article reviews these sum rules for the spin-dependent cross sections of the nucleon by presenting an overview of recent experiments and theoretical approaches. The generalization from real to virtual photons provides a microscope of variable resolution: At small virtuality …

Determination of theE2/M1ratio in theγN→Δ(1232)transition from a simultaneous measurement ofp(γ→,p)π0andp(γ→,π+)n

Tagged linearly polarized photons have been used at the Mainz Microtron (MAMI) for simultaneous measurements of the $p(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},p){\ensuremath{\pi}}^{0}$ and $p(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}},{\ensuremath{\pi}}^{+})n$ reaction channels to study the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\Delta}(1232)$ transition. The energy dependence of the magnetic dipole ${M}_{1+}^{3/2}$ and electric quadrupole ${E}_{1+}^{3/2}$ amplitudes have been extracted from these data in the photon energy range from $270$ to 420 MeV. The $E2/M1$ ratio for the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow…

Compton scattering on the pion and radiative pion photoproduction from the proton

The contribution of the pion polarizabilities to radiative pion photoproduction has been investigated. It has been shown how an extrapolation of future experimental data on radiative pion photoproduction to the pion pole can give information on the polarizabilities of pion.

<‘γ*N→Δtransition form factors: A new analysis of data onp(e,e′p)π0atQ2=2.8and4.0 (GeV/c)2

Recent JLab data of the differential cross section for the reaction ${p(e,e}^{\ensuremath{'}}p){\ensuremath{\pi}}^{0}$ in the invariant mass region of $1.1lWl1.4 \mathrm{GeV}$ at four-momentum transfer squared ${Q}^{2}=2.8$ and $4.0 (\mathrm{GeV}{/c)}^{2}$ are analyzed with two models, both of which give an excellent description of most of the existing pion electroproduction data below $Wl1.5 \mathrm{GeV}.$ We find that at up to ${Q}^{2}=4.0 (\mathrm{GeV}{/c)}^{2},$ the extracted helicity amplitudes ${A}_{3/2}$ and ${A}_{/2}$ remain comparable with each other, implying that hadronic helicity is not conserved at this range of ${Q}^{2}.$ The ratios ${E}_{1+}{/M}_{1+}$ obtained show, starting …

Measurement of the Recoil Polarization in thep(e→,e′p→)π0Reaction at theΔ(1232)Resonance

The recoil proton polarization has been measured in the $p(\stackrel{\ensuremath{\rightarrow}}{e}{,e}^{\ensuremath{'}}\stackrel{\ensuremath{\rightarrow}}{p}){\ensuremath{\pi}}^{0}$ reaction in parallel kinematics around $W\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1232\phantom{\rule{0ex}{0ex}}\mathrm{MeV}$, ${Q}^{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.121\phantom{\rule{0ex}{0ex}}(\mathrm{GeV}/c{)}^{2}$, and $\ensuremath{\epsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.718$ using the polarized cw electron beam of the Mainz Microtron. All three proton polarization components, ${P}_{x}/{P}_{e}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(\ensuremath{-…

Precise pion electroproduction in thep(e, e? ?+)n reaction at W=1125 MeV

The reactione+p →> e+π ++n at c.m. energyW=1125MeV and momentum transfer Q2=0.117GeV2/c2 has been measured. The transverse and longitudinal structure functions have been separated by varying the polarization of the virtual photon (Rosenbluth plot) with a 3 to 4% error. In addition the longitudinal-transverse interference term has been determined measuring the right-left asymmetry with an accuracy of 3%. The experimental data are compared to model calculations, and the sensitivity of the results to the axial and pion formfactors is discussed.

