Chew-Low Extrapolation Research Articles

Phenomenological πN→ππN amplitude and the modelling of the Olsson–Turner and Chew–Low approaches

The phenomenological amplitude for the reaction πN→ππN fixed by fittings to the experimental data in the energy region 0.300 ≤PLab≤ 500 MeV/c is used for modelling the Chew–Low extrapolation and Olsson–Turner threshold approach. It is shown that the uncritical application of the former results in enermous theoretical errors, the extracted values being in fact random numbers. The results of the Olsson–Turner method are characterized by significant systematic errors coming from unknown details of the isobar physics.

Phenomenological πN→ππN amplitude and analysis of low energy data on total cross sections and 1--D distributions

We develop the phenomenological amplitude of the $\pi N \to \pi \pi N$ reaction describing the exchanges of $\Delta$ and $N_{*}$ along with the OPE mechanism. The contribution of the latter contains 4 independent low energy parameters (up to $O(k^{4})$ order). The terms of the polynomial background are added to stand for far resonances and for contact terms originating from the off-mass-shell interactions. These terms are introduced with the account of isotopic, crossing, $ C $, $ P $ and $ T $ symmetries of strong interactions. The data consisting of total cross sections in the energy region $ 0.300 \le P_{Lab} \le 500 $~MeV/c and 1D distributions from the bubble-chamber experiments for three reaction channels were undergoing fittings to determine free parameters of the amplitude. The best solutions are characterized by $ \chi^{2}_{DF} = $ 1.16. At the considered energies the isobar exchanges are found to be more important than OPE. The obtained solutions reveal the need in more precise data and/or in polarization measurements because of large correlations of isobar parameters with the OPE ones. The theoretical solutions were used for modeling the Chew-Low extrapolation and the Olsson-Turner threshold approach. It is shown that the noncritical application of the former results in 100% theoretical errors, the extracted values being in fact the random numbers. The results of the Olsson-Turner method are characterised by significant systematic errors coming from unknown details of isobar physics.

On the influence ofK + diffractive dissociation (Q production) on a test of extraction of ?+ p elastic scattering fromK+ p ? K* (890)?+ p at 12 GeV/c by Chew-Low extrapolation

In a study of the reaction K+ p → K* (890)π+ p at 12 GeV/c it has been shown that the extrapolated moments in thet channel for the π+ p system do not agree very well with those calculated from the real π+ p elastic scattering phase shifts for π+ p effective masses larger than 1.4 GeV, and that theQ is dominant in this region even for very small momentum transfer. In the present work it is shown that a simple parametrization of theQ leads to a considerably better description of the extrapolated 〈Y 0 2 〉, 〈Y 0 3 〉 and 〈Y 0 4 〉 moments. Furthermore it is shown that the dominance of theQ in this region will lead to high order moments at low mass in thes-channel frame.

The quasi-free 3He(e, e′p) reaction

The proton spectral function has experimentally been determined with the 3He(e, e′p) reaction for missing energies, 0< E m<70MeV, and recoil momenta, 0< P B<310 MeV/ c. Experimental results are obtained for both the two-body, 3He(e, e′p) 2H, and three-body breakup processes. Proton momentum density distributions, obtained in a PWIA analysis, are compared with theoretical calculations: Faddeev solutions with the RSC and Paris potentials, and variational calculations with various potentials, including those with a three-nucleon interaction term. Energy-weighted sum rule results are presented and compared with theoretical predictions. The coincidence cross sections are also compared with calculations which include the effects of final state interactions and meson exchange currents. Consistency of the results with PWIA is investigated in the framework of the Chew-Low extrapolation procedure.

SU(3), the2+nonet, and gluonic bound states

Theoretical curves based on the one-pion-exchange Chew-Low extrapolation scheme have been fitted to the moment distribution curves obtained from ..pi../sup -/p..-->..K/sup +/K/sup -/n and ..pi../sup +/n..-->..K/sup +/K/sup -/p. A sign difference is found between the coupling constants of the processes allowed by the Okubo-Zweig-Iizuka (OZI) rule and the OZI-rule-forbidden processes which contradicts the sign difference found from the chi/sup 2/ /sub min/ fit of most of the tensor-meson-nonet decay rates. We explore a way to resolve this contradiction by introducing a non-qq-bar admixture.

Analysis of quasi-free scattering data in the impulse approximation

We propose a set of variables to be used in place of the customary energies and angles in the analysis of quasi-free scattering data. In terms of these variables one can reduce the usual fivefold differential cross section to a threefold differential including the effects of experimental acceptance without resorting to Monte Carlo techniques. In this form the dependence of the data on nuclear and two-particle variables is clearly separated. Finally, two simple tests of the impulse approximation, the Treiman-Yang test and the Chew-Low extrapolation, can be applied directly to the data in particularly simple form.

