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

We have analyzed 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 Omnès and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π⁺ and π⁰ production on the proton as well as π⁻ production on the neutron, in the energy range 160 MeV ⩽ E_γ ⩽ 420 MeV. The lack of high precision data on the neutron and of polarization observables leads to some limitations of our results. Especially the multipole M₁₋ connected with the Roper resonance P₁₁ (1440) cannot be determined to the required precision. Our predictions for the threshold amplitudes are in good agreement with both the data and chiral perturbation theory. In the region of the Δ(1232) we have determined the ratio of electric quadrupole and magnetic dipole excitation. The position of the resonance pole is obtained in exellent agreement with pion-nucleon scattering, and the complex residues of the multipoles are determined with the speed-plot technique.     

On pole terms in the fixed angle approach to photoproduction of pions on nucleons

This note has two aims. The first one is to study the properties of well known pole contributions to photoproduction amplitudes but in the space of c.m. three-momentum squared and scattering angle. Some conclusions essential to the fixed angle approach are drawn. The second aim is to give some results of more general character. These are plots and numerical tables of pole contributions to multipole amplitudes.     

A dispersion analysis of pion photoproduction from nucleons. I

The paper gives an account of numerical results forl=0 andl=1 multipole amplitudes of pion photoproduction. They have been obtained by solving integral equations which originate from fixed-angle dispersion relations that have been deduced in an earlier paper. In this Part I outlined are some difficulties usually encountered in course of solving the problem of pion photoproduction by dispersion techniques, and proposed is an approach which introduces arbitrary parameters — cutoffs in the integral equation for transition amplitudes. Numerical results show some implications of this philosophy on the rôle played by the terms representing physical singularities and terms representing left-hand singularities controlled by one-particle (Born) contributions.     

Elastic photoproduction of neutral pions from helium

Zeitschrift für Physik A Hadrons and nuclei - Differential cross sections are calculated for the elastic photoproduction of neutral pions from He4 under the impulse approximation. We use a...     

High energy pion photoproduction amplitudes from fixed-t dispersion relations and duality

Contributions to the high energy imaginary parts of the charged and neutral pion photoproduction amplitudes from degenerate ? and A₂ exchanges and ω and B exchanges are parametrized similarly to the dual absorptive model. These contributions together with the imaginary parts of the amplitudes found at low energies from partial-wave analyses are then used to evaluate the high energy real parts of the photoproduction amplitudes from fixed-t dispersion relations. A fit is made to data on pion photoproduction at 3.4 and 16 GeV incident photon energies, for momentum transfers up to ?1(GeV/c)². It is shown that much of the data is reproduced both qualitatively and quantitatively by our model. The high energy imaginary parts of the photoproduction amplitudes given by the fit are shown to be in accord with their average low energy behaviour.     

Threshold photoproduction of charged pions on14N

Pion photoproduction processes¹⁴N_gs(γ, π ⁺)¹⁴C and¹⁴N_gs(γ, π ^?)¹⁴O have been studied in the threshold region. These processes provide an excellent tool to study the corrections to soft pion theorems and Kroll-Ruderman limit as applied to nuclear processes. The agreement with the available experimental data for these processes is better with the empirical wave functions while the shell-model wave functions predict a much higher value. Detailed experimental studies of these reactions at threshold, it is shown, are expected to lead to a better understanding of the shell-model inputs and radial distributions in the 1p state.     

Polarization effects in dispersion relations for photoproduction of π-mesons on deuterons

The photoproduction amplitude of ⁰-mesons on deuterons is calculated for different cases of polarization of the spin of deuterons by means of impulse approximation. The calculations carried out in the two-nucleon approximation in the Breit system are valid up to a maximum photon energy 236 MeV. In the unobservable region only a free proton and a free neutron contribute to the continuous part of the spectrum.The dispersion relations are given for all cases of deuteron-spin polarization.This paper is a continuation of the author's papsr elaborated in the Laboratory of Theoretical Physics of the Joint Institute of Nuclear Research, Dubna USSR, published in Nuclear Physics26 (1961), 681, which is hereafter referred to as I.     

Radiative photoproduction of pions and pion compton scattering

The cross section for the radiative photoproduction of ⁺ mesons on hydrogenp ⁺ n in dependence on the momentum transfer squared has been measured at the 1·2 GeV electron synchrotron PACHRA. Using extrapolation of the data to pion pole the differential cross section for the pion Compton scattering ^{+ +} has been obtained, and the electric polarizability of the ⁺ meson has been estimated to be =(20±12) x 10^-43cm³.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.The authors thank P. A. Cherenkov for his constant attention to this work and helpful discussions at all stages of the work.     

Inclusive photoproduction of neutral pions in the photon hemisphere at HERA

The inclusive cross section for the photoproduction of neutral pions has been measured as a function of the transverse momentum, rapidity, and Feynman x of the mesons at an average photon–proton centre-of-mass energy of 208 GeV and for photon virtualities below GeV. The measurement extends the range covered by previous charged particle measurements at HERA by two units of rapidity in the photon direction down to a value of in the centre-of-mass frame. The transverse momentum distribution is well described over the whole measured range by a power law ansatz, while an exponential fit falls below the data at transverse momentum values above 1.5 GeV/c. Good agreement with the predictions of the Monte Carlo models PYTHIA and PHOJET is found. In the context of the PYTHIA model the data are inconsistent with large intrinsic transverse momentum values in the photon. Received: 14 June 2000 / Published online: 27 November 2000     

Forward photoproduction of neutral pions on protons in the third resonance region

Four angular distributions of the differential cross section of the reaction γ + p → π⁰ + p have been measured at the Bonn 2.5 GeV Synchrotron at pion c.m. angles between 3° and 63° in the photon energy range from 0.9 GeV to 1.2 GeV. The π⁰ mesons were detected by their two decay photons. The data are compared with data of other laboratories and predictions of two recent partial-wave analyses.     