Electromagnetic sum rules for light nuclei

Electromagnetic sum rules describe gross features of the electromagnetic structure of nuclei 1). A well known example is the Thomas-Reiche-Kuhn (TRK) sum rule, which relates the integrated total El-absorption cross section to the ground state expectation value of the double commutator of the dipole operator D with the nuclear Hamiltonian. While the k inet ic energy gives a model independent contr ibut ion, i . e . , the classical sum rule ~cl = 60 NZ/A MeV mb, the nuclear twobody potential gives an additional contr ibution in the presence of exchange and/or momentum dependent (or nonlocal) forces. In this case, I

Quasi-free electron scattering in a relativistic model of the nucleus

Longitudinal and transverse response functions of quasi-free electron scattering have been calculated in mean field approximation for a relativisticσ-ω model, including non-linearities in theσ-field. As a consequence of the completely consistent and fully relativistic treatment of wave functions and current operators, gauge invariance is perfectly satisfied throughout the calculation. The results indicate that models with the same nuclear bulk properties lead to similar response functions within 10%. Our results agree with the experimental data for12C and238U, but cannot describe the longitudinal response in the Ca-Fe region. Predictions for208Pb are given for comparison with future experim…

Isobar excitation in proton-proton bremsstrahlung

Abstract The contribution of intermediate nucleon isobars to proton-proton bremsstrahlung is calculated in a relativistic model. Using conventional coupling constants and form factors for the exchange of π - and ρ-mesons we find that for photon energies ω > 100 MeV isobar excitation increases the cross section markedly over the prediction of soft-photon calculations. Our results agree well with recent experiments at incident proton energy T lab =730 MeV.

On the pion cloud of the nucleon

We evaluate the two--pion contribution to the nucleon electromagnetic form factors by use of dispersion analysis and chiral perturbation theory. After subtraction of the rho--meson component, we calculate the distributions of charge and magnetization in coordinate space, which can be interpreted as the effects of the pion cloud. We find that the charge distribution of this pion cloud effect peaks at distances of about 0.3 fm. Furthermore, we calculate the contribution of the pion cloud to the isovector charges and radii of the nucleon.

The Generalized Gerasimov-Drell-Hearn Integral and the Spin Structure of the Nucleon

The spin structure functions g1 and g2 have been calculated in the resonance region and for small and intermediate momentum transfer. The calculation is based on a gauge-invariant and unitary model for one-pion photo- and electroproduction. The predictions of the model agree with the asymmetries and the spin sturcture functions recently measured at SLAC, and the first moments of the calculated spin structure functions fullfil the Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules within an error of typically 5-10 %.

Baryon resonance analysis from MAID

The unitary isobar model MAID2007 has been used to analyze the recent data of pion electroproduction. The model contains all four-star resonances in the region below W=2 GeV and both single-Q^2 and Q^2 dependent transition form factors could be obtained for the Delta, Roper, D13(1520), S11(1535), S31(1620), S11(1650), D15(1675), F15(1680) and P13(1720). From the complete world data base, including also pi- data on the neutron, also Q^2 dependent neutron form factors are obtained. For all transition form factors we also give convenient numerical parameterizations that can be used in other reactions. Furthermore, we show how the transition form factors can be used to obtain empirical transver…

Electromagnetic investigations of nucleon resonances and sum rules

Abstract Pion photoproduction is analyzed by dispersion relations at fixed t . The results for s-wave production at threshold and p-wave production in the Δ(1232) resonance region are compared to the experimental data. These investigations are extended to the case of pion electroproduction in the framework of the Unitary Isobar Model. Recent developments to explore the spin structure of the nucleon by double-polarization observables are summarized, and new results for the spin polarizability, the Gerasimov-Drell-Hearn and related sum rules are presented.

Higher Order Polarizabilities of the Proton

Compton scattering results are used to probe proton structure via measurement of higher order polarizabilities. Values for $\alpha_{E2}^p,\beta_{E2}^p,\alpha_{E\nu}^p,$ $\beta_{E\nu}^p$ determined via dispersion relations are compared to predictions based upon chiral symmetry and from the constituent quark model. Extensions to spin-polarizabilities are also discussed.

A two-center-oscillator-basis as an alternative set for heavy ion processes

The two-center-oscillator-basis, which is constructed from harmonic oscillator wave functions developing about two different centers, suffers from numerical problems at small center separations due to the overcompleteness of the set. In order to overcome these problems we admix higher oscillator wave functions before the orthogonalization, or antisymmetrization resp. This yields a numerically stable basis set at each center separation. The results obtained for the potential energy surface are comparable with the results of more elaborate models.

