Symmetry constraints in optimal polarization formalisms with an application to p−p scattering

The paper contains results (a) for the general optimal polarization formalism with constraints from time reversal invariance, identical particles, and parity conservation, (b) for the specific reaction involving four $\text{spin}\text{-}\text{1}\text{2}$ particles, (c) for the application of the formalism to elastic p?p scattering at 6 GeV/c and at 800 MeV. The choice of the orientation axes under various symmetry constraints is discussed for the general optimal formalism, showing the narrowing of the choices which nevertheless retains an infinite continuum of possibilities. The transformation properties of amplitudes among these various optimal frames are specified. The transformation of observables among these frames is also discussed for the reaction with four $\text{spin}\text{-}\text{1}\text{2}$ particles. Then the relationship between the observables and the bilinear combination of amplitudes is given for the reaction with four $\text{spin}\text{-}\text{1}\text{2}$ particles, for the constraints of identical particles, identical particles and time reversal invariance, and identical particles and time reversal invariance and parity conservation. The results are applied to the analysis of the Argonne data at 6 GeV/c, t = ?0.6 GeV²/c², for elastic p?p scattering. The amplitudes are easily determined when the proper optimal frame is used, and the display of the amplitudes in other optimal frames suggest some features that may be significant in searching for dynamics. Another application is presented to 800 MeV elastic p?p scattering at several angles, showing that in the proper optimal frame very accurate results can be obtained about a subset of amplitude parameters on the basis of an incomplete set of data. Such an analysis is shown to be helpful in the design of future experiments.     

Impact parameter analysis of KN and πN scattering in the intermediate energy region

We have evaluated the s-channel-helicity partial-wave amplitudes for $\text{K}\text{N and πN}$ scattering as functions of the impact parameter using partial-wave data in the energy range P_L≈1.0–2.0 GeV/c. We find that the $\text{K}\text{N}$ background and resonance amplitudes exhibit features consistent with the dual absorptive picture for pomeron and f + ω and A₂ + ? exchanges. Comparison of the πN low-energy amplitude with the partial-wave decomposition of a quantitative Regge model gives evidence for local duality between the s-channel resonance and t- and u-channel Regge exchanges.     

On the rigorous determination of the spin-0-spin-12 elastic scattering amplitudes from experimental data and unitarity

The contraction-mapping principle is used to study rigorously the elastic unitarity equations for the scattering of a spin-0 particle by a $\text{spin}\text{-}\text{1}\text{2}$ particle when the unpolarized differential cross section dσ/dΩ and the polarization P at fixed energy below the first inelastic threshold are known from experiment. It is shown that when dσ/dΩ, P and the region where the scattering amplitudes are searched are suitably restricted, the scattering amplitudes exist, are unique and can be found by iterating the unitary equations. Besides, there are other solutions outside that space associated with well-known ambiguities. We show that those ambiguities are solved by measuring the parameters R and A and the sign of the real part of the forward amplitude.     

Single-pion production in antiproton-proton interactions

Single-pion production in $\text{p}\text{p}$ interactions at 9.1 GeV/c is analysed and cross sections are given. The p_lab dependence of the isospin amplitudes is determined by a fit to the world data. The data are also compared with the predictions of a reggeized Deck model. The results and the $\text{N}\text{π}\text{N}$ amplitudes are compared with the results at other energies and with the corresponding NπN amplitudes.     

Features of diffractive scattering and the nature of the N1(1400) observed in NN→N(Nπ) reactions at 5.7 GeV/c

The results for the diffractive scattering contribution ($\text{F}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^0$) obtained in a cross channel isospin analysis of the $\text{N}\text{N}\text{→}\text{N}\text{(}\text{N}\text{π)}$ reactions at 5.7 GeV/c are compared with those obtained for other ZN → Z′(Nπ) reactions where Z stands for N, π and the carbon nucleus. The dependence of the diffractive scattering on the mass M_πN and the momentum transfer t seems very weakly related to the nature of Z and the incident momentum.A comparison between amplitudes of the isospin exchange I_ex = 0 and I_ex = 1 leading to $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ production shows that $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(1492)}$ and $\text{N}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(1670)}$ are produced essentialy through I_ex = 1.     

Dispersion relations for elastic n-d scattering in the Amado model

The formulation of rigorous, dispersion relations for on-shell three-body amplitudes in a separable model is reported. The results of approximate $\text{N}\text{D}$ calculations of s-wave n-d elastic scattering are compared with exact, numerical solutions of the Faddeev equations.     

Elastic antiproton-deutron scattering below 1.0 GeV/c

We present differential cross sections for elastic $\text{p}$d scattering at beam momenta 0.735 and 0.940 GeV/c and momentum transfers in the range 0.04<|t|<0.5(GeV/c)². The $\text{p}$d elastic differential cross section is expressed in terms of a deutron form factor and the I=0 t-channel exchange $\text{N}$N amplitudes, enabling us to isolate the corresponding I=0 t-channel exchange cross sections.     

