Theoretische Untersuchungen zur Asymmetrie der Pionphotoproduktion mit einem polarisierten Target

The theoretical importance of experiments with polarised targets for pion photoproduction at high energies is discussed. In an introductory chapter the basic formulas and simple Regge pole models are introduced in connection with elastic pion-proton scattering. The relevance of Regge-cut models is considered in connection with pion-charge-exchange scattering. In the main part we write down formulas for the polarisation parameters in terms of the helicity amplitudes for pion photoproduction. Then we concentrate on the target asymmetry A for photoproduction of neutral and charged pions. Several models with Regge poles and Regge cuts generated by absorption are presented and discussed concerning the results forA. In the last part we report a fit to π^± photoproduction data and give predictions of A for γp → π⁺n and γn → π−p.     

Near-Threshold Photo- and Electroproduction of Neutral Pions on Protons

The state of the art of the problem on threshold neutral-pion production on protons by photons and electrons is examined. New experimental data on the threshold of pion production are analyzed within the phenomenological model based on the gauge invariance, the hypothesis of partial conservation of the axial-vector current, and allowance for obvious chiral-symmetry breaking. The amplitudes of the p-wave threshold multipoles and the photon asymmetry are derived for the pion photoproduction on protons with a photon energy of 159.5 MeV. The differential cross sections are calculated as functions of the pion emission angle and amplitudes of the s- and p-wave multipoles for the threshold pion electroproduction on protons at the squared momentum transfer k ² = 0.05 GeV²/c². The total reaction cross sections are also obtained as functions of k ². The results obtained are compared with new experimental data and available theoretical predictions.     

Initial State Interaction in the (π+,3p) Reaction on N, Ar and Xe

The pion absorption reaction (π^{+,3 p} ) on Ar was studied at pion energies of 70, 118, 162 and 239 MeV, and on N and Xe at 239 MeV. The 3p cross section with a 50 MeV cut on the missing energy is presented. The existence of an initial state interaction (ISI) component to the reaction was investigated. The portion of the 3p cross section assigned to the ISI process is less than one half and at lower energies significantly so. Received: 11 December 1997     

A relativistic description of πd scattering: Effects of small πN waves,NN rescattering, ρ-exchange and π absorption and emission

Using a relativistic three-body theory we calculated elastic differential cross sections, polarisations and total cross sections for pion-deuteron scattering in the (3, 3) resonance region. Effects of pion absorption and emission have been calculated rigorously, including pion rescattering effects and ρ-meson exchange to all orders. Inclusion of pion absorption and emission produces appreciable changes in the large angle differential cross section and in all polarisation parameters. The inclusion of non-resonant πN partial waves leads to significantly improved agreement with experiment for T_π = 142 MeV and at forward angles for 256 MeV. None of these effects, nor the inclusion of selected NN partial waves other than ³S₁-³D₁, produces the deep minimum observed at 256 MeV.     

Pion-nucleus optical potential: The pion-absorption contribution

The real and imaginary parts of pion-nucleus optical potential arising from pion absorption channel have been computed. A two-nucleon model of pion absorption which includesπ andρ rescattering andS-wave interaction has been used. The effects of short-range nucleon-nucleon correlations, Pauli blocking and formfactors have been included. The threshold values of imaginary absorption potential are reasonably close to density-squared terms of phenomenological potentials. The real part ofP-wave potential is attractive and that ofS-wave potential is weakly attractive at lower pion energies and changes sign as pion energy is increased. The calculation shows that the real part of absorption is significantly affected by short-range correlations and Pauli-blocking.     

Pion absorption and proton k.o. reaction in4He

The experimental results obtained by the Torino—Dubna—Frascati collaboration in the study of the ⁺ absorption in⁴He and of the⁴He ³H knock-out reactions induced by ⁺ and ^– mesons are presented. The analysis of the data shows that the absorption by a quasideuteron is the principal mechanism as in the case of the ⁺ absorption in light nuclei, that the isobaric resonance excitation is dominant in the proton k.o. reactions, that the pion interaction on quasi-free³H is not negligible. The quasi-free processes appear to play a major role in the nonelastic pion interaction on nuclei, but the clustering effects are also important.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.It seems to be possible to conclude that in the future important nuclear information will be extracted in the accurate study of the different channels of pion interactions with nuclei.     

