Regge phenomenology in π0 and η photoproduction

The $\ensuremath{\gamma}N\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}N$ and $\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\eta}N$ reactions at photon beam energies above 4 GeV are investigated within Regge models. The models include $t$-channel exchanges of vector ($\ensuremath{\rho}$ and $\ensuremath{\omega}$) and axial-vector (${b}_{1}$ and ${h}_{1}$) mesons. Moreover, Regge cuts of $\ensuremath{\rho}\mathbb{P},\phantom{\rule{0.28em}{0ex}}\ensuremath{\rho}{f}_{2},\phantom{\rule{0.28em}{0ex}}\ensuremath{\omega}\mathbb{P}$, and $\ensuremath{\omega}{f}_{2}$ are investigated. A good description of differential cross sections and polarization observables at photon beam energies fr…

Measurement of the decay η′→π0π0η at MAMI

An experimental study of the eta' -> pi(0)pi(0)eta -> 6 gamma decay has been conducted with the best up-to-date statistical accuracy, by measuring. 0 mesons produced in the gamma p -> eta'p reaction with the A2 tagged-photon facility at the Mainz Microtron, MAMI. The results obtained for the standard parametrization of the eta' -> pi(0)pi(0)eta matrix element are consistent with the most recent results for eta' -> pi pi eta decays, but have smaller uncertainties. The available statistics and experimental resolution allowed, for the first time, an observation of a structure below the pi(+)pi(-) thorn p-mass threshold, the magnitude and sign of which, checked within the framewo…

Electromagnetic transition form factors of the Roper resonance in a phenomenological field theory

We analyze the form factors of the electromagnetic nucleon-to-Roper-resonance transition in the framework of a low-energy phenomenological field theory. A systematic power-counting procedure is generated by applying the complex-mass scheme. Within this power counting we calculate the form factors to next-to-next-to-leading order and fit the results to empirical data.

Compton scattering off nucleons near threshold

The energy dependence of the magnetic polarizability β has been evaluated by use of the delta resonance in the s- and u-channel of the Compton scattering amplitude. It was the idea to extract the influence of higher order terms (higher than ω2, ω = |k| being the photon energy) in the analysis of the polarizability. The static paramagnetic polarizability βPara(0) has been substituted by an energy dependent βδPara(k) and the result is compared with experimental data.

Vector form factor of the pion in chiral effective field theory

The vector form factor of the pion is calculated in the framework of chiral effective field theory with vector mesons included as dynamical degrees of freedom. To construct an effective field theory with a consistent power counting, the complex-mass scheme is applied.

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…

Electromagnetic transition form factors of the Roper resonance in effective field theory

We analyze the form factors of the electromagnetic nucleon-to-Roper-resonance transition in the framework of low-energy effective field theory. A systematic power-counting procedure is generated by applying the complex-mass scheme. Within this power counting we calculate the form factors to next-to-next-to-leading order and fit the results to empirical data.

Review of Particle Physics

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,143 new measurements from 709 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, …

Two-body Mechanisms in Pion Scattering and Pion Photoproduction on the Trinucleon

A breakdown of the Impulse Approximation is studied in pion photoproduction and pion charge exchange on 3He at high momentum transfers. The usual DWIA formalism with Faddeev wave functions which works well for small momentum transfers deviates from experimental measurements by up to two orders of magnitude for Q 2 > 6 fm−2. It is found that the explicit inclusion of two-body mechanisms, where the photon or pion is absorbed on one nucleon and the pion is emitted from another nucleon removes most of the disagreement with the data.