Evaluation of ππ → NN d-waves for −25μu2 ⩽ t ⩽ 4μ2

A Froissart-Gribov projection of πN phase shifts and Regge amplitudes is used to evaluate the $\text{ππ→}\text{N}\text{N}$ scattering length at t=4μ², and partial waves for ?25μ² ? t < 4μ². The new value of the scattering length is 15% higher than a previous estimate made in the narrow width resonance approximation. The values for the partial waves are confronted with previous estimates, and lower bounds. As a result, the latter become saturated near t=0, but less restrictive near t=4μ².     

An application of dispersion relations to Kaon-nucleon scattering

In this paper we have made predictions for the invariant KN and $\text{K}$N scattering amplitudes in the kinematical region q_lab < 15 GeV/c and 0 >; t > -0.7 (GeV/c)².We have performed a direct fit to medium and high-energy data using a parametrization where the imaginary part of the amplitudes for energies above the phase-shift region is identical with the imaginary part of a Regge-pole amplitude, and the real part of the amplitudes has been obtained from a dispersion relation.The s-channel helicity amplitudes are compared with their counterparts in pion-nucleon scattering and other reactions. Exact exchange degeneracy can not be verified.Also the real part of the amplitudes are compared with the real part of phase-shift solutions. There is a qualitative agreement between these two real parts even though they differ in detail.     

News item

When β-bell particles (particles occupying β contiguous lattice sites) are placed in a random manner on a one-dimensional array of N compartments, we are simultaneously creating sequences of 1, 2, 3, …, β ? 1, vacant compartments. Clearly, after a long period of time a saturation situation arises in which the probability of placing a β-bell particle on such an array becomes zero even though the coverage has not attained the value of one. It is shown that v(β, N), the average fraction of vacant compartments when β-bell particles are placed in a random manner on a linear array of N compartments is exactly described by the recursion relation:

$\text{v(β, N)=}\text{N ? β}\text{N(N ? β + 1}\text{[(N ? 1) v(β, N ? 1) + 2v(β, N ? β)]}$

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A t-channel isospin analysis of the chew-low plot for NN → N(Nπ) interactions at 5.7 GeV/c

A new approach to the t-channel isospin analysis of ZN → Z′(Nπ) reactions is presented. This approach, useful for $\text{Z = N,}\text{N}\text{, K}{}^{\mathrm{?}}$ when only five independent sets of data are availables, is used to analyse data of $\text{N}\text{N →}\text{N}\text{(Nπ)}$ reactions obtained in a $\text{p}\text{p →}\text{N}\text{N}\text{π}$ experiment at $\text{5.7}\text{GeV}\text{/c}\text{and a}\text{p}\text{d →}\text{N}\text{Nπp}{}_{\mathrm{s}}$ experiment at 5.5 GeV/c. the t behaviour of the different isospin exchange amplitudes, suggests their exchange mechanism production. The mass spectrum, M_πN, of the contributions produced by exchanged isospin I_ex = 1, shows enhancements corresponding to N(1490) N(1670) and Δ(1230) isobars, while the mass spectrum for I_ex = 0 presents only a large bump at ～1350 MeV commonly identified as N¹(1400).     

Current algebra of quarks confined to a cavity

Equal-time commutators of fields with charges are calculated in a cavity approximation to the MIT bag model, with N flavours of non-interacting quarks confined to a rigid spherical cavity and SU(N) symmetry arbitrarily broken by mass terms. It is proved that inside the cavity the algebra is identical with that of free field theory, whilst on the boundary quark fields commute with axial charges. Vector divergences and sigma commutators belong to a $\text{(N,}\text{N}\text{) + (}\text{N}\text{, N)}$ multiplet of chiral SU(N) × SU(N). Axial divergences contain additional surface terms which do not contribute to sigma commutators. A non-strange quark mass in the range 20–44 MeV is required to give a value 30–70 MeV for the nucleon matrix element of the sigma commutator relevant to pion-nucleon scattering.     

Isospin analysis of the reactions pp→N(Nπ) at 12 and 24 GeV/c

The reaction pp → nucleon + nucleon + pion at 12 and 24 GeV/c is analyzed in terms of the isospin amplitudes for the production of the (Nπ) system. The energy dependence of the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ amplitude is weak, while the $\text{I(}\text{N}\text{π) =}\text{3}\text{2}$ contribution shows the strong energy dependence known from meson exchange reactions. The slope parameter B of the dσ/dt′ distributions of the $\text{I(}\text{N}\text{π)=}\text{1}\text{2}$ contribution is a strong function of the (Nπ) mass, decreasing sharply from about 12 GeV^?2 at threshold to about 4 GeV^?2 above 1700 MeV. Comparing our results for the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ cross section with those of similar investigations in πp and Kp reactions, we find that factorisation is valid within experimental errors. The results support the conclusion that the $\text{I(}\text{N}\text{π) =}\text{1}\text{2}$ contribution is dominated by diffraction dissociation of the proton.     

