A partial-wave analysis for proton compton scattering in the Δ(1232) energy region

Based on the nowadays available phenomenological multipoles for pion photoproduction, a systematic dispersion theoretic calculation of Compton partial amplitudes has been performed. By comparing with the new experimental data in the Δ(1232) region it is found that the hitherto existing discrepancies between the data and theory remain. Our results allow us to isolate the basis of this problem. It is due to the fact that the imaginary parts of the Compton amplitudes determined already by unitarity, give too large contributions to the cross section thus leaving no space for real parts required by the dispersion integrals.Therefore a simultaneous partial-wave analysis for Compton scattering and pion photoproduction was carried through employing only the unitarity connections between both. The resulting amplitudes give a good fit to the Compton cross section and all photoproduction data; moreover the photoproduction multipoles agree essentially with those of the previous analyses. On the other hand for Compton scattering, phenomenological amplitudes are obtained for the first time and a model independent test of dispersion theoretic amplitudes can be carried out. For the resonating f_MM¹⁺ amplitude which describes the M1 excitation and deexcitation to the Δ-isobar, large discrepancies have been found. Possible consequences especially for the forward scattering amplitude and the validity of the Kramers-Kronig relation are discussed.     

Dispersion theory and the low-energy constants for neutral-pion photoproduction

The relativistic amplitudes of pion photoproduction are evaluated by dispersion relations at t = const. The imaginary parts of the amplitudes are taken from the MAID model covering the absorption spectrum up to center-of-mass energies W = 2.2GeV. For sub-threshold kinematics the amplitudes are expanded in powers of the two independent variables ν and t related to energy and momentum transfer. Subtracting the loop corrections from this power series allows one to determine the counter terms of covariant baryon chiral perturbation theory. The proposed continuation of the amplitudes into the unphysical region provides a unique framework to derive the low-energy constants to any given order as well as an estimate of the higher-order terms by global properties of the absorption spectrum.     

An application of dispersion relations to Kaon-nucleon scattering

In this paper we have made predictions for the invariant KN and $\text{K}$N scattering amplitudes in the kinematical region q_lab < 15 GeV/c and 0 >; t > -0.7 (GeV/c)².We have performed a direct fit to medium and high-energy data using a parametrization where the imaginary part of the amplitudes for energies above the phase-shift region is identical with the imaginary part of a Regge-pole amplitude, and the real part of the amplitudes has been obtained from a dispersion relation.The s-channel helicity amplitudes are compared with their counterparts in pion-nucleon scattering and other reactions. Exact exchange degeneracy can not be verified.Also the real part of the amplitudes are compared with the real part of phase-shift solutions. There is a qualitative agreement between these two real parts even though they differ in detail.     

Exchange ofA 1 andZ 1 (J PC=2−−) mesons in charged pion photoproduction

Finite energy sum rules are evaluated for the amplitudes corresponding to the exchange of theA ₁ and its exchange degenerate partner, theZ ₁ (J ^PC=2^??), in charged pion photoproduction. Both sum rules are roughly compatible with theoretical estimates of these exchanges, and a definiteA ₁ signal found.     

Scale of corrections to the t-channel pole approximation in quasielastic pion knockout from a nucleon by high-energy electrons

An investigation of a dominant role of the simplest t-channel pole diagrams in pion electroproduction on nucleons for quasielastic-knockout kinematics at an electron energy of a few GeV is completed-namely, the competition between the t-channel pion and rho-meson pole amplitudes, on one hand, and the s-channel pole amplitude (tree diagram), on the other hand, is considered. When the virtual-photon mass is sufficiently large [Q ²>2(GeV/c)²], the last amplitude does not make significant contributions to relevant cross sections, either the longitudinal (dσ _L/dt) or the transverse (dσ _T/dt) one. At Q ²=0.7(GeV/c)², the term associated with the interference between the t-channel pion-pole amplitude and the s-channel pole amplitude is still noticeable in the longitudinal cross section. The vertex functions g _ρ NN(t) as obtained from the cross section for the quasielastic knockout of rho mesons and from the cross section for pion photoproduction are compared. Their disagreement must give impetus to a further development of the gauge-invariant theory of pion photoproduction.     

Positive pion photoproduction from hydrogen at photon energies between 500 MeV and 1,400 MeV in forward direction

The differential cross section of the reactionγ+p→π ⁺ was measured at pion CM-angles of 20° and 30° for photon energies between 500 MeV and 1,400 MeV. The pions were detected in a magnetic spectrometer. By measuring each pion trajectory and by offline calculation of the initial pion parameters an energy resolution of about 2.5% FWHM was achieved. The results complete a set of data which were measured in recent years at the Bonn 2.5 GeV synchrotron. In comparison to photoproduction analyses two effects were revealed: The η cusp appears in the energy dependence of the cross section as a sharp drop atK _γ=710 MeV. In the region of the third resonance the data show a greater enhancement than predicted by most of the analyses.     