Accurate Test of Chiral Dynamics in the \boldmath$\vec{\gamma} p \rightarrow \pi^0p$ Reaction

A precision measurement of the differential cross sections $d\sigma/d\Omega$ and the linearly polarized photon asymmetry $\Sigma \equiv (d\sigma_\perp - d\sigma_\parallel) \slash (d\sigma_\perp + d\sigma_\parallel)$ for the $\vec{\gamma} p \rightarrow \pi^0p$ reaction in the near-threshold region has been performed with a tagged photon beam and almost $4\pi$ detector at the Mainz Microtron. The Glasgow-Mainz photon tagging facility along with the Crystal Ball/TAPS multi-photon detector system and a cryogenic liquid hydrogen target were used. These data allowed for a precise determination of the energy dependence of the real parts of the $S$- and all three $P$-wave amplitudes for the first t…

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.

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 %.

Pion interaction with the trinucleon up to the eta production threshold

Pion elastic, charge exchange scattering and induced eta production on the trinucleon systems are investigated in a coupled-channels approach in momentum space with Fadeev wave functions. The channel $\pi N \rightarrow \eta N$ is included using an isobar model with S-, P-, and D-wave resonances. While the coherent reactions like $^3$He($\pi,\pi)^3$He can be reasonably well reproduced up to $T_{\pi}$=500 MeV, large discrepancies appear for the incoherent processes, $^3$He($\pi^-,\pi^0)^3$H and $^3$He($\pi^-,\eta)^3$H at backward angles and energies above $\Delta$-resonance. In the forward direction the $(\pi,\eta)$ calculations underestimate the experimental measurements very close to thresh…

Asymmetries in elastic scattering of 100 MeVπ+from a polarizedHe3target

We report the observation of a large asymmetry in the elastic scattering of 100 MeV {pi}{sup +} from a polarized {sup 3}He target. Measurements have been made at laboratory angles of 60{degree}, 80{degree}, and 100{degree}, with the largest value {ital A}{sub {ital y}}=0.89{plus minus}0.12 occurring at 80{degree}, near a cross-section minimum. This asymmetry is the largest observed to date in pion scattering from a spin-1/2 nucleus. The {ital A}{sub {ital y}} data are qualitatively reproduced by a schematic model; however, agreement with the data is significantly improved when realistic three-body Faddeev wave functions and a full nonlocal distorted-wave impulse approximation reaction model…

Exact PWBA virtual photon spectrum for a(γv, D)R

Baryon transition form factors at the pole

Electromagnetic resonance properties are uniquely defined at the pole and do not depend on the separation of the resonance from background or the decay channel. Photon-nucleon branching ratios are nowadays often quoted at the pole, and we generalize the considerations to the case of virtual photons. We derive and compare relations for nucleon to baryon transition form factors both for the Breit-Wigner and the pole positions. Using the MAID2007 and SAID SM08 partial wave analyses of pion electroproduction data, we compare the $G_M$, $G_E$, and $G_C$ form factors for the $\Delta(1232)$ resonance excitation at the Breit-Wigner resonance and pole positions up to $Q^2=5$ GeV$^2$. We also explore…

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…

New Insights into the Coupling of $\eta $ and $f_1$ Mesons to the Nucleon

We show that the contact couplings of neutral pseudoscalar and axial mesons to the nucleon are proportional to $\Delta s$, the fraction of nucleon spin carried by the strange quark sea, and thus are strongly suppressed relative to the couplings of charged mesons to the nucleon. On the other side, recent high accuracy data on $\eta $ photoproduction at threshold reveal the need for non--negligibile $\eta NN$ vertices, while fitting $\bar N N$ phase shifts by means of effective meson exchange potentials requires a substantial presence of $f_1$ mesons there. We here advocate the idea to attribute the couplings of neutral pseudoscalar and axial vector mesons to effective triangular diagrams con…

Study of $\eta$ and $\eta'$ photoproduction at MAMI

The reactions $\gamma p\to \eta p$ and $\gamma p\to \eta' p$ have been measured from their thresholds up to the center-of-mass energy $W=1.96$GeV with the tagged-photon facilities at the Mainz Microtron, MAMI. Differential cross sections were obtained with unprecedented accuracy, providing fine energy binning and full production-angle coverage. A strong cusp is observed in the total cross section and excitation functions for $\eta$ photoproduction at the energies in vicinity of the $\eta'$ threshold, $W=1896$MeV ($E_\gamma=1447$MeV). This behavior is explained in a revised $\eta$MAID isobar model by a significant branching of the $N(1895)1/2^-$ nucleon resonance to both, $\eta p$ and $\eta'…