Nucleon strangeness and unitarity

The strange-quark vector current form factors of the nucleon are analyzed within the framework of dispersion relations. Particular attention is paid to contributions made by $K\bar{K}$ intermediate states to the form factor spectral functions. It is shown that, when the $K\bar{K}\to N\bar{N}$ amplitude is evaluated in the Born approximation, the $K\bar{K}$ contributions are identical to those arising from a one-loop calculation and entail a serious violation of unitarity. The mean square strangeness radius and magnetic moment are evaluated by imposing unitarity bounds on the kaon-nucleon partial wave amplitudes. The impact of including the kaon's form factor in the dispersion integrals is a…

Dispersion theoretical analysis of the nucleon spin polarizabilities

The spin polarizabilities of the nucleon have been calculated from pion photoproduction data using forward dispersion relations. The feasibility of an experimental determination of these structure constants is discussed by focusing on polarization observables of the reaction \( \vec{\gamma }\vec{p} \to \gamma p \)→ γ p.

Analysis of eta production using a generalized Lee model

We have investigated the processes N($\pi$, $\pi$)N and N($\pi$, $\eta$)N close to eta threshold using a simple, nonrelativistic Lee model which has the advantage of being analytically solvable. It is then possible to study the Riemann sheets of the S-matrix and the behavior of its resonance poles especially close to threshold. A theoretical simulation of the experimental cusp effect at eta threshold leads to a characteristic distribution of poles on the Riemann sheets. We find a pole located in the $4^{th}$ Riemann sheet that up to now has not been discussed. It belongs to the cusp peak at eta threshold. In addition we obtain the surprising result using the Lee model that the resonance $S_…

Dispersion relation analysis of neutral pion photoproduction and electroproduction at threshold

Neutral pion photoproduction and electroproduction at threshold is analyzed in the framework of dispersion relations. For this purpose, we evaluate the real threshold amplitudes in terms of Born contributions and dispersion integrals determined by the imaginary parts of the multipoles of the unitary isobar model (MAID) and the phenomenological partial-wave analysis (SAID). The results show considerable cancellations between Born terms and resonance contributions. Good agreement with the data is found for photoproduction. While our dispersion analysis suggests considerable discrepancies for electroproduction, the present state of the experimental multipole analysis at finite ${Q}^{2}$ does n…

Multipole analysis of pion photoproduction based on fixed t dispersion relations and unitarity

We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelishvili. The free parameters were determined by a fit to the most recent data for \pi^{+} and \pi^{0} production on the proton as well as \pi^{-} production on the neutron, in the energy We have analysed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnes and Muskhelis…

Dispersion relations and the spin polarizabilities of the nucleon

A forward dispersion calculation is implemented for the spin polarizabilities $\gamma_1, ... ,\gamma_4$ of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at ${\cal O}(\omega^3)$. In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory.

Recent results from the MAID and Dubna-Mainz-Taipei PWA analysis

The unitary isobar model MAID2007 has been developed to analyze the world data of pion photo- and electroproduction. The model contains both a common background and several resonance terms. The background is unitarized according to the K-matrix prescription, and the 13 four-star resonances with masses below 2 GeV are described by appropriately unitarized Breit-Wigner forms. The data have been analyzed by both single-energy and global fits, and the transverse and longitudinal helicity amplitudes have been extracted for the four-star resonances below 2 GeV. Because of its inherent simplicity, MAID2007 is well adopted for predictions and analysis of the observables in pion photo- and electropr…

Generalized polarizabilities of the nucleon in chiral effective theories

Using the techniques of chiral effective field theories we evaluate the so called generalized polarizabilities of the nucleon, which characterize the structure dependent components in virtual Compton scattering (VCS) as probed in the electron scattering reaction e N \to e' N gamma. Results are given for both spin-dependent and spin-independent structure effects to O(p^3) in SU(2) Heavy Baryon Chiral Perturbation Theory and to O(epsilon^3) in the SU(2) Small Scale Expansion. Finally we compare our calculations with results from the pioneering VCS experiment on the proton from Mainz.

