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.     

Partial-wave decomposition of pion and photoproduction amplitudes

Partial-wave amplitudes for production and decay of baryon resonances are constructed in the framework of the operator expansion method. The approach is fully relativistically invariant and allows us to perform combined analyses of different reactions imposing directly analyticity and unitarity constraints. All formulas are given explicitly in the form used by the Crystal Barrel Collaboration in the (partly forthcoming) analyses of the electro-, photo- and pion-induced meson production data.     

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.     

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.     

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.     

Charged pion photoproduction from light nuclei

The photoproduction of 0–150-MeV charged pions from light nuclei is studied from a distorted wave impulse approximation (DWIA) approach. The final nuclear states are restricted to a finite set of isospin analogs of excited states of the target nucleus. The final state interactions of the pion with the residual nucleus are incorporated via optical potentials. The elementary photoproduction operator used is that of Blomqvist and Laget which is derived in a general reference frame. To gain insight into the predictive power of this DWIA approach, total and differential cross sections for π^± production from ⁶Li, ⁷Li, ¹⁰B, ¹²C, and ¹⁴N are calculated and compared with available data. It is found that, with a few exceptions, reasonable agreement is obtained between theory and experiment as long as the nuclear wave functions are constrained to fit other electromagnetic and weak processes and the optical potentials are constrained to fit pion-nucleus elastic scattering data. We conclude that, at this stage, using the Blomqvist-Laget operator in a DWIA calculation adequately describes the dynamics of charged pion photoproduction from complex nuclei. We illustrate how this reaction can be used to obtain information on the short range nature of the pion wave function and on nuclear wave functions. Shortcomings of and improvements on this calculation are also suggested.     

Exchange amplitudes and dispersion relations for electron-atom scattering

The analytic structure of the second Born approximation to the forward elastic exchange amplitude is analyzed for e^?+H scattering, and the importance of the interplay between bound and continuum intermediate state contributions is emphasized.     

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.     

Invariant amplitudes and double dispersion relations for electron-muon scattering

For electron-muon scattering, a set of six invariant amplitudes free from kinematical singularities is determined. A simple proof of this freedom is given. Projection operators for this set are constructed. Double dispersion relations using natural subtraction points are derived for the box diagram.     

Quasi-free pion photoproduction from carbon above 300 MeV

The momentum spectra of charged pions produced in the reaction ¹²C(γ, π^±) have been measured for incident photon energies in the interval between 300 and 850 MeV in steps of 50 MeV. Pions with relatively high momenta have been detected by a magnetic spectrometer set at the lab angles 28.4° and 44.2°. All these spectra exhibit a clear singly peaked structure. Detailed features of the structure are quantitatively investigated and compared with a plane-wave impulse-approximation calculation. Calculated results are found to reproduce the spectral shape very well and the absolute magnitude is also rather well fitted by introducing the pion absorption effect properly.     

Double pion photoproduction from3He at low energies

A generalization of the “Gauge-invariant OPE model” to double pion photoproduction on³He is presented. Results for the total and differential cross-sections are shown. The relevance of double pion photoproduction in the nuclear shadowing of photons is remarked.     

Effective Lagrangian Approach to pion photoproduction from the nucleon

We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances (Δ(1232), N(1440), N(1520), N(1535), Δ(1620), N(1650), and Δ(1700)), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the parameters of the nucleon resonances on the basis of world data on electromagnetic multipoles. We present results for electromagnetic multipoles, differential cross-sections, asymmetries, and total cross-sections for all one pion photoproduction processes on free nucleons. We find overall agreement with data from threshold up to 1 GeV in laboratory frame.     

A critical study of finite energy sum rule difficulties in pion photoproduction

The difficulties that have emerged in recent phenomenological applications of pion photoproduction FESRs are surveyed and analysed. The main cause of failure, it is concluded, is the systematic lack of suitable cancellations among low-lying resonance poles, which are necessary to ensure the correct FESR reproduction of high-energy zeros. In order for such cancellations to hold, definite conspiracies among the relevant resonance poles should exist. Conspiracies of this type are indeed found to be an essential ingredient in the Veneziano model to have FESRs satisfied, and a number of instances of them are shown to actually occur in π^?p → π⁰n. The observed low-lying pole conspiracy default in pion photoproduction is traced back to spin complications which are higher in this process than in the FESR successful case of π^?p → π⁰n. Moreover, in general the interplay of FESRs and spin structure is shown to be far from trivial, and governed by rules (supposing that they exist) yet to be established.     

Smoothness of pion amplitudes and PCAC

We point out the essentially obvious result that if the massless pion amplitude is the smooth finite limit of the massive pion world, the Adler self-consistency condition must be true.     

Neutral pion photoproduction from protons at forward angles in the energy region between 350 MeV and 1175 MeV

The differential cross section for the reaction γp → π⁰p at forward angles has been measured in the energy region between 350 MeV and 1175 MeV. A phenomenological multiple analysis was carried out on the present data together with other data.     

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.     

Quark-hadron duality and meson-meson scattering amplitudes

We investigate a special concept of quarkhadron duality in meson physics at low and intermediate energies. With a relativistic propagator for confined quarks, we calculated masses and widths of the mesons which areS- andP-wave states ofq¯q (J ^P=0^?, 1^?, 0⁺, 1^+c, 2⁺) as well as meson-meson scattering amplitudes at energies up totrs ≤ 1.3 GeV by including light pseudoscalar and vector mesons into the interaction dynamics. Our investigation shows that the influence of the light meson dynamics resutls in:

1. a contribution to the constituent quark mass of approximately 200 MeV.
2. the appearance of a new soft confinement force barrier responsible for the formation of the highly excited meson states.