Pion photoproduction on3He including final-state interaction

Coherent π0 and π+ photoproduction and elastic and charge-exchange pion scattering on3He has ben calculated in a consistent model. Realistic three-body Faddeev wave functions have been used and full nonlocal DWIA results for pion photoproduction are obtained. Furthermore, two-step processes such as3He(γ, π0)3He(π0, π+)3H are included giving rise to unexpected large results. The comparison with experimental data is very good over a wide range of photon energies and nuclear momentum transfers. A long-time discrepancy between previous impulse-approximation calculations and experimental data has been removed.

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…

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…

Photo- and Electroproduction of Eta Mesons on Nucleons and Nuclei

Eta photo- and electroproduction off the nucleon is investigated in an approach that contains Born terms, vector meson and nucleon resonance contributions. In a comparison with the new Mainz data we find a large sensitivity on the elementary ηN N coupling. Our analysis results in a pseudoscalar ηN N coupling with a coupling constant of g ηN N 2 /4π=0.4. Furthermore, we also study coincidence cross sections for eta electroproduction and present calculations for structure functions and kinematical conditions that are most sensitive to the S 11(1535) and the D 13(1520) resonances. Finally, we show results on the inclusive eta photoproduction off complex nuclei with a very good agreement with r…

Single-energy partial wave analysis for pion photoproduction with fixed-t analyticity

Experimental data for pion photoproduction including differential cross sections and various polarization observables from four reaction channels, $\gamma p \to \pi^0 p$, $\gamma p \to \pi^+n$, $\gamma n \to \pi^- p$ and $\gamma n \to \pi^0 n$ from threshold up to $W=2.2$ GeV have been used in order to perform a single-energy partial wave analysis with minimal model dependence by imposing constraints from unitarity and fixed-$t$ analyticity in an iterative procedure. Reaction models were only used as starting point in the very first iteration. We demonstrate that with this procedure partial wave amplitudes can be obtained which show only a minimal dependence on the initial model assumptions…

Measurement ofN14(γ, π+)C14(g.s.)at 200 MeV: A Test of the Distorted-Wave Impulse Approximation for Charged-Pion Photoproduction below theΔ(1232)Resonance

Differential cross sections for $^{14}\mathrm{N}(\ensuremath{\gamma}, {\ensuremath{\pi}}^{+})^{14}\mathrm{C}(\mathrm{g}.\mathrm{s}.)$ (${0}^{+}$1) have been measured for an incident photon energy ${E}_{\ensuremath{\gamma}}=200$ MeV at laboratory angles of 45\ifmmode^\circ\else\textdegree\fi{}, 60\ifmmode^\circ\else\textdegree\fi{}, 75\ifmmode^\circ\else\textdegree\fi{}, 90\ifmmode^\circ\else\textdegree\fi{}, 120\ifmmode^\circ\else\textdegree\fi{}, and 140\ifmmode^\circ\else\textdegree\fi{}. Momentum-space distorted-wave-impulse-approximation calculations, using a complete treatment of a one-body pion-photoproduction operator, are found to be in excellent agreement with the experimental data…

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.

Accurate Test of Chiral Dynamics in theγ→p→π0pReaction

A precision measurement of the differential cross sections dσ/dΩ and the linearly polarized photon asymmetry Σ≡(dσ⊥-dσ∥)/(dσ⊥+dσ∥) for the γp→π0p reaction in the near-threshold region has been performed with a tagged photon beam and almost 4π detector at the Mainz Microtron. The Glasgow-Mainz photon tagging facility along with the Crystal Ball/TAPS multiphoton detector system and a cryogenic liquid hydrogen target were used. These data allowed for a precise determination of the energy dependence of the real parts of the S- and all three P-wave amplitudes for the first time and provide the most stringent test to date of the predictions of chiral perturbation theory and its energy region of a…

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.