Nucleon resonances inπNscattering up to energiess⩽2.0GeV

A meson-exchange model for pion-nucleon scattering was previously constructed using a three-dimensional reduction scheme of the Bethe-Salpeter equation for a model Lagrangian involving $\ensuremath{\pi},\ensuremath{\eta},N,\ensuremath{\Delta},\ensuremath{\rho}$, and \ensuremath{\sigma} fields. We thereby extend our previous work by including the $\ensuremath{\eta}N$ channel and all the $\ensuremath{\pi}N$ resonances with masses $~2$ GeV, up to the $F$ waves. The effects of the $\ensuremath{\pi}\ensuremath{\pi}N$ channels are taken into account by introducing an effective width in the resonance propagators. The extended model gives an excellent fit to both $\ensuremath{\pi}N$ phase shifts an…

An isobar model for eta photo- and electroproduction on the nucleon

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 extract very small (<0.1%) N* --> eta N decay branching ratios of the D13(1520) and F15(1680) res…

Proton spin polarizabilities from polarized Compton scattering

Polarized Compton scattering off the proton is studied within the framework of subtracted dispersion relations for photon energies up to 300 MeV. As a guideline for forthcoming experiments, we focus the attention on the role of the proton's spin polarizabilities and investigate the most favorable conditions to extract them with a minimum of model dependence. We conclude that a complete separation of the four spin polarizabilities is possible, at photon energies between threshold and the $\Delta(1232)$ region, provided one can achieve polarization measurements with an accuracy of a few percent.

Parity violating pion electroproduction off the nucleon

Parity violating (PV) contributions due to interference between $\gamma$ and $Z^0$ exchange are calculated for pion electroproduction off the nucleon. A phenomenological model with effective Lagrangians is used to determine the resulting asymmetry for the energy region between threshold and $\Delta(1232)$ resonance. The $\Delta$ resonance is treated as a Rarita-Schwinger field with phenomenological $N \Delta$ transition currents. The background contributions are given by the usual Born terms using the pseudovector $\pi N$ Lagrangian. Numerical results for the asymmetry are presented.

Structure analysis of the virtual Compton scattering amplitude at low energies

We analyze virtual Compton scattering off the nucleon at low energies in a covariant, model-independent formalism. We define a set of invariant functions which, once the irregular nucleon pole terms have been subtracted in a gauge-invariant fashion, is free of poles and kinematical zeros. The covariant treatment naturally allows one to implement the constraints due to Lorentz and gauge invariance, crossing symmetry, and the discrete symmetries. In particular, when applied to the $ep\to e'p'\gamma$ reaction, charge-conjugation symmetry in combination with nucleon crossing generates four relations among the ten originally proposed generalized polarizabilities of the nucleon.

Third and fourth S11 resonances in pion scattering and pion photoproduction

Abstract A self-consistent analysis of pion scattering and pion photoproduction within a coupled channels dynamical model is presented. The results indicate the existence of a third and a fourth S11 resonance with the masses 1803 ± 7 and 2117 ± 64 MeV.

Generalized polarizabilities of the proton in a constituent quark model revisited

We study low-energy virtual Compton scattering off the proton within the framework of a nonrelativistic constituent quark model. The Compton tensor is divided into two separately gauge-invariant contributions. The first consists of the groundstate propagation in the direct and crossed channels together with an appropriately chosen term to satisfy gauge invariance. The residual part contains the relevant structure information characterized by the so-called generalized polarizabilities. We discuss two different schemes to obtain the generalized polarizabilities from the residual term. Explicit predictions for the generalized polarizabilities are presented for the Isgur-Karl model. Our results…

Magnetic dipole moment of theΔ+(1232)from theγp→γπ0preaction

The $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\gamma}{\ensuremath{\pi}}^{0}p$ reaction in the $\ensuremath{\Delta}(1232)$-resonance region is investigated as a method to access the ${\ensuremath{\Delta}}^{+}(1232)$ magnetic dipole moment. The calculations are performed within the context of an effective Lagrangian model containing both the $\ensuremath{\Delta}$-resonant mechanism and a background of nonresonant contributions to the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\gamma}{\ensuremath{\pi}}^{0}p$ reaction. Results are shown both for existing and forthcoming $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\…

Gerasimov-Drell-Hearn sum rule and related integrals

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.

