Nucleon Pole Research Articles

Uniqueness of the Interaction Involving Spin-32Particles

The free-field Lagrangian as well as the propagator for spin-$\frac{3}{2}$ particles contains an arbitrary parameter $A$. However, the $S$-matrix elements for the interaction of a spin-$\frac{3}{2}$ field with other fields are always independent of this parameter, provided the interaction Lagrangian is properly chosen. For a system of a spin-$\frac{3}{2}$ field coupled to a nucleon field and a pion field, a two-parameter ($A,Z$) interaction Lagrangian is introduced in such a way that it is invariant under a point transformation of the spin-$\frac{3}{2}$ field. The transition amplitude for such an interaction is independent of the parameter $A$. However, it does depend on the second parameter $Z$. By requiring the interaction to be consistent with the principles of second quantization, the value of the second parameter has been fixed. Therefore, the $\ensuremath{\Delta}(1238)$ contribution to the elastic $\ensuremath{\pi}N$ scattering amplitudes can be uniquely determined. Using this model for the evaluation of the $\ensuremath{\Delta}(1238)$ contribution and the chiral-invariant Lagrangians for the calculation of the nucleon pole and $\ensuremath{\rho}$-pole contributions, the $\ensuremath{\pi}N$ scattering lengths have been computed and compared with the experimental data. The calculated results are in good agreement with experiment.

Two-Pion-Exchange Contribution to Nucleon-Nucleon Scattering

The two-pion-exchange contribution to nucleon-nucleon scattering is calculated, following the method of Goldberger, Grisaru, MacDowell, and Wong. The results are shown for two cases. In the first case, the input $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{\rightarrow}\overline{N}N$ amplitude is approximated by a nucleon pole term only; in the second case it is approximated by a nucleon pole term plus a $\ensuremath{\Delta}(1236)$ pole term. It is found that for the physical value of the $\ensuremath{\Delta}(1236)$ width, ${\ensuremath{\Gamma}}_{\ensuremath{\Delta}}=120$ MeV, there is very little difference for the two cases in the resulting effect on nucleon-nucleon scattering below 400 MeV. The model is mathematically equivalent to the Amati-Leader-Vitale approach for all but $^{1}S_{0}$, $^{3}P_{0}$, and $^{3}P_{1}$ $\mathrm{NN}$ partial waves. The results are found to be sensitive to the value of ${\ensuremath{\Gamma}}_{\ensuremath{\Delta}}$.

Baryonic Fixed Poles in Meson-Baryon Scattering

By using a fixed-pole sum rule, it is established that there is a fixed pole at $J=\ensuremath{-}\frac{1}{2}$ in the $\ensuremath{\pi}N$ partial wave amplitude containing the nucleon trajectory. Whether the dip at $u=\ensuremath{-}0.13$ Ge${\mathrm{V}}^{2}$ in backward ${\ensuremath{\pi}}^{+}p$ scattering is due to a nucleon wrong-signature nonsense zero then depends on how this fixed pole and the nucleon pole combine. A class of meson-baryon amplitudes expected to be free of nonsense fixed poles is identified.

On the construction of pion photoproduction amplitudes from experimental data

New formulae for constructing the pion photoproduction amplitude J from experimental data are presented. The phase of J is expressed in terms of its zeroes in the energy plane, the particle poles and a dispersion integral over the modulus of J, the latter being given, except for a finite unphysical interval, in terms of differential cross sections and recoil nucleon polarizations. For γp→ π +n at t≈−0.870 μ 2, where the unphysical-region contribution vanishes, the zeroes are found approximately, so that the phase of J can be uniquely determined from the experimental data.

(3,3) Resonance and nucleon pole for NN → NN π at low and moderate energy

The nucleon pole as generated by soft-pion techniques and the (3,3) resonance pole of the isobar model are included in a relativistic treatment of pp → pp π 0 for low and moderate incident proton energies. The total and various differential cross section are calculated and found in agreement with experiment. Except for several well-known coupling constants this description is parameter-free.