Study of eta and eta' Photoproduction at MAMI

The reactions γp→ηp and γp→η′p are measured from their thresholds up to the center-of-mass energy W=1.96 GeV with the tagged-photon facilities at the Mainz Microtron, MAMI. Differential cross sections are obtained with unprecedented statistical accuracy, providing fine energy binning and full production-angle coverage. A strong cusp is observed in the total cross section for η photoproduction at the energies in the vicinity of the η′ threshold, W=1896 MeV (Eγ=1447 MeV). Within the framework of a revised ηMAID isobar model, the cusp, in connection with a steep rise of the η′ total cross section from its threshold, can only be explained by a strong coupling of the poorly known N(1895)1/2− sta…

Study of η and η' Photoproduction at MAMI

The reactions γp → ηp and γp → η0\ud p are measured from their thresholds up to the center-of-mass\ud energy W ¼ 1.96 GeV with the tagged-photon facilities at the Mainz Microtron, MAMI. Differential cross\ud sections are obtained with unprecedented statistical accuracy, providing fine energy binning and full\ud production-angle coverage. A strong cusp is observed in the total cross section for η photoproduction at the\ud energies in the vicinity of the η0 threshold, W ¼ 1896 MeV (Eγ ¼ 1447 MeV). Within the framework of a\ud revised ηMAID isobar model, the cusp, in connection with a steep rise of the η0 total cross section from its\ud threshold, can only be explained by a strong coupling of …

First measurement of target and beam-target asymmetries in the γp→π0ηp reaction

The first data on target and beam-target asymmetries for the γp→π0ηp reaction at photon energies from 1050 up to 1450 MeV are presented. The measurements were performed using the Crystal Ball and TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. The general assumption that the reaction is dominated by the Δ3/2− amplitude is confirmed. The data are in particular sensitive to small contributions from other partial waves.

The E0 transition in pion photoproduction and radiative pion capture on 13C

Abstract The E0 contribution of the reactions 13 C( γ , π − ) 13 N g.s. as well as 13 C( π + , γ ) 13 N g.s. has been calculated in an extended shell-model space using a nonlocal DWIA framework. A realistic shell-model wave function that includes configurations from the (2s, 1d) as well as the (2p, 1f) shells has been employed for the A = 13 system and leads to a significant suppression of the E0 transition. The large suppression can be understood in terms of the E0 radial integrals over the relevant single-particle densities. A variety of angular distributions demonstrates the good overall agreement with experimental data.

0+-0+transition in charged photopion reactions

In the near-threshold region for the (\ensuremath{\gamma},${\mathrm{\ensuremath{\pi}}}^{\ifmmode\pm\else\textpm\fi{}}$) reaction the spin-flip (Kroll-Ruderman) term dominates most nuclear reactions. The smaller non-spin-flip term is of considerable interest because it is very sensitive to the reaction dynamics and in particular to the \ensuremath{\Delta} channel, even in the near-threshold region. We propose to study the non-spin-flip term via the ${0}^{+}$\ensuremath{\rightarrow}${0}^{+}$ transition in the $^{14}\mathrm{C}$(\ensuremath{\gamma},${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$${)}^{14}$N reaction; the cross section is shown to be insensitive to the details of nuclear …

Elastic pion scattering on the deuteron in a multiple scattering model

Pion elastic scattering on deuterium is studied in the KMT multiple scattering approach developed in momentum space. Using a Paris wave function and the same methods and approximations as commonly used in pion scattering on heavier nuclei excellent agreement with differential cross section data is obtained for a wide range of pion energies. Only for $T_{\pi}>250$ MeV and very backward angles, discrepancies appear that are reminiscent of disagreements in pion scattering on $^3$He, $^3$H, and $^4$He. At low energies the second order corrections have been included. Polarization observables are studied in detail. While tensor analyzing powers are well reproduced, vector analyzing powers exhibit…