Electroproduction of hyperons

Abstract We present some estimates for the reaction ep → e ′ Σ + . At small scattering angles, the differential cross section is completely determined by the experimental data for the radiative decay Σ + → pγ . For kinematical values typical of the proposed parity experiment at MAMI, we find a suppression factor of about 5 · 10 −15 as compared to elastic electron scattering. On the basis of conservative models for the transition form factors, this ratio might increase by about a factor of 20 at backward angles. Even higher values could be expected if the presently unknown convection currents should turn out to be large. Due to the parity violation involved in this process, we also expect a …

Dispersion relations in real and virtual Compton scattering

A unified presentation is given on the use of dispersion relations in the real and virtual Compton scattering processes off the nucleon. The way in which dispersion relations for Compton scattering amplitudes establish connections between low energy nucleon structure quantities, such as polarizabilities or anomalous magnetic moments, and the nucleon excitation spectrum is reviewed. We discuss various sum rules for forward real and virtual Compton scattering, such as the Gerasimov-Drell-Hearn sum rule and its generalizations, the Burkhardt-Cottingham sum rule, as well as sum rules for forward nucleon polarizabilities, and review their experimental status. Subsequently, we address the general…

Higher order forward spin polarizability

As a guideline for future experiments to extract the four (leading) spin polarizabilities of the nucleon, we have constructed the forward amplitude for polarized Compton scattering by dispersion integrals. These integrals have been saturated by recently measured helicity-dependent photoabsorption cross sections as well as predictions for pion photoproduction multipoles from several phenomenological descriptions and chiral perturbation theory. The comparison of these results corroborates the strategy to extract the spin polarizabilities by fitting them to polarized Compton data and fixing all higher order spin effects by dispersion relations based on pion photoproduction multipoles.

Hadron structure at lowQ2

This review deals with the structure of hadrons, strongly interacting many-body systems consisting of quarks and gluons. These systems have a size of about 1 fm, which shows up in scattering experiments at low momentum transfers $Q$ in the GeV region. At this scale the running coupling constant of Quantum Chromodynamics (QCD), the established theory of the strong interactions, becomes divergent. It is therefore highly intriguing to explore this theory in the realm of its strong interaction regime. However, the quarks and gluons can not be resolved at the GeV scale but have to be studied through their manifestations in the bound many-body systems, for instance pions, nucleons and their reson…

Dispersion relation formalism for virtual Compton scattering and the generalized polarizabilities of the nucleon

A dispersion relation formalism for the virtual Compton scattering (VCS) reaction on the proton is presented, which for the first time allows a dispersive evaluation of 4 generalized polarizabilities at a four-momentum transfer $Q^2 \leq$ 0.5 GeV$^2$. The dispersive integrals are calculated using a state-of-the-art pion photo- and electroproduction analysis. The dispersion formalism provides a new tool to analyze VCS experiments above pion threshold, thus increasing the sensitivity to the generalized polarizabilities of the nucleon.

Rare decay η→ππγγ in chiral perturbation theory

We investigate the rare radiative {eta} decay modes {eta}{r_arrow}{pi}{sup +}{pi}{sup {minus}}{gamma}{gamma} and {eta}{r_arrow}{pi}{sup 0}{pi}{sup 0}{gamma}{gamma} within the framework of chiral perturbation theory at {ital O}({ital p}{sup 4}). We present photon spectra and partial decay rates for both processes as well as a Dalitz contour plot for the charged decay. {copyright} {ital 1996 The American Physical Society.}

The polarizability of the pion: no conflict between dispersion theory and chiral perturbation theory

Recent attempts to determine the pion polarizability by dispersion relations yield values that disagree with the predictions of chiral perturbation theory. These dispersion relations are based on specific forms for the absorptive part of the Compton amplitudes. The analytic properties of these forms are examined, and the strong enhancement of intermediate-meson contributions is shown to be connected with spurious singularities. If the basic requirements of dispersion relations are taken into account, the results of dispersion theory and effective field theory are not inconsistent.