A study of ππ → NN partial-wave amplitudes using hyperbolic dispersion relations

We investigate $\text{ππ →}\text{N}\text{N}$ partial-wave amplitudes, using a spin separation method based on hyperbolic dispersion relations. Partial-wave amplitudes with J ? 3 are dominant in the pseudophysical region between the ππ and $\text{N}\text{N}$ thresholds, but we find clear evidence for J = 4 and J = 5 contributions from regions near and above the $\text{N}\text{N}$ threshold. We isolate J = 2 and J = 3 partial waves and determine the couplings of f₀(1270) and g (1680). Knowing the high-spin contributions, we are able to eliminate thse and to study s- and p-waves. We find evidence for small p-wave contributions above the ?, having the same sign as the ? contributions. We develop methods for determining the I = J = 0 ππ scattering length a₀⁰ and find a₀⁰ = 0.30 ± 0.15.     

The NN cross sections and resonances

The N$\text{N}$ amplitudes for J ? 2 are calculated using Bryan-Phillips non static OBEP and treating annihilation in the framework of a many channel N/D-formalism. For the first time all poles are found simultaneously with cross sections, reasonably well reproduced by adjusting only the coupling of the annihilation channel. The resonances have large widths and partial wave cross sections do not show any structure, suggesting that the recently found N$\text{N}$ resonances, both narrow and wide, are not of quasi nuclear origin.     

Dual parton model and the photoproduction of pseudoscalar and vector mesons in the high energy region

On the basis of the dynamical dual model of strong interactions followed from the parton model of hadrons as discussed in an earlier paper, we study here the photo-production of pseudoscalar and vector mesons in the high energy region. To incorporate the concept of duality, it is taken that any two spin $\text{1}\text{2}$ pointlike constituents (partons) can form a π-meson cluster in the structure of a nucleon and the basic interaction involved in MB scattering is the interaction of the incident meson with the π meson in the structure of the nucleon. In this scheme, the amplitudes for the photoproduction of mesons such as γN → Nπ, γN → N?, and γN → Nω in the high energy region can be related with the amplitudes for the process γπ → ππ, γπ → π?, and γπ → πω, respectively. To calculate the amplitudes for the relevant process we also consider a factor corresponding to the structural rearrangement of partons involved in duality diagrams. To obtain the cross sections, we take into account the photon-vector meson analogy, though the naive form of the vector dominance model (VDM) has not been considered here. From a knowledge of the coupling constants $\text{γ?}{}^2\text{4π}$, $\text{γω}{}^2\text{?π}$, , and we obtain the differential cross sections which are in excellent agreement with experimental results. Also we obtain a good fit for the scattering process γN → Nπ at backward angles. For the vector meson production processes, we have contributions from the diffraction mechanism also apart from the amplitudes considered here. In the region where the contribution from the diffraction part is negligible, we obtain the relation

which is in nice agreement with experiments. Finally, it is shown that, though the vector meson dominance is not considered here, the universality of the vector meson coupling with hadrons follows directly from the present model.     

Non-string two-magnon configurations in the isotropic Heisenberg magnet

By means of the $\text{1}\text{N}$ expansion we study the Bethe-ansatz equations for two-magnon states in the one-dimensional isotropic Heisenberg spin chain of N spins $\text{1}\text{2}$. A qualitative picture of complex solutions for N → ∞ is obtained which substantially disagrees with the string hypothesis. For example, the solutions $\text{λ}{}_{\mathrm{<mtext>1,2</mtext>}}\text{= x ±}\text{i}\text{y, x ～ N,y ～}\text{N}$ are found, whereas according to the string hypothesis $\text{y →}\text{1}\text{2}$ if N → ∞.     

Determination by polarization analysis of the scattering amplitudes a+ and a- and of the degree of orientation of nuclei polarized by hyperfine fields in magnetically ordered substances

Improvements of the Ito-Shull techniques are suggested for measuring the scattering amplitudes a₊ and a_- associated with the compound states $\text{I +}\text{1}\text{2}$ and $\text{I -}\text{1}\text{2}$ which are formed by the nucleus of spin I and the incident neutron. In ferro- and ferri-magnets one can increase the sensitivity by suppressing the electronic part of the magnetic scattering when polarizing the neutrons along the scattering vector. In anti-ferromagnets one can separate the nuclear magnetic part by substracting the electronic magnetic scattering with unpolarized neutrons from the total magnetic scattering (electronic + nuclear) obtained by measuring the spin-flip amplitudes U^+- or U^-+.