The real part of the non-flip amplitude in πN charge exchange scattering

We evaluate the real non-flip amplitude for πN charge exchange from high energy polarization data and also from phase shift analyses. The implications of this evaluation for current high energy models is noted.     

Testing of analyticity of the πN forward scattering amplitude and the determination of the πN coupling constant

We propose a new method for the testing of analyticity. Instead of using dispersion relations with traditional uncertainties in estimating the errors of the principal value integrals we work with a suitably defined set of moments.As an example we discuss the pion-nucleon CEX forward amplitude. The results indicate that the errors of the phase shift analysis used should probably be increased by a factor of two. Taking this into account we calculate the pion-nucleon coupling constant by analytic extrapolation and we find f² = 0.0835 ± 0.0040.     

Cross sections and asymmetries for elastic π3He scattering in the energy region around the Δ resonance

For a polarized target, π³He interaction is studied in the fixed-center approximation with all rescatterings included. Only the P ₃₃ wave is taken for the πN interaction. The nuclear wave function is taken either as a sum of Gaussian functions or as a Faddeev wave function in the s-wave approximation. The differential cross sections and asymmetries for elastic π⁺³He scattering at the laboratory energies of T _π, 180, and 256 MeV are calculated. The results are compared with experimental data.     

On the decoupling of a second RHO in forward πN scattering

A general sum rule is used to provide accurate information about the Regge ϱ parameters in the forward direction. When combined with high energy data an upper limit for a ϱ′ pole is placed at one-tenth the strength of the ϱ pole.     

Coherent π+ photoproduction on 3He in the region of the Δ1236 resonance

An experimental study of the ³He(γ, π⁺)³H reaction has been performed in the region of the Δ₁₂₃₆ resonance between 227 MeV and 453 MeV. The experiment shows two main features: at fixed four-momentum transfer q², the resonance is shifted towards lower energies, this shift increasing with q²; at a fixed angle, but variable q², the minimum of the charge form factor observed in the elastic scattering of electrons on ³He does not appear. Recent calculations explain partly these two effects. This experiment might be used as part of a test of time-reversal invariance in the electromagnetic interaction of hadrons.     

Positivity as a constraint on the positions of the zeros of theK − p forward scattering amplitude

Stringent constraints on the positions of the zeros of theK ^? p forward scattering amplitude in the complex energy plane are obtained using only information on the modulus of the amplitude on its cuts, together with the requirement of positivity of the imaginary part of the amplitude in the physical region.     

Photoemission of protons from4He in theΔ-resonance region

High resolution proton energy spectra from the⁴He(γ,p) reaction have been measured with tagged photons in the range E_γ = 130?525 MeV using the large Mainz NaI(T1) spectrometer atΘ _p ^lab =37.1°. Three separate reaction channels were identified, viz.⁴He(γ,p)t two-body breakup,⁴He photodisintegration via two-nucleon photon absorption processes and the quasifree pion production channel. Differential cross sections are presented for each of these channels as a function of photon energy. The sum of the two-nucleon photon absorption and the quasifree pion production differential cross sections, in the CM system, resembles that of the corresponding free-nucleon differential cross section when Fermi motion is taken into account.     

Local duality in the invariant amplitudes for πN scattering

Local duality for πN scattering in the low- and intermediate-energy regions is investigated from comparisons of the invariant amplitudes constructed from phase-shift data with the interpolated Regge ones.The following results are obtained: (i) Local duality is satisfied with the order A ′⁽⁺⁾, B⁽⁻⁾, A ′⁽⁻⁾ and B⁽⁺⁾. In particular, local duality for the A ′⁽⁺⁾ amplitude is valid even for the c.m. energy down to 1.5 GeV and finite t-region. (ii) The crossing-even amplitudes having excellent local duality are made up constructively by the prominent resonances which lie on the leading trajectories and have the regularity of the Kycia-Riley rule. (iii) The Freund-Harari conjecture is examined for isospin nonflip amplitudes A ′⁽⁺⁾ and B⁽⁺⁾. The conjecture works well for the imaginary part but not for the real part. Moreover, the modified interference model proposed by Coulter, Ma and Shaw is also examined for the B⁽⁻⁾ amplitude: The real part of the background term fills up the dip near t = −0.6, in contradiction with the observations.     