Reggeized model forηandη′photoproduction

A Reggeized model for $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$ photoproduction on the nucleon is presented. In this model, $t$-channel vector meson exchanges are described in terms of Regge trajectories to comply with the correct high energy behavior. We compare this Reggeized model with an isobar model ($\ensuremath{\eta}$-MAID), where the $t$-channel exchanges are described by $\ensuremath{\rho}$ and $\ensuremath{\omega}$ poles. Both models contain the same resonance contributions, and describe current $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\eta}p$ data up to ${E}_{\ensuremath{\gamma}}^{\text{lab}}=2\phantom{\rule{0.3em}{0ex}}\text{GeV}$ quite well,…

Baryon Properties with Three-Quark Forces

The Constituent Quark Model (CQM) is very useful for the description of many baryon properties, leading to a fair agreement with the experimental data, especially in the case of the baryon spectrum 1) and of the electromagnetic processes involving baryons2,3). The model is based on a non relativistic QCD-inspired dynamics, which includes a confinement potential and a spin-dependent short-range part, the so called hyperfine interaction4,1). The confinement potential contains as its major part a harmonic oscillator (h.o.) interaction, which has however a too degenerate spectrum with respect to the experimental one and leads to an unreasonable damping of the form factors even at moderate momen…

Reply to “Comment on ‘Polarizability of the pion: No conflict between dispersion theory and chiral perturbation theory’”

We show that the alleged discrepancies between chiral perturbation theory (ChPT) and dispersion theory, reported for the polarizability of the pion by Fil'kov and Kashevarov [Phys. Rev. C 72, 035211 (2005)], result from applying dispersion theory to nonanalytic functions.

Excitation of S11 resonances in pion scattering and pion photoproduction on the proton

A self-consistent analysis of pion scattering and pion photoproduction within a coupled channels dynamical model is presented. In the case of pion photoproduction, we obtain background contributions to the imaginary part of the S-wave multipole which differ considerably from the result based on the K-matrix approximation. Within the dynamical model these background contributions become large and negative in the region of the S_{11}(1535) resonance. Due to this fact much larger resonance contributions are required in order to explain the results of the recent multipole analyses. For the first S_{11}(1535) resonance we obtain as a value of the dressed electromagnetic helicity amplitude: A_{1/…

Photoproduction of delta and Roper resonances in the cloudy bag model.

The photoproduction of delta and Roper resonances has been calculated within the framework of the cloudy bag model. Two alternative formulations, the original pseudoscalar surface coupling and the pseudovector volume coupling of pions, have been used, and the results are compared. The helicity amplitudes are in fair agreement with experimental data, the prediction for the small ${E}_{1+}$/${M}_{1+}$ ratio for delta production is -1.8% for a bag radius of 1 fm and pseudovector coupling.

Photoproduction of the hypertriton

In the framework of the impulse approximation we study the photoproduction of the hypertriton $^3_{\Lambda}$H by using realistic $^3$He wave functions obtained as solutions of Faddeev equations with the Reid soft-core potential for different $^3_{\Lambda}$H wave functions. We obtain relatively small cross sections of the order of 1 nb. We also find that the influence of Fermi motion is important, while the effect of different off-shell assumptions on the cross section is not too significant.

Dispersion relation formalism for virtual Compton scattering of the proton

We present in detail a dispersion relation formalism for virtual Compton scattering (VCS) off the proton from threshold into the $\Delta(1232)$-resonance region. Such a formalism can be used as a tool to extract the generalized polarizabilities of the proton from both unpolarized and polarized VCS observables over a larger energy range. We present calculations for existing and forthcoming VCS experiments and demonstrate that the VCS observables in the energy region between pion production threshold and the $\Delta(1232)$-resonance show an enhanced sensitivity to the generalized polarizabilities.

Non-adiabatic treatment of fission mass distribution

The influence of dynamical corrections to fission mass yields has been studied within the frame work of the macroscopic-microscopic approach and solving the time-dependent Schrodinger equation for the asymmetry degree of freedom, treating the fragment separation classically. The results indicate that the actual motion lies in between the adiabatic and sudden approximations. In particular the dynamic effects tend to increase considerably the probability for symmetric fission as compared to the static case.

Analysis of resonance multipoles from polarization observables in eta photoproduction

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 state. The new GRAAL photon asymmetry data at higher energy show a clear signal of the F15(1680) exci…

First measurement of the helicity-dependent γ p↦pη differential cross-section

The helicity dependence of the (γ) over right arrow(p) over right arrow -+ peta reaction has been measured for the first time at a center-of-mass angle theta(eta)*= 70degrees in the photon energy range from 780 MeV to 790 MeV. The experiment, performed at the Mainz microtron MAMI, used a 4pi-detector system, a circularly polarized, tagged photon beam. and a longitudinally polarized frozen-spin target. The helicity 3/2 cross-section is found to be small and the results for helicity 1/2 agree with predictions from the MAID analysis.