On the reactions pp ↔ dπ+

The total cross section for π⁺d → pp and the angular distribution and asymmetry parameters for the inverse reaction $\text{p}\text{p}\text{→ π}{}^{\mathrm{+}}\text{d}$ have been calculated with different models for the pion absorption (and production) operator and several sets of nuclear wave functions. The absorption operator includes both single-nucleon and two-nucleon operators. Fair agreement can be achieved with all empirical parameters at low energies, but significant discrepancies occur at high energies. The results are very sensitive to the model for the nucleon-nucleon interaction used to generate the wave functions.     

Asymptotic bounds on pion form factor

A technique recently developed for inelastic electron proton scattering is applied for inelastic electron pion scattering. It is found that all the derivatives of off-shell form factor of pion nears=m _π ² and for largeQ ² are bounded from above, provided that the dispersion relation for the form factor requires no more than one subtraction. The elastic pion form factor is bounded by [lnQ ²] ^c /Q ², wherec is any positive constant.     

A study of the generalized Schwinger model in the Hamiltonian formulation

Semileptonic τ decays to two and three pions are considered. Based on recent data for the pion form factor a new prediction for Γ(τ→vπ^{- 0})/Γ(τ→vev_e) of 1.32±0.05 is derived. The chiral model-supplemented by vector dominance-is used to predict rate and differential distributions for the three pion mode in good agreement with present data. The parity violating asymmetry which has been predicted theoretically and observed experimentally is studied and found to be fairly insensitive towards the details of the model for the hadronic decays.     

Nuclear pion absorption and the axial exchange-charge operator

We demonstrate the equality between the axial exchange-charge density operator and the phenomenological two-body rescattering model for the S-wave pion absorption operator in nuclei. The equivalence appears in a natural way in the Skyrme model in which the pion-nucleus vertex is given by the axial charge density of the nucleus. As a consequence there is a close relationship between the rates for nuclear pion absorption and weak ΔT = 1, 0⁺↔0⁻ transitions.     

Charged Particle Production in Stopped Pion Absorption by Nuclei

The spectra of ^3,4He charged particles produced in stopped pion absorption by nuclei were measured for 17 nuclei in the mass-number range of 6 ≤ A ≤ 209 by means of a semiconductor spectrometer. These data were analyzed on the basis of a phenomenological model where the absorption reaction in question is treated as a three-stage process: primary absorption by intranuclear clusters, preequilibrium stage, and evaporation stage. It is shown that a dominant contribution to the production of helium isotopes with energies not less than 20 MeV comes from the preequilibrium stage. The contribution of the knockout and pickup mechanisms to ^3,4He production is estimated.

     

Branching ratio for radiative pion capture in 6Li and 12C

The radiative pion capture rate in ¹²C and ⁶Li leading to bound final states is calculated using the impulse approximation. The T-matrix is obtained from the time-reversed pion photo-production amplitude and initial-state distortion of the bound pion is taken into account. Using recently published capture schedules for pionic atoms the branching ratio R is calculated and compared to experimental values. The agreement is excellent if those experimental values are used that have been obtained by direct observation of the emitted γ-ray and if an optical-model value for the total 2P absorption width in ¹²C is used.     

Theoretical study of deuteron polarization in γ+d → π0+d

The state of polarization of the recoil deuteron in γ+d → π⁰+d on unpolarized and target polarized deuterons is analyzed in detail. A new set of statistical tensors is introduced to describe non-oriented systems, such as the recoil deuteron in γ+d → π⁰+d, and their relationships to the vector and tensor polarization parameters are established. The new statistical tensors reduce, in the case of oriented systems, to Fano's statistical tensors. Numerical results are computed using two different deuteron models for polarized photon asymmetry, polarized target asymmetry and the vector and tensor polarizations of the recoil deuteron, and these are presented at various c.m. pion production angles at different energies in the region of the first π-N resonance. The study of these parameters is suggested as a promising source of information on isoscalar pion photoproduction amplitudes.     