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…

Backward electroproduction ofπ0mesons on protons in the region of nucleon resonances at four momentum transfer squaredQ2=1.0GeV2

Exclusive electroproduction of pi{sup 0} mesons on protons in the backward hemisphere has been studied at Q2 = 1.0 GeV2 by detecting protons in the forward direction in coincidence with scattered electrons from the 4 GeV electron beam in Jefferson Lab's Hall A. The data span the range of the total (gamma*p) center-of-mass energy W from the pion production threshold to W = 2.0 GeV. The differential cross sections sigma{sub T} + epsilon sigma{sub L}, sigma{sub TL}, and sigma{sub TT} were separated from the azimuthal distribution and are presented together with the MAID and SAID parameterizations.

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.

Pion electroproduction in the 3He(e,é π+)3H reaction at intermediate energies

Abstract The differential coincident pion electroproduction cross section in the 3 He(e,e π + ) 3 H reaction has been measured with high resolution with the three-spectrometer set-up at the Mainz Microtron (MAMI) electron accelerator. Measurements were performed at the four incident energies E 0 = 855, 675, 600, and 555 MeV at fixed four-momentum transfer Q 2 = 0.045 GeV 2 , with the pions detected in parallel kinematics. This enables a separation of the measured cross section into the transverse and longitudinal structure functions by means of the Rosenbluth method. The experimental data are compared to model calculations, in which the elementary pion production amplitude includes the stan…

Single-energy partial wave analysis for π0 photoproduction on the proton with fixed- t analyticity imposed

High-precision data of the $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}p$ reaction from its threshold up to $W=1.9\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$ have been used in order to perform a single-energy partial-wave analysis with minimal model dependence. Continuity in energy was achieved by imposing constraints from fixed-$t$ analyticity in an iterative procedure. Reaction models were only used as starting point in the very first iteration. We demonstrate that, with this procedure, partial-wave amplitudes can be obtained which show only a minimal dependence on the initial model assumptions.

TandFasymmetries inπ0photoproduction on the proton

The γp→π0p reaction was studied at laboratory photon energies from 425 to 1445 MeV with a transversely polarized target and a longitudinally polarized beam. The beam-target asymmetry F was measured for the first time and new high precision data for the target asymmetry T were obtained. The experiment was performed at the photon tagging facility of the Mainz Microtron (MAMI) using the Crystal Ball and TAPS photon spectrometers. The polarized cross sections were expanded in terms of associated Legendre functions and compared to recent predictions from several partial-wave analyses. The impact of the new data on our understanding of the underlying partial-wave amplitudes and baryon resonance c…

Virtual Compton Scattering and Neutral Pion Electroproduction in the Resonance Region up to the Deep Inelastic Region at Backward Angles

We have made the first measurements of the virtual Compton scattering (VCS) process via the H$(e,e'p)\gamma$ exclusive reaction in the nucleon resonance region, at backward angles. Results are presented for the $W$-dependence at fixed $Q^2=1$ GeV$^2$, and for the $Q^2$-dependence at fixed $W$ near 1.5 GeV. The VCS data show resonant structures in the first and second resonance regions. The observed $Q^2$-dependence is smooth. The measured ratio of H$(e,e'p)\gamma$ to H$(e,e'p)\pi^0$ cross sections emphasizes the different sensitivity of these two reactions to the various nucleon resonances. Finally, when compared to Real Compton Scattering (RCS) at high energy and large angles, our VCS data…

Experimental study of theγp→ηpreaction with the Crystal Ball detector at the Mainz Microtron (MAMI-C)