A unitary isobar model for pion photo- and electroproduction on the proton up to 1 GeV

A new operator for pion photo- and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances ($P_{33}(1232)$, $P_{11}(1440)$, $D_{13}(1520)$, $S_{11}(1535)$, $F_{15}(1680)$, and $D_{33}(1700)$). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The $Q^2$ dependence of electromagnetic resonance vertices is described with appropriate form factors in the electromagnetic helicity amplitudes. Within this model we have obtained good agreement with the experimental data for pion photo- and elect…

Photoproduction of neutral pions and low energy theorems

Magnetic moment of the S11 (1535) resonance

Abstract The γ p a γη p reaction in the S 11 (1535) resonance region is investigated as a method to access the S 11 (1535) magnetic dipole moment. To study the feasibility, we perform calculations of the γ p → γη p process within an effective Lagrangian approach containing both the S 11 resonant mecanism and a background of non-resonant contributions. Predictions are made for the forthcoming experiments. In particular, we focus on the sensitivity of cross sections and photon asymmetries to the S 11 (1535) magnetic dipole moment.

Three-body forces in the quark model

The constituent quark model has been very useful for the description of many physical properties of baryons, achieving in most cases a fair agreement with the experimental data 1 The model is based on a non relativistic QCD-inspired dynamics including a harmonic oscillator (h.o.) confinement potential and a spin dependent (hyperfine) interaction. The use of Lovelace coordinates p, ~ avoides any problem with the center of mass motion, while the h.o. potential provides a simple basis for ana ly t ica l calculations, which is a very important feature for many applications, like the evaluation of form factors and Meson Exchange Currents 2. On the other hand the h.o. spectrum is too degenerate w…

Working group on hadron polarizabilities and form factors

Photo- and electroproduction of eta mesons

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 resonances beyond the dominant $S_{11}$(1535) resonance.

Polarized structure functions of the nucleon in the resonance region

Abstract We present predictions for the spin structure functions of the proton in the framework of a unitary isobar model for one-pion photo- and electroproduction. Our results are compared with recent experimental data from SLAC. The first moments of the calculated structure functions fullfil the Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules within an error of typically 5–10%.

The influence of a bag deformation on N-N-scattering

We present a model calculation to study the influence of an intrinsic nucleon deformation on the elastic scattering of nucleons. The nucleons are visualized as deformed sources for the exchange of bosons. Both static changes in the derived OBEP and the admixtures of rotational states give rise to only small effects even for large bag deformation, in addition, the two contributions tend to cancel each other.

Threshold π0 photo- and electro-production in a meson-exchange model

We show that, within a meson-exchange dynamical model describing well most of the existing pion electromagnetic production data up to the second resonance region, one is also able to obtain a good agreement with the pi^0 photo- and electroproduction data near threshold. In the case of pi^0 production, the effects of final state interaction in the threshold region are nearly saturated by single charge exchange rescattering. This indicates that in ChPT, it might be sufficient to carry out the calculation just up to one-loop diagrams for threshold neutral pion production.

Pion Photo- and Electroproduction on the Proton

Using a unitary isobar model a new operator for pion photo- and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances (P 33(1232), P 11(1440), D 13(1520), S 11(1535), F 15(1680), and D 33(1700)). Within this model we have obtained good agreement with the experimental data for pion photo- and electroproduction on the nucleon for both differential cross sections and polarization observables.

A model study of Hartree-Fock and Linear Response in coordinate space

A fast procedure for spherical Hartree-Fock is obtained by coordinate space representation and a modification of gradient iteration. Along similar lines, the corresponding Linear Response equations are derived and solved, in order to achieve a fully consistent treatment. The Linear Response equations are applied to a change in particle numbers, i.e. to the description of isotopic differences. In a model study we look for their physical and numerical properties, i.e. linearity of the response, numerical stability and consistency requirements for the Hartree-Fock basis.