Study of the inclusive reaction K +p → Δ++(1232) + X 0 at 32 GeV/ c

Inclusive production of Δ ++(1232) with >| t p, Δ ++>|<0.6 (GeV/ c) 2 is studied in 32 GeV/ c K +p interactions. A systematic comparison with the reaction K +p→pX for >| t p,p>| < 0.6 (GeV/ c) 2 is made. The production properties of the Δ ++(1232), of associated π +, π − and K 0 production and of the recoiling system X 0 are investigated in detail. The polarization of the Δ ++ and the energy dependence of the total K + π − cross sections, determined by a Chew-Low extrapolation, are presented and discussed.

Results onπ+π−→π0π0cross section from peripheral dipion production in the reactionπ−p→π0π0nat 2.01 GeV/c

We report results on ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ total and differential cross sections from threshold to 1.1-GeV $\ensuremath{\pi}\ensuremath{\pi}$ mass. These results have been obtained from a high-statistics experiment studying the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}n$ at 2.01 GeV/c incident ${\ensuremath{\pi}}^{\ensuremath{-}}$ momentum with the Chew-Low extrapolation method. The ${\ensuremath{\pi}}^{0}$'s have been detected and their momenta analyzed in a large-gap cylindrical spark chamber placed in a magnetic field. The results show three salient features: (i) A large $I=0$ production with ${\ensuremath{\sigma}}_{\mathrm{tot}}({\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0})$ approaching the $S$-wave unitarity limit in the 550-750-MeV $\ensuremath{\pi}\ensuremath{\pi}$ mass region, without any narrow structure. (ii) A slow fall of ${\ensuremath{\sigma}}_{\mathrm{tot}}({\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0})$ in the region of 750-950-MeV $\ensuremath{\pi}\ensuremath{\pi}$ mass. This feature is not predicted by the "down" solution for the $I=0$ $S$-wave $\ensuremath{\pi}\ensuremath{\pi}$ phase shift which has been reported recently. (iii) The presence of $D$-wave effects above 850 MeV as indicated by our extrapolated angular distributions.

Cross-section measurement for the reaction π+π+ → π+π+π+π− in the quad-pion mass region 1.5–1.9 GeV

We report on a study of inelastic π +π + scattering using the reaction π +p → n π + π + π + π − at an incident π + momentum of 10.3 GeV/ c. The inelastic π +π + scattering cross section in the quad-pion mass region 1.5–1.9 GeV has been extracted using both a pure and a modified Chew-Low extrapolation to the pion pole. The latter appears to give an excellent description of the experimental data.

Study of K −π − inelastic scattering from K −p interactions at 4.2 GeV/ c

The isospin I = 3 2 K −π − inelastic scattering cross section is determined from the reactions K − p→Δ ++ ( K + pions) −− at 4.2 GeV/c incident K − momentum, using a Chew-Low extrapolation method. The available statistics also allowed a determination of the cross sections for individual K −π − reactions by this method. The total inelastic K −π − scattering cross section is found to increase almost linearly with K −π − mass from <0.1 mb at 0.9 GeV to 2.3 mb at 1.5 GeV. Below 1.3 GeV only the reactions K − π − → (K ππ) −− contribute to the inelastic cross section; higher multiplicity K −π − interactions start to play a rôle above this mass.

Determination of the K +π− total cross section for c.m. energy up to 1.8 GeV

The reaction K +p → Δ ++(1236) + anything is studied at beam momentum 8.2 GeV/ c. The spin density matrix of the Δ ++ shows than one-pion exchange is dominant at low-momentum transfer. The total and topological K + π − cross sections have been determined by a Chew-Low extrapolation in the cm energy range from threshold to 1.8 GeV, using three different methods of extrapolation.

Study of the K +π − total cross section for c.m. energy up to 3.4 GeV

The reaction K +p→Δ ++(1236) + anything is studied at a beam momentum of 16.0 GeV/ c. The total and topological cross sections for K +π − interactions are estimated by a Chew-Low extrapolation from threshold to the c.m. energy of 3.4 GeV by the maximum likelihood method.