The gamma p - = W >= 1.87 GeV). Bremsstrahlung photons produced by the 1.5-GeV electron beam of the Mainz Microtron MAMI-C and momentum analyzed by the Glasgow tagging spectrometer were used for the eta-meson production. Our accumulation of 3.8 x 10(6) gamma p -< eta p -< 3 pi(0) p -< 6 gamma p events allows a detailed study of the reaction dynamics. The gamma p -< eta p differential cross sections were determined for 120 energy bins and the full range of the production angles. Our data show a dip near W = 1680 MeV in the total cross section caused by a substantial dip in eta production at forward angles. The data are compared to predictions of previous SAID and MAID partial-wave analyses a…

Nucleon-to-Delta transition form factors in chiral effective field theory using the complex-mass scheme

We calculate the form factors of the electromagnetic nucleon-to-$\Delta$-resonance transition to third chiral order in manifestly Lorentz-invariant chiral effective field theory. For the purpose of generating a systematic power counting, the complex-mass scheme is applied in combination with the small-scale expansion. We fit the results to available empirical data.

Pion photo- and electroproduction with chiral MAID

We present a calculation of pion photo- and electroproduction in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including order $q^4$. We fix the low-energy constants by fitting experimental data in all available reaction channels. Our results can be accessed via a web interface, the so-called chiral MAID. We explain how our program works and how it can be used for further analysis.

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…

Pion Scattering and Pion Photoproduction on 3He

Using realistic 3-body Faddeev wave functions π± scattering and π+ photoproduction on 3He have been calculated in a consistent model. We demonstrate that at T π ≤ 180MeV polarization observables in pion scattering contain very little information about nuclear structure and can be understood in terms of free πN amplitudes. At higher energies the sign-flip of the asymmetry A y offers a new possibility to study higher-order effects of pion nuclear interaction. In pion photoproduction we find that two-step processes such as 3 He(γ, π°)3 He(π°, π+)3 H give rise to unexpected large contributions to the differential crosssection as well as to γ-asymmetry and with this improved a long time discrepa…

Study of η and η′ Photoproduction at MAMI

The reactions γp→ηp and γp→η′p are measured from their thresholds up to the center-of-mass energy W=1.96  GeV with the tagged-photon facilities at the Mainz Microtron, MAMI. Differential cross sections are obtained with unprecedented statistical accuracy, providing fine energy binning and full production-angle coverage. A strong cusp is observed in the total cross section for η photoproduction at the energies in the vicinity of the η′ threshold, W=1896  MeV (Eγ=1447  MeV). Within the framework of a revised ηMAID isobar model, the cusp, in connection with a steep rise of the η′ total cross section from its threshold, can only be explained by a strong coupling of the poorly known N(1895)1/2− …

Recoil Polarization and Beam-Recoil Double Polarization Measurement ofηElectroproduction on the Proton in the Region of theS11(1535)Resonance

The beam-recoil double polarization P{sub x{sup '}}{sup h} and P{sub z{sup '}}{sup h} and the recoil polarization P{sub y{sup '}} were measured for the first time for the p(e-vector,e{sup '}p-vector){eta} reaction at a four-momentum transfer of Q{sup 2}=0.1 GeV{sup 2}/c{sup 2} and a center of mass production angle of {theta}=120 deg. at the Mainz Microtron MAMI-C. With a center of mass energy range of 1500 MeV<W<1550 MeV the region of the S{sub 11}(1535) and D{sub 13}(1520) resonance was covered. The results are discussed in the framework of a phenomenological isobar model (Eta-MAID). While P{sub x{sup '}}{sup h} and P{sub z{sup '}}{sup h} are in good agreement with the model, P{sub y{sup '…

Photoproduction of neutral pions and low energy theorems

The complete experiment for photoproduction of pseudoscalar mesons in a truncated partial wave analysis