Determination of the πN charge exchange scattering amplitude from the experimental data at high energies

The difference between theπ ⁺ p andπ ^? p diffraction peaks is used for an estimate of the imaginary part of the charge exchange scattering amplitude. The imaginary part has a narrow peak in the forward direction and passes over to negative values at a momentum transfert of about ?0.15(GeV/c)². If the charge exchange amplitude is dominated by the contribution of theρ Regge pole, the peak is mainly due to thet-dependence of the residue function and a narrow forward peak is expected in the charge exchange angular distribution.     

Elastic π±-d and π±-4He scattering below 70 MeV

Elastic scattering differential cross section data of ^± d at 65 MeV and ^{± 4}He at 51 MeV are presented and compared respectively to fully relativistic 3-body and optical potential calculations including true pion absorption.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

P-Odd effects in the γ+He4 → He4 + π0 reaction

P-Odd effects with the elastic photoinformation of neutral pions in He⁴ nuclei are due to the interference of the P-odd amplitude of weak interaction with the P-even amplitude of strong interaction, and originate only for polarized photons. It is shown that close to the reaction threshold P-odd effects should be small. The interference amplitude of the mechanisms corresponding to exchange with a Regge or-pole and a neutral Z-boson at high energies is studied. P-Odd effects in this case increase with increase of energy of the interacting particles and with the square of the imparted momentum. P-Odd effects due to interference of the s ingle-photon and Z-boson mechanisms are also investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 71–76, September, 1978.     

Analyticity of scattering for the ϕ4 theory

We consider scattering for the equation (+m ²)+³=0 on four-dimensional Minkowski space. Form>0, one-to-one and onto wave operatorsW _± :HH are known to exist for all 0, whereH denotes the Hilbert space of finite-energy Cauchy data. We prove that the maps (,u)W _± (u) and (,u)(W _± )^–1 (u) are continuous from [0, )×H toH, and extend to real-analytic functions from an open neighborhood of {0}×H×{0}×H to the Hilbert spaceH _–1 of Cauchy data with Poincaré-invariant norm. Form=0, wave operatorsW _± are known to exist as diffeomorphisms ofH for all 0, where hereH denotes the Hilbert space of finite Einstein energy Cauchy data. In this case we prove that the maps (,u)(W _± ) (u) and (,u)(W _± )^–1 (u) extend to real-analytic functions from a neighborhood of [0, )×H×H toH.     

Polarization in the high-energy πp charge-exchange scattering

Phenomenological discussion of the polarization parameter P_ex in high-energy πp charge-exchange scattering is given following the suggestions of Białas and Svensson. The sign and the energy dependence of P_ex are estimated and found to agree with the present experimental data.     

Charge-symmetry-breaking effects from phase-shift analysis of elastic π± He scattering

A phase-shift analysis of elastic π^±4 He scattering at energies 20–160 MeV was performed to determine pure hadronic phase shifts. No statistically significant difference between the hadronic phase shifts deduced from π⁺⁴ He and π⁻⁴ He scattering was observed.     

Electroproduction of πo mesons in the region of the first pion-nucleon resonance

The reaction e⁻+p→e⁻+p+π^o has been studied in the π−N centre of mass range from 1130 to 1340 MeV/c² by detecting the final proton in coincidence with the scattered electron. The four-momentum transfer to the pion-nucleon system was between 0.40 and 0.50 (GeV/c)² and the polarisation of the exchanged virtual photon near unity. The proton angular distribution is analysed phenomenologically in terms of the multipoles M₁₊, E₁₊, S₁₊ contributing to the resonant partial wave and E_o+, S_o+ contributing to the s-wave background. The magnetic dipole excitation M₁₊ is shown to dominate the cross section but clear evidence is obtained for a significant contribution from the scalar multipole S₁₊.