Lack of a Burnett-Kroll Theorem for Soft-Pion Emission

It is shown that, in the context of the reaction $\mathrm{NN}\ensuremath{\rightarrow}\mathrm{NN}\ensuremath{\pi}$, when more than one nucleon pole graph contributes, the soft-pion analog of the Burnett-Kroll extension of the Low soft-photon theorem cannot be established.

Polarization in Elastic Nucleon-Deuteron Scattering

An approximate $K$-matrix calculation of elastic nucleon-deuteron scattering is carried out including the effects of two-nucleon tensor forces. The results of these computations, which are carried out in the energy range from 11 to 40 MeV, are in reasonable agreement with the experimental nucleon polarizations and differential cross sections.

A simultaneous description of two- and three-body data with the generalized Veneziano model

A generalized Veneziano model which describes the three-body reactions K + p→ K oπ + p, K − p→ K oπ − p , and π −p→K o K −p is applied to study the two-body reactions K − p→ K o n, K + n→ K o p, π − p→ K oΛ , K −n→ π − Λ, which are given by the three-body amplitude at the nucleon and lambda pole. With no free parameters it is found that with one exception one can give a simultaneous description of these two and three-body reactions at energies between 2.5 and 13 GeV/ c, and at all momentum transfers except the extreme forward (− t<0.2 GeV/ c 2) and extreme backward (− u<0.2 GeV/ c 2) directions. The one exception to this description is briefly discussed.

The ΛKN coupling and backward scattering

The K − n → Λπ − and πN → Nπ backward differential cross-sections yield a ratio of nucleon Regge residues to ΛK and πN of 1.01 ± 0.3 (corresponding to F D = 0.57 −0.28 +0.37) . At the nucleon pole this extrapolates to g Λ KN 2 4π = 14.5 ± 5 .

Theπ π πNÑ-five-point function

Choosing a suitable covariant decomposition of theπ π πNN-five-point function the crossing relations are derived and a complete reduction of them is given. The implications of the known factorization properties at the one-particle singularities of the invariant functions on their assumed Regge behaviour is investigated and a set of asymptotic relations between them is found. A mass degenerate parity doublet of the nucleon can remove the relations connected with the nucleon poles.

Annular polarimeter for measurements of nucleon polarization in nuclear reactions

The method of the annular polarimeter for measuring the nucleon polarization in nuclear reactions is described here in details and its advantages against the usual left-right asymmetry method are shown. The calculations of the geometrical factor and the averaged analysing power were carried out using the Monte-Carlo method. For an example the polarization of protons from the reaction 12C( 3He, p 0) 14N(g.s) at E( 3 He) = 2.87 MeV was measured as a function of the scattering angle using the elastic scattering 12C(p, p) 12C as an analyser.

Problem of Neutron-Proton Mass Difference

The problem of the $n\ensuremath{-}p$ mass difference is carefully analyzed in the framework of dispersion theory. The author has studied the models recently used to obtain interesting properties of the electroproduction structure functions, in order to calculate an important piece of the mass shift coming from the subtraction constant that enters into the dispersion relation for the spin-nonflip forward Compton amplitude of the nucleon. It was hoped that in some simple model one might enhance this piece in the right direction and thereby obtain at least the required sign reversal. It is shown that this is not so. Thus, unless the contributions of the higher resonance states (in addition to the nucleon pole) or those of the fixed poles to the Compton amplitude are important, the $n\ensuremath{-}p$ mass shift cannot be understood from the viewpoint of dispersion theory.

Nucleon Polarization Transfer in High-Energy Electron Scattering

Nucleon Polarization Transfer in High-Energy Electron Scattering

Polarization of spin-half particles

Formulae for the cross section and polarization of nucleons elastically scattered at large angles are obtained from the optical model assumptions using a semiclassical approximation. The formulae thus obtained agree well with experimental data.