Hadron production near threshold

Final state interaction effects inpp→ pΛK ⁺ andpd →³Heη reactions are explored near threshold to study the sensitivity of the cross-sections to thepΛ potential and theηN scattering matrix. The final state scattering wave functions between Λ andp andη and³He are described rigorously. The Λ production is described by the exchange of one pion and aK-meson between two protons in the incident channel. Theη production is described by a two-step model, where in the first step a pion is produced. This pion then produces anη by interacting with another nucleon     

Production of charged pions, kaons and antikaons in relativistic C + C and C + Au collisions

Production cross-sections of charged pions, kaons and antikaons have been measured in C+C and C+Au collisions at beam energies of 1.0 and 1.8 AGeV for different polar emission angles. The kaon and antikaon energy spectra can be described by Boltzmann distributions whereas the pion spectra exhibit an additional enhancement at low energies. The pion multiplicity per participating nucleon M(π⁺)/<A _part> is a factor of about 3 smaller in C+Au than in C+C collisions at 1.0 AGeV whereas it differs only little for the C and the Au target at a beam energy of 1.8 AGeV. The K⁺ multiplicities per participating nucleon M(K⁺)/ <A _part> are independent of the target size at 1 AGeV and at 1.8 AGeV. The K^- multiplicity per participating nucleon M(K^-)/ <A _part> is reduced by a factor of about 2 in C+Au as compared to C+C collisions at 1.8 AGeV. This effect might be caused by the absorption of antikaons in the heavy target nucleus. Transport model calculations underestimate the K^-/K⁺ ratio for C+C collisions at 1.8 AGeV by a factor of about 4 if in-medium modifications of K-mesons are neglected. Received: 10 December 1999 / Accepted: 14 November 2000     

Study of correlation of production and decay planes in π → 3π diffractive dissociation process on nuclei

A large correlation of production and decay planes of the π^?π⁺π^? system in dissociation of a 40-GeV/c π^? beam on nuclear targets was observed. The dependence of the correlation on atomic number, Feynman variable, and transversal momentum, as well as on invariant mass of the pion triple and neutral pion pair, was investigated. It was shown that the phenomenon has a clear dynamical origin and resembles the single-spin asymmetry behavior.     

Low energy pion absorption and the quasi-deuteron mechanism

We have re-examined the quasi-deuteron model for pion absorption in complex nuclei. A purely phenomenological parametrization of the π NN → NN absorption operator is constructed, based on a partial wave decomposition. For low energy pion absorption on NN pairs in relative s-states, six partial wave amplitudes enter. We apply our model to the absorption of stopped pions. Within a PWIA we first clarify which information is contained in the various (π⁻, nn) coincident distributions. Realistic DWIA calculations have been performed for ¹²C and ¹⁶O and compared with both inclusive and exclusive data. It appears that most existing data can be understood independently from any detailed dynamical model for the elementary absorption process. An upper limit on absorption mechanisms other than quasi-deuteron absorption of 25% at threshold has been obtained.     

Investigation of low energy pion-nucleus interaction using electrofission data for heavy nuclei at the pion threshold

A theoretical approach to describe electro- and photofission processes at intermediate energies was worked out. Photopion reabsorption mechanisms by two and three nucleons (2NA and 3NA) were incorporated in the calculations. The comparison with electrofission data for preactinides showed that a substantial 3NA component should be added in the pion absorption to fit the data near photopion threshold, in accordance with a recent theoretical estimate. It was also shown that the shape of the fission response curve is sensitive to detailed aspects of the pion mean free path. Received: 10 March 1998 / Revised version: 12 March 1999     

Contributions of γd → πNN + π0 d channels to the spin asymmetry and the Gerasimov-Drell-Hearn integral for the deuteron

Contributions from the semi-exclusive channels γd → π^± NN + π⁰ d and γd → π⁰ X (X=pn or d) to the deuteron spin asymmetry and the Gerasimov-Drell-Hearn (GDH) integral are explicitly evaluated using an enhanced elementary pion photoproduction operator and a realistic, high-precision potential model for the deuteron wave function. The sensitivity of the results to the elementary pion photoproduction operator is also investigated and considerable dependence is found. Results for the deuteron GDH integral are compared with the measurements from A2 and GDH@MAMI Collaborations.     

Pion form factor in QCD: How to calculate?

The calculation of the pion form factor F _π(Q ²) in QCD is discussed. The main points of the nonlocal condensate QDC sum rule approach are considered and its results for the pion form factor are shown compared with the predictions of the perturbative and lattice QCD. The local duality (LD) approach for the pion FF in QCD is studied. It is shown that the main parameter of the approach for Q ² ≥ 2 GeV², namely, s ₀^LD(Q ²) should grow with an increase in Q ², rather than remain constant.