The complete experiment problem in the truncated partial wave analysis of pseudoscalar meson photoproduction with suppressed t-channel exchanges is investigated. The focus is set to ambiguities of the group S observables with the unpolarized differential cross section, $\sigma_0$, and the three single-spin observables, $\Sigma$, $T$ and $P$. For this purpose, the approach and formalism already worked out by Omelaenko in 1981 is revisited in this work. A numerical study using multipoles of the PWA solution MAID2007 shows how only one additional double polarization observable can resolve all ambiguities. Therefore, the possibility emerges to perform a complete experiment with only five observ…

E0 suppression in pion photoproduction on 13C

Abstract Recently measured anomalously low cross sections for 13 C(γ, π − ) 13 N at low energy and θ π lab = 90° 0761 have been analyzed in a DWIA calculation. It has been found that the EO contribution alone is able to explain the data, so that the M1 cross section is expected to vanish. Using constraints from recent magnetic electron scattering, an explanation is possible by assuming a significantly lower reduced density matrix element for spin-flip isovector transitions with angular momentum L = 2 than predicted by Cohen and Kurath.

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…

First measurement of target and beam-target asymmetries in theγp→π0ηpreaction

The first data on target and beam-target asymmetries for the gamma p -> pi(0)eta p reaction at photon energies from 1050 up to 1450 MeV are presented. The measurements were performed using the Crystal Ball and TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. The general assumption that the reaction is dominated by the Delta 3/2-amplitude is confirmed. The data are in particular sensitive to small contributions from other partial waves.

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.

Amplitude- and truncated partial-wave analyses combined: A single-channel method for extracting photoproduction multipoles directly from measured data

Amplitude- and truncated partial-wave analyses are combined into a single-channel method for extracting multipoles directly from measured data. In practice, we have created a two-step procedure which is fit to the same database: in the first step we perform an energy-independent amplitude analysis where continuity is achieved by constraining the amplitude phase, and the result of this first step is then taken as a constraint for the second step where a constrained, energy-independent, truncated partial-wave analysis is done. The method is tested on the world collection of data for $\ensuremath{\eta}$ photoproduction, and the obtained fit results are very good. The sensitivity to different p…

First measurement of target and beam-target asymmetries in the $\gamma p\to \pi^0\eta p$ reaction

The first data on target and beam-target asymmetries for the $\gamma p\to\pi^0\eta p$ reaction at photon energies from 1050 up to 1450 MeV are presented. The measurements were performed using the Crystal Ball and TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. The general assumption that the reaction is dominated by the $\Delta 3/2^-$ amplitude is confirmed. The data are in particular sensitive to small contributions from other partial waves.

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%.

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.

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.

Model Dependence of Nucleon Resonance Parameters

Nucleon resonance parameters as mass, width, branching ratios and electromagnetic helicity amplitudes cannot be determined in a model independent way. The best way to obtain such elementary quantities is in terms of a partial wave analysis and a separation of resonance and background. In this work we have concentrated on the extraction of the e.m. helicity amplitudes A l p and A312 from electric and magnetic multipole analyses that were obtained from different groups with different techniques. We make a comparison of our results for the resonances P11(1440), 013(1520) and s11(1535). The variation that we find can be considered as a measure of the model uncertainty in these quantities.

The asymmetry in π−3He scattering

Abstract We show that the π + − 3 He asymmetry data obtained in a recent TRIUMF experiment at T π = 100 MeV can be understood in terms of the elementary π N amplitudes. Through a comparison to a full optical-potential calculation that employs realistic Faddeev wave functions for the trinucleon we show that all nuclear-structure dependence cancels for A y at lower energies. At higher pion energies around the Δ-resonance region the sign flip of A y offers the possibility of extracting information about the smaller partial waves.

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.