Partial-Wave Analysis ofπ−+p→η+n

It is shown that by using the nucleon pole and a sum of direct-channel resonances, a reasonable fit to both the differential and total cross sections, for the process ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}\ensuremath{\eta}+n$, is obtained for incident-pion laboratory kinetic energies (${T}_{\ensuremath{\pi}}$) between threshold and 1.3 GeV. Inelastic branching ratios for the $\ensuremath{\eta}n$ channel are predicted with results consistent with experiment. The $\ensuremath{\eta}$-nucleon coupling constant is found to be $\frac{{{g}_{\ensuremath{\pi}\mathrm{NN}}}^{2}}{4\ensuremath{\pi}}\ensuremath{\lesssim}{10}^{\ensuremath{-}4}$. By assuming the spin and parity of the $N(2650)$ to be ${J}^{P}={\frac{11}{2}}^{\ensuremath{-}}$, agreement with the polarization data near the $N(2650)$ is obtained. However, this model can not give a good fit to the differential cross-section data at ${T}_{\ensuremath{\pi}}=2.41 \mathrm{and} 2.93$ GeV.

Lorentz Invariance in Reggeization of Pion Photoproduction Amplitudes

We study the implications of Lorentz and gauge invariance for Reggeization of the pion trajectory in charged pion photoproduction and find that the pion need not be introduced as a kinematical singularity. As a consequence of having a dynamical Regge pion pole, we find that effects characteristic of an $s$-channel nucleon pole appear automatically.

Conspiracy and Evasion inπandKPhotoproduction

We attempt to fit ${\ensuremath{\pi}}^{+}$ and ${K}^{+}$ photoproduction data near the forward direction by Reggeized $\ensuremath{\pi}$ and $K$ exchange, respectively, allowing for possible conspiracies. We argue that the pion trajectory conspires, with a strength given by the nucleon pole term, while the kaon evades or conspires weakly. We show that the unequal-mass kinematics of $K$ photoproduction in no way prevents or restricts the possibility of conspiracy. In the Appendix we discuss the choice of kinematics-free amplitudes, including the effect of gauge invariance.

Anomalous nucleon magnetic moment sum rules without current algebra

The off-shell gauge violation in the photoproduction of a soft pion or axial spurion is shown to be completely contained in the nucleon pole terms of the amplitude. Using this one can show that the partially conserved axial vector current hypothesis, so modified as to take first-order electromagnetic interactions into account, is sufficient to determine sum rules between the anomalous isoscalar and isovector nucleon magnetic moments and the soft-pion forward photoproduction amplitude. Such sum rules have been previously obtained using the techniques of current algebra.

Backward Compton Scattering Sum Rule and theπ0→2γ,η0→2γDecay Rates

We use the superconvergence of certain Compton scattering ($s$-channel) helicity amplitudes for fixed $s$ and large $t$, to derive a sum rule for $t$- and $u$-channel processes. The $u$-channel ($\ensuremath{\gamma}N\ensuremath{\rightarrow}\ensuremath{\gamma}N$) contribution contains the well-known nucleon pole terms and the continuum, which we replace by just the $\ensuremath{\pi}\ensuremath{-}N$ intermediate states; we then feed in photoproduction data. The $t$-channel ($\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}N\overline{N}$) contribution consists of the $\ensuremath{\pi}$, $\ensuremath{\eta}$ poles and the continuum. We choose a suitable combination of superconvergent amplitudes such that the effects of ${0}^{+}$, ${2}^{+}$, and ${1}^{+}$ resonances in the $t$ channel are eliminated. Assuming that this takes care of most of the $t$-channel continuum, we get a sum rule for the ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ and ${\ensuremath{\eta}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ widths, or alternatively, by using the experimental widths, we can check the consistency of the superconvergence in question. A brief comparison is made with related work by Goldberger and Abarbanel, and by Pagels.

A covariant theory of the pionic disintegration of the deuteron

The pionic disintegration of the deuteron and its inverse process are studied in a covariant theory from threshold to 300 MeV pion kinetic energy. The singularity structure of the scattering amplitude as found from box diagrams makes it possible to select the leading contributions that come from the nucleon pole, the deuteron structure and the NN and NN π intermediate states. The latter is treated as an NN ∗ state where N ∗ is the (3.3) pion nucleon resonance. Dispersion relations are written for partial wave amplitudes and the contribution of the NN ∗ state to unitarity is explicitly calculated, taking into account the spin and the unstability of N ∗. A detailed comparison in the medium energy region shows a good agreement with the existing data.