Measurement of the Beam-Helicity Asymmetry in thep(e→,e′p)π0Reaction at the Energy of theΔ(1232)Resonance

In a p((e) over right arrow, e' p)pi(0) out-of-plane coincidence experiment at the three-spectrometer setup of the Mainz Microtron MAMI, the beam-helicity asymmetry has been precisely measured around the energy of the Delta(1232) resonance and Q(2) = 0.2(GeV/c)(2). The results are in disagreement with three up-to-date model calculations. This is interpreted as a lack of understanding of the nonresonant background, which in dynamical models is related to the pion cloud.

Generalized polarizabilities of the pion in chiral perturbation theory

We present a calculation of the virtual Compton scattering amplitude for $\gamma^\ast+\pi\to \gamma+\pi$ in the framework of chiral perturbation theory at ${\cal O}(p^4)$. We explicitly derive expressions for generalized electromagnetic polarizabilities and discuss alternative definitions of these quantities.

Radiative Pion Photoproduction from the Proton and π + Meson Polarizabilities

We study the possibility of investigating radiative pion photoproduction from the proton at the microtron MAMI-B with the aim to obtain an experimental information about the π + meson polarizabilities. It is shown that an exposition time of about 30 days will allow to determine the π + meson polarizability with quite high accuracy.

Electromagnetic Production of the Hypertriton

Kaon photoproduction on He3, gamma + He3 --> K+ + Hypertriton, is studied in the framework of the impulse approximation. Realistic He3 wave functions obtained as solutions of Faddeev equations with the Reid soft-core potential are used along with different Hypertriton wave functions. Results are compared for several elementary operator models, which can successfully describe the elementary kaon production off the proton up to a photon lab energy of k = 2.2 GeV. It is found that the corresponding cross sections are small, of the order of several nanobarns. It is also shown that the influence of Fermi motion is important, while the effect of different off-shell assumptions on the cross sec…

Variable masses in fission and heavy-ion collisions

With the use of the cranking formula, the coordinate-dependent mass parameters of the kinetic-energy operator in fission processes and heavy-ion collisions are calculated in the two-center oscillator model. It is shown that the reduced mass and also the classical moment of inertia are obtained for large separations of the fragments. For small separations, however, the mass parameter for the motion of the centers of mass of the fragments is larger than the reduced mass by an order of magnitude.

Threshold Electroproduction of Charged Pions from Light Nuclei

Double-differential cross sections for the electroproduction of pions of both charges have been measured. We compare the data obtained for production near threshold from $^{12}\mathrm{C}$ and $^{16}\mathrm{O}$ with theoretical treatments employing both shell-model and sum-rule nuclear descriptions with full inclusion of the final-state interaction.

Unitary model for theγp→γπ0preaction and the magnetic dipole moment of theΔ+(1232)

Radiative pion photoproduction in the $\ensuremath{\Delta}(1232)$-resonance region is studied with the aim of accessing the ${\ensuremath{\Delta}}^{+}(1232)$ magnetic dipole moment. We present a unitary model of the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}N$ ($\ensuremath{\pi}N={\ensuremath{\pi}}^{0}p,\phantom{\rule{0.6em}{0ex}}{\ensuremath{\pi}}^{+}n$) reactions, where the $\ensuremath{\pi}N$ rescattering is included in an onshell approximation. In this model, the low-energy theorem which couples the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\pi}N$ process in the limit of a soft final photon to the $\ensuremath{\gamm…

S11 RESONANCES IN A COUPLED-CHANNEL DYNAMICAL MODEL

A self-consistent analysis of pion scattering and pion photoproduction within a coupled channels dynamical model is presented. The results indicate the existence of a third and a fourth S11 resonance with the masses 1846±47 and 2113±70 MeV . In the case of pion photoproduction, we found that background contributions to the imaginary part of the S-wave multipole become large and negative in the region of the S11(1535) resonance. Due to this fact, much larger resonance contributions are required in order to explain the results of the recent multipole analysis. For the first S11(1535) resonance we obtain a value of 72±2×10-3 GeV -1/2 for the electromagnetic helicity amplitude A1/2.

Effects of wave function correlations on scaling violation in quasi-free electron scattering

Abstract The scaling law in quasi-free electron scattering is broken due to the existence of exchange forces, leading to a finite mean value of the scaling variable y . This effect is considerably increased by wave function correlations, in particular by tensor correlations, similar to the case of the photonuclear enhancement factor κ.

Electron-nucleus interactions (Part 1)