Measurement of the polarization of the recoil proton from the photoproduction of neutral pions on hydrogen in the region of the first resonance. I

The polarization of the recoil proton from the reactionγ+p→π ⁰+p has been measured using liquid helium as polarization analyser. The photon energy has been varied between 250 and 360 MeV, the pion angle (CM) between 58° and 100°.     

Current-algebra calculation of low-energy pion electro- and photoproduction for physical pions

A hard-pion current-algebra model is employed to derive expressions for the pion electro- and photoproduction amplitudes. The low-energy predictions for the multipole amplitudes and differential cross sections of photoproduction are analysed and compared with the experimental data.     

Forward photoproduction of neutral pions on polarized protons in the third resonance region

Angular distributions of the target symmetry for the reaction γ + p → π⁰ + p have been measured at the Bonn 2.5 GeV Electron Synchrotron at pion c.m. angles between 13° and 63° and photon energies of 1.0 and 1.1 GeV. The π⁰ mesons were detected by their two decay photons with total absorption lead-glass ?erenkov counters. Butanol was used as target material in a continuous flow ³He cryostat operating at 0.5 K and 25 kG. The π⁰ counting rate from free protons in the butanol target was derived from the measurements of the differential cross section on hydrogen. The data are compared with data of other laboratories and the results of two recent partial-wave analyses.     

A dispersion analysis of pion photoproduction from nucleons. II

The paper gives an account of numerical results forl=0 andl=1 multipole amplitudes of pion photoproduction. They have been obtained by solving integral equations which originate from fixed angle dispersion relations that have been deduced in an earlier paper. In this Part II presented are solutions of truncated integral equations for photoproduction amplitudes, which take into account coupling with the most important transitionsM ₁₊ ⁽³⁾ (in the isovector case) andE ₀₊ ⁽⁰⁾ (in the isoscalar case). Discussed are implications of such an approach and a comparison of results obtained by a different method is being made.     

Appearance of P-odd nuclear forces in photoproduction of pions on6Li

P-odd effects in the photoproduction of pions on⁶Li nuclei, +⁶Li ⁺ +⁶He, are studied. Collisions of linearly and circularly polarized photons with a polarized nuclear target are studied, and in addition both vectorial and tensorial polarization are taken into account. It is shown that in the general case P-odd effects in +⁶Li ⁺ +⁶He are characterized by 18 real structure functions, which determine different P-odd asymmetries in the angular distribution of the pions. The structure functions in their turn depend on different products of three p-even and three p-odd amplitudes of the process +⁶Li ⁺ +⁶He. The P-odd effects at the threshold of the reaction +⁶Li ⁺+⁶He are analyzed. Using available experimental data on the behavior of the cross section of the reaction +⁶Li ⁺ +⁶He at threshold, the ⁶Li⁶He strong-interaction constant is evaluated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 78–82 July 1985.     

Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials

For the two-dimensional Schrödinger equation $$[ - \Delta + v(x)]\psi = E\psi , x \in \mathbb{R}^2 , E = E_{fixed} > 0 (*)$$ at a fixed positive energy with a fast decaying at infinity potentialv(x) dispersion relations on the scattering data are given. Under “small norm” assumption using these dispersion relations we give (without a complete proof of sufficiency) a characterization of scattering data for the potentials from the Schwartz classS=C _∞ ^(∞) (?²). For the potentials with zero scattering amplitude at a fixed energyE _fixed (transparent potentials) we give a complete proof of this characterization. As a consequence we construct a family (parametrized by a function of one variable) of two-dimensional spherically-symmetric real potentials from the Schwartz classS transparent at a given energy. For the two-dimensional case (without assumption that the potential is small) we show that there are no nonzero real exponentially decreasing, at infinity, potentials transparent at a fixed energy. For any dimension greater or equal to 1 we prove that there are no nonzero real potentials with zero forward scattering amplitude at an energy interval. We show that KdV-type equations in dimension 2+1 related with the scattering problem (*) (the Novikov-Veselov equations) do not preserve, in general, these dispersion relations starting from the second one. As a corollary these equations do not preserve, in general, the decay rate faster than |x|^?3 for initial data from the Schwartz class.     

The photoproduction of neutral pions from protons at forward angles in the resonance region

Differential cross sections for the photoproduction of pi-zero mesons from protons have been measured at angles between 10° and 70° c.m. in the energy range 0.85 GeV to 1.30 GeV. The values are compared with the fits to pion photoproduction data from three recent partial-wave analyses.     

Analysis of the dispersion relations of nonlinear slab-guided waves

The dispersion relations of TE-polarized nonlinear guided waves (NGW) were investigated in detail. These waves travel along a dielectric slab embedded between two different nonlinear media. A simple relation between the effective nonlinear dielectric constants was established. All dispersion curves exhibit a particular transition point, where one evanescent field maximum changes from a virtual into a real one, and vice versa. Depending on the type of the remaining invariant evanescent field maximum, all NGW's split into two families. The lowest-order membres of every family play a particular role. The power flux supported by a NGW is derived, too.Preliminary results were presented at the XVI^th European Congress of Molecular Spectroscopy, Sofia, Bulgaria (1983)     

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.     

A study of photoproduction of charged pions from 16O

Photoproduction of π⁺ from ¹⁶O leading to the four bound states in ¹⁶N has been studied using different dynamical amplitudes and considering particle-hole correlations in the nuclear wave functions. It is shown that the total cross section is strongly affected by the choice of dynamical amplitudes whereas the effect of 3p - 3h correlations in ¹⁶N is small.