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 (P₃₃(1232), P₁₁(1440), D₁₃(1520), S₁₁(1535), F₁₅(1680), and D₃₃(1700)). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The Q² 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 electroproduction on the nucleon for both differential cross sections and polarization observables. The model can be used as a starting point to predict and analyze forthcoming data.     

Photoproduction of π+ mesons on polarized protons

The asymmetry of the cross sections for the photoproduction of π⁺ mesons on polarized protons γ + p↑ → π⁺ + n has been studied in the four-momentum transfer range 0.1 ? |t| ? 1.25 (GeV/c)² for photon energies of 2.5, 3.4 and 5.0 GeV. The measurements were carried out on a polarized butanol target. Both particles in the final state were detected: the pion by a magnetic spectrometer, the recoil nucleon in a scintillation counter matrix. The asymmetry was found to be negative with values around ?0.4.     

Determination of resonance couplings and high energy amplitudes in γN → πN using fixed-t dispersion relations

The real parts of the amplitudes are generated entirely from their imaginary parts via d.rs., and essentially all available data is included at all energies with momentum transfer |t| < 1 GeV². A total of 46 resonance couplings and 50 high energy parameters are varied to fit all the data simultaneously with a χ² of 4.8 per data point.     

Amplitude analysis of Kaon-nucleon scattering data

The KN scattering amplitudes have been extracted from experimental data in the energy range 3 ? k ? 14 GeV/c and for transfer values between ?0.05 and ?0.6 GeV².The ω and P+f helicity-flip amplitudes and the A₂ helicity non-flip amplitude have been neglected; it is shown, that these simplifications are compatible with the data and have no significant influence on our results. One needs to assume the approximate validity of SU(3) symmetry for the ? and A₂ couplings. A very important constraint for this analysis comes from recent experimental data for the reaction K_L⁰p → K_S⁰p. The results for A₂ and ω exchanges are analysed as functions of momentum transfer and energy and we test several current theoretical ideas. Information about f-exchange is also obtained when some further assumptions are made concerning SU(3) symmetry and duality at t = 0. Extrapolating the amplitudes to t = 0 a comparison is made with dispersion relation calculations; at other t-values we compare with results obtained from finite energy sum rules and other analyses based on fixed f analyticity. The predictions for KN data which have not been considered in this analysis are shown to be in good agreement. One of our results is that the ?-ω universality rule is approximately satisfied; we also find a strong indication for a peripheral behaviour of the imaginary part of the non-flip f-exchange amplitude.     

Construction of π± photoproduction amplitudes at high energy from dispersion relations and local duality

We investigate the charged-pion photoproduction amplitudes at all energies. We first show that low-energy s-channel helicity amplitudes exhibit, in most cases, a Bessel-function structure of zeroes. At high energy we therefore parametrize the imaginary parts of helicity amplitudes according to the Harari model, and compute the real parts using fixed-t dispersion relations as proposed recently. Such an evaluation of scattering amplitudes presents some very nice properties. In particular, it allows one to understand from duality arguments how the Born contribution may survive with full strength in the forward direction but not at large t-values. Furthermore FESR are identically satisfied by the model.     

Soft π−p and pp elastic scattering in the energy range 30 to 345 GeV

Differential cross sections for π^?p and pp elastic scattering have been measured at incident momenta ranging from 30 to 345 GeV and in the t range 0.002 (GeV/c)² ? |t| ? 0.04 (GeV/c)². From the analysis of the data, the ratio ? (t = 0) of the real to the imaginary parts of the forward scattering amplitude was determined together with the logarithmic slope b of the diffraction cone.The results on the real parts confirm the validity of the forward dispersion relations at high energies. Using the dispersion relations, it was shown that the experimental data on ?_{π?p(t = 0)} require a continuous rise of the total πp cross sections, at least up to the energy of 2000 GeV, thus revealing a close similarity in high-energy behaviour of πp and pp interactions.The results on the slope parameters from this experiment together with the analysis of the available world data demonstrate that the existing experimental data are consistent with the hypothesis of a universal shrinkage of the hadronic diffraction cone at high energies. The value of the asymptotic shrinkage parameter α_p^′ was found to be independent of the kind of the incident hadron and of the momentum transfer in the t range |t| ? 0.2 (GeV/c)² : 2α_{p^′ = ± 3 (GeV/c)^?2}.     

The structure of t-channel exchanges in KN scattering

Recent phase-shift solutions are used to evaluate KN FESR integrals in order to examine zeros and phases of the t-channel exchange amplitudes in the most model-independent way. The results suggest that the line reversal breaking in KN CEX observed for pL ? 5.5 GeV/c is due to a large EXD breaking component in the A₂ exchange flip amplitude. The ? exchange flip amplitude is well described by a Regge pole amplitude with NWSZ at ?t ≈ 0.5 (GeV/c)². The imaginary parts of ? and ω exchange non-flip amplitudes are both peripheral.     