Measurements of Double-Polarized Compton Scattering Asymmetries and Extraction of the Proton Spin Polarizabilities

The spin polarizabilities of the nucleon describe how the spin of the nucleon responds to an incident polarized photon. The most model-independent way to measure the nucleon spin polarizabilities is through polarized Compton scattering. Double-polarized Compton scattering asymmetries on the proton were measured in the $\Delta(1232)$ region using circularly polarized incident photons and a transversely polarized proton target at the Mainz Microtron. Fits to asymmetry data were performed using a dispersion model calculation and a baryon chiral perturbation theory calculation, and a separation of all four proton spin polarizabilities in the multipole basis was achieved. The analysis based on a…

Pion photo- and electroproduction in relativistic baryon chiral perturbation theory and the chiral MAID interface

We present a calculation of pion photo- and electroproduction in manifestly Lorentz-invariant baryon chiral perturbation theory up to and including order ${q}^{4}$. We fix the low-energy constants by fitting experimental data in all available reaction channels. Our results can be accessed via a Web interface, the so-called chiral MAID. We explain how our program works and how it can be used for further analysis.

Beam-Recoil Polarization Measurement of π0 Electroproduction on the Proton in the Region of the Roper Resonance

The helicity-dependent recoil proton polarizations P_{x}^{'} and P_{z}^{'} as well as the helicity-independent component P_{y} have been measured in the p(e[over →],e^{'}p[over →])π^{0} reaction at four-momentum transfer Q^{2}≃0.1  GeV^{2}, center-of-mass proton emission angle θ_{p}^{*}≃90°, and invariant mass W≃1440  MeV. This first precise measurement of double-polarization observables in the energy domain of the Roper resonance P_{11}(1440) by exploiting recoil polarimetry has allowed for the extraction of its scalar electroexcitation amplitude at an unprecedentedly low value of Q^{2}, establishing a powerful instrument for probing the interplay of quark and meson degrees of freedom in t…

Measurement of the decay η′→π0π0η at MAMI

An experimental study of the η′→π0π0η→6γ decay has been conducted with the best up-to-date statistical accuracy, by measuring η′ mesons produced in the γp→η′p reaction with the A2 tagged-photon facility at the Mainz Microtron, MAMI. The results obtained for the standard parametrization of the η′→π0π0η matrix element are consistent with the most recent results for η′→ππη decays, but have smaller uncertainties. The available statistics and experimental resolution allowed, for the first time, an observation of a structure below the π+π− mass threshold, the magnitude and sign of which, checked within the framework of the nonrelativistic effective-field theory, demonstrated good agreement with t…

"Table 6" of "Precise pion electroproduction in the p (e, e-prime pi+) n reaction at W = 1125-MeV"

Angle PHI(P=4) is the angle between the scattering plane (defined by 1 and 3 particles) and the reaction plane (defined by 4 and 5 particles).

"Table 4" of "Precise pion electroproduction in the p (e, e-prime pi+) n reaction at W = 1125-MeV"

Angle PHI(P=4) is the angle between the scattering plane (defined by 1 and 3 particles) and the reaction plane (defined by 4 and 5 particles).

"Table 2" of "Precise pion electroproduction in the p (e, e-prime pi+) n reaction at W = 1125-MeV"

Angle PHI(P=4) is the angle between the scattering plane (defined by 1 and 3 particles) and the reaction plane (defined by 4 and 5 particles).

"Table 5" of "Precise pion electroproduction in the p (e, e-prime pi+) n reaction at W = 1125-MeV"

Angle PHI(P=4) is the angle between the scattering plane (defined by 1 and 3 particles) and the reaction plane (defined by 4 and 5 particles).

"Table 3" of "Precise pion electroproduction in the p (e, e-prime pi+) n reaction at W = 1125-MeV"

Angle PHI(P=4) is the angle between the scattering plane (defined by 1 and 3 particles) and the reaction plane (defined by 4 and 5 particles).

"Table 1" of "Precise pion electroproduction in the p (e, e-prime pi+) n reaction at W = 1125-MeV"

Angle PHI(P=4) is the angle between the scattering plane (defined by 1 and 3 particles) and the reaction plane (defined by 4 and 5 particles).