Isotensor π- π phase shifts below the ρ mass

We present the results of a Chew-Low extrapolation of the reaction π +p → π + π +n at pion beam momenta 1.4 and 1.5 GeV/ c. By extrapolating the π + π + → π + π + cross section and the asymmetry of the π- π angular distribution, isotensor ( I = 2) S and D waves were determined at energies up to the ϱ mass. Our S wave was greater than previous estimates, and our D wave roughly constant at a value of −1 1 2 ° , much greater than the Lovelace-Veneziano prediction.

Study of the [formula omitted] scattering amplitude (I). Threshold to 1 GeV mass region

Kπ scattering from threshold to 1 GeV in Kpi; mass is studied by modified Chew-Low extrapolation in the reactions K −p→K − π +n and K +n→K + π −p. Although the cross section and moments of these two reactions differ significantly in the physical region, similar values are found for the Kπ phases in the two processes. The necessary modifications of one pion exchange are sizeable and although they do not agree quantitatively with the poor man's absorption model, they can be understood in a more general absorption framework. The experimental Kπ s-wave scattering length is much larger than naive current algebra predictions but consistent with a straight forward dispersion theory method of extrapolating current algebra to the physical region.

Determination of the K −π− inelastic cross sections for c.m. energy up to 2.8 GeV

The reaction K −p→ Δ ++ + anything was studied at 14.3 GeV/ c and is production mechanism was found to be consistent with one pion exchange at low momentum transfer. K − π − inelastic and total cross sections have been determined by a Chew-Low extrapolation method in the c.m. energy range from threshold to 2.8 GeV. Cross sections for various K − π − final states are presented.

A study of π−π− scattering from π−p interactions at 3.93 GeV/c

A modified Chew-Low extrapolation procedure is applied to the reaction π −p→ Δ ++ π − π − to extract the I = 2 ππ elastic cross sections from threshold to 1260 MeV. The predictions of the one-pion-exchange model are used to estimate the contributions from background processes of the type π −p→ Δ 0 ϱ 0. The moments of the π − π − angular distribution are also extrapolated to the pion pole and a phase shift analysis performed. The s-wave inelasticity is constrained using information on the inelastic cross section coming from six-body final states. The magnitude of the s-wave phase shift at the K 0 mass is found to be 7.2 0 ± 1.0 0, increasing to 26.2 0 ± 2.5 0 at 1 GeV. d- and g-waves contribute above about 900 MeV, but the corresponding phase shifts are small compared with the s-wave. All three phase shifts have the same sign.

Measurement of the reaction γd → π−pp, and determination of cross sections for the reaction γn → π−p, at photon energies between 0.2 and 2.0 GeV

The reaction γd→ π −pp has been measured in a bubble chamber experiment at DESY with a bremsstrahlung beam of E γ max = 5.5 GeV. Total and differential cross sections are presented for the energy region from 0.2 to 2.0 GeV. The extraction of cross sections on the neutron is discussed in detail. The impulse approximation and the closure relation, with corrections for the exclusion principle and the Fermi motion effects, as well as the Chew-Low extrapolation technique are applied. Total cross sections and angular distributions for the reaction γn→ π −p, deduced by these methods, are presented in graohs and tables. The results are compared with other experiments and with various predictions. No positive evidence for an isotensor electromagnetic current is found. The results disagree with some of the measurements of radiative pion capture, if detailed balance is assumed to connect the two reactions.

Study of the I=2 ππ scattering from the reaction π−d → π−π−p sp at 9.0 GeV/ c

We have studied the I=2, ππ scattering using the classical Chew-Low extrapolation method. Results are given on the cross sections and the phase shifts δ 0 2, δ 2 2 and δ 4 2 up to 2.2. GeV. δ 0 2 values are -7.8 ∓ 3.0° at the K o mass, -15. ∓ 1.5° at the ϱ mass and -29. ∓ 2.2° of the f o mass. Above the f o mass | δ 0 2| decreases.

ππ scattering in the I = 2 channel

I=2 π + π + scattering is studied in π +p reactions at 5.45 GeV/ c. The π + π + cross sections and phase shifts have been determined from the reaction π +p → π + π +n using first a pure and then a modified Chew-Low extrapolation to the pion pole.

K−π− elastic scattering cross section measured in 14.3 GeV/c K−p interactions

Results are presented on a measurement of the I = 3/2 Kπ elastic scattering cross section by applying the Chew-Low extrapolation method in the reaction K−p → K−π−Δ++at14.3GeV/c. The magnitude of σ(K−π− → K−π−) is found to be about 3 mb at threshold and slowly falling with energy to about 1.5 mb at 2.8 GeV. The off-mass-shell moments of the differential elastic cross section are given. The absolute value of δ30 is found to be increasing slowly from 0° to 20° between threshold and 1.2 GeV.