Photoabsorption on nuclei

We calculate the total photoabsorption cross section on nuclei in the energy range from 300 MeV to 1 GeV within the framework of a semi-classical phase space model. Besides medium modifications like Fermi motion and Pauli blocking we focus on the collision broadening of the involved resonances. The resonance contributions to the elementary cross section are fixed by fits to partial wave amplitudes of pion photoproduction. The cross sections for NR → NN, needed for the calculation of collision broadening, are obtained by detailed balance from a fit to NN → NNπ cross sections. We show that a reasonable collision broadening is not able to explain the experimentally observed disappearance of the D₁₃(1520)-resonance in the photoabsorption cross section on nuclei.     

Evaluation of the photoproduction of negative pions on neutrons in the region of the first resonance

In this paper we extend our systematic investigation of pion photoproduction to the case of negative pion production on neutrons. In our approach two phenomenological parameters occur in the electric and magnetic dipole amplitudesE ₀₊ andM _1?. These constants have been determined by a least squares fit of the total cross section data of the ABBHHM collaboration. We obtain a very good fit, also the prediction of the asymmetry ratio for polarized photons agrees with experiment at energies below and at the resonance. Serious discrepancies between theory and experiment are found for theπ ^?/π ⁺ ratio, moreover the relationship between the electric dipole at threshold, the Panofsky ratio and the difference ofs-waveπN-scattering lengths is fulfilled only within 20%. These discrepancies are discussed thoroughly.     

Photoproduction of neutral pions at backward angles in the resonance region and the η-cusp

At the Bonn 2.5 GeV electron synchrotron we have measured the differential cross section of the reaction γp→π⁰ p at a pion CM angle of 170° and at photon energiesK _γ between 0.6 and 1.8 GeV. In comparison to previous measurements the accuracy of the data was improved substantially. For the first time in neutral pion photoproduction a cusp structure at the η-threshold has been confirmed [1].     

Multipole analysis of π+ and π0 photoproduction from threshold to Eγ = 330 MeV

We present results of an energy independent multipole analysis of π⁺ and π⁰ photoproduction on protons for photon energies between 160 MeV and 330 MeV. Each isospin part of the l ? 1 amplitudes has been parametrized; the 1 ? 2 amplitudes have been approximated by the Born terms. Unambiguous solutions for all the multipoles in the whole range of E_γ have been obtained. The continuity of the solutions as functions of the energy is very good.     

Elastic unitarity and the K-matrix in a Lorentz covariant representation of the NN interaction

A Lorentz covariant representation of the NN t-matrix has been obtaained over the energy range from 150 to 500 MeV by solving the integral equation that connects the t-matrix with the K-matrix. The K-matrix is expanded in a complete set of on-shell Lorentz invariant amplitudes represented phenomenologically by isoscalar and isovector “meson” exchanges. The real part of the K-matrix is fit over the energy range from 150 to 500 MeV using coupling strengths that are allowed to vary quadratically with energy. Above the pion production threshold at T_lab = 280 MeV, the real K-matrix is supplemented by an imaginary part with linear energy dependence. The K-matrix parameters are fit to thesmost recent (January 1999) Arndt amplitudes [R.A. Arndt, D. Roper, VPI and SU Scattering Analysis Interactive Dial-in Program and Data Base]. Direct and exchange contributions to the K-matrix are handled explicitly in the formalism. The resulting t-matrix satisfies elastic unitary below the pion production threshold and contains non-local terms that are not present in direct Love-Franey parameterizations of the t-matrix. Results are given for the NN amplitudes and compared with both the Arndt amplitudes and amplitudes obtained from a direct fit of the t-matrix [O.V. Maxwell, Nucl. Phys. A 600 (1996) 509]. Results are also given for a selected set of np and pp observables.     

Measurement of elastic ω photoproduction at HERA ZEUS Collaboration

The reaction γp →ωp(ω → π⁺π^?π⁰ and π⁰ → γ γ) has been studied in ep interactions using the ZEUS detector at photon-proton centre-of-mass energies between 70 and 90GeV and ∣t∣ < 0.6GeV², where t is the squared four momentum transferred at the proton vertex. The elastic ω photoproduction cross section has been measured to be σ_{γp → ωp} = 1.21 ±0.12 ±0.23 μb. The differential cross section dσ_γp→ωp/d¦t¦ has an exponential shape e^?b∣t∣ with a slope b =10.0 ± 1.2 ± 1.3 GeV^?2. The angular distributions of the decay pions are consistent with s-channel helicity conservation. When compared to low energy data, the features of ω photoproduction as measured at HERA energies are in agreement with those of a soft diffractive process. Previous measurements of the ρ⁰ and ? photoproduction cross sections at HERA show a similar behaviour.