Nucleon Pole Terms Research Articles

Nucleon Resonances in the π−p → K0Γ Reaction near Threshold

We investigate the two-body reaction π−p → K0Γ within the effective Lagrangian approach and the isobar model. In addition to the “background” contributions from t-channel K* exchange, u-channel Σ(1192) and Σ*(1385) exchanges, and s-channel nucleon pole terms, the contributions from the nucleon resonances N* (1535), N* (1650), and N* (1720) are investigated. It is shown that the inclusion of these nucleon resonances contributions leads to a good description of the experimental total and differential cross sections data at low energy region. The s-channel N* (1535), N* (1650), and N* (1720) resonances and the t-channel K* exchange give the dominant contributions below W = 1.76 GeV, while the s-channel nucleon pole, u-channel Σ(1192) and Σ*(1385) exchanges give the minor contributions.

Role of theN*(2080)inpp→pK+Λ(1520)andπ−p→K0Λ(1520)reactions

We investigate the $\Lambda(1520)$ hadronic production in the $p p \to p K^+ \Lambda(1520)$ and $\pi^- p \to K^0 \Lambda(1520)$ reactions within the effective Lagrangian method. For $\pi^- p \to K^0 \Lambda(1520)$ reaction, in addition to the "background" contributions from $t-$channel $K^*$ exchange, $u-$channel $\Sigma^+$ exchange, and $s-$channel nucleon pole terms, we also consider the contribution from the nucleon resonance $N^*(2080)$ (spin-parity $J^P = 3/2^-$), which has significant coupling to $K\Lambda(1520)$ channel. We show that the inclusion of the nucleon resonance $N^*(2080)$ leads to a fairly good description of the low energy experimental total cross section data of $\pi^- p \to K^0 \Lambda(1520)$ reaction. From fitting to the experimental data, we get the $N^*(2080)N\pi$ coupling constant $g_{N^*(2080)N \pi} = 0.14 \pm 0.04$. By using this value and with the assumption that the excitation of $N^*(2080)$ is due to the $\pi^0$-meson exchanges, we calculate the total and differential cross sections of $p p \to p K^+ \Lambda(1520)$ reaction. We also demonstrate that the invariant mass distribution and the Dalitz Plot provide direct information of the $\Lambda(1520)$ production, which can be tested by future experiments.

Role of theN*(2080)resonance in theγ⃗p→K+Λ(1520)reaction

We investigate the $\ensuremath{\Lambda}(1520)$ photoproduction in the $\mathrm{\ensuremath{\gamma}P\vec}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}(1520)$ reaction within the effective Lagrangian method near threshold. In addition to the ``background'' contributions from the contact, $t$-channel $K$-exchange, and $s$-channel nucleon pole terms, which were already considered in previous studies, the contribution from the nucleon resonance ${N}^{*}(2080)$ (spin-parity ${J}^{P}=3/{2}^{\ensuremath{-}}$) is also considered. We show that the inclusion of the nucleon resonance ${N}^{*}(2080)$ leads to a fairly good description of the new LEPS differential cross-section data, and that these measurements can be used to determine some of the properties of this latter resonance. However, serious discrepancies appear when the predictions of the model are compared to the photon-beam asymmetry,which was also measured by the LEPS Collaboration.

PRODUCTION OF TWO PIONS INDUCED BY NEUTRINOS

We study the threshold production of two pions induced by neutrinos in nucleon targets. The contribution of nucleon pole, pion and contact terms is calculated using a chiral Lagrangian. The contribution of the Roper resonance, neglected in earlier studies, has also been taken into account.

Theπ−p→ηnreaction at low energies in a chiral constituent quark model

A chiral quark-model approach is extended to the study of the $\ensuremath{\pi}N$ scattering at low energies. The process of ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\eta}n$ near threshold is investigated. The model is successful in describing the differential cross sections and total cross section near the \ensuremath{\eta} production threshold. The roles of the resonances in $n\ensuremath{\leqslant}2$ shells are clarified. Near threshold, the ${S}_{11}(1535)$ dominates the reactions, whereas the interferences from the ${S}_{11}(1650)$ turn out to be destructive around $W\ensuremath{\lesssim}1.6$ GeV. The ${D}_{13}(1520)$ is crucial to give correct shapes of the differential cross sections. The nucleon pole term contributions are significant. The ${P}_{11}(1710)$ plays an important role around the center-of-mass energy $W=1.7$ GeV, it is crucial to produce an enhancement in the region of $W>1.6$ GeV as suggested by the data for total cross section. The $t$-channel is negligible in the reactions.

Photoproduction of $\eta$ -mesons on protons in the resonance region: The background problem and the third S 11-resonance

We have constructed an isobar model for the $\eta$ -photoproduction on the proton in the energy region up to the photon lab energy K 0 = 3 GeV. The database involved into the fitting procedure includes precise results for the cross-section and for the T-asymmetry of the process $\gamma p\to\eta p$ near threshold obtained at MAMI and ELSA as well as recent results for the $\Sigma$ -asymmetry and for the angular distribution measured at higher energies in Grenoble and also more recent measurements performed at JLab for the photon energies up to 2 GeV. The model includes twelve nucleon resonances: S 11(1535), S 11(1650), S 11(1825), P 11(1440), P 13(1720), D 13(1520), D 15(1675), F 15(1680), F 17(1990), G 17(2190), G 19(2250), H 19(2220), and the background consisting of the nucleon pole term and the vector meson exchange in the t-channel. To explain the observed energy dependence of the integrated cross-section, two s-wave resonances, S 11(1650) and S 11(1825), have to be taken into account along with the dominating S 11(1535). The integrated cross-section as well as the angular distribution and $\Sigma$ -asymmetry predicted by the model are in good agreement with the data. Above the photon energy K 0 = 2 GeV, the calculated cross-section exhibits an appreciable dependence on the $\rho$ - and $\omega$ -meson contribution, whose coupling with nucleons is not well defined. Several versions of extending the model to higher energies are considered.

Structure analysis of the virtual Compton scattering amplitude at low energies

We analyze virtual Compton scattering off the nucleon at low energies in a covariant, model-independent formalism. We define a set of invariant functions which, once the irregular nucleon pole terms have been subtracted in a gauge-invariant fashion, is free of poles and kinematical zeros. The covariant treatment naturally allows one to implement the constraints due to Lorentz and gauge invariance, crossing symmetry, and the discrete symmetries. In particular, when applied to the $e\stackrel{\ensuremath{\rightarrow}}{p}{e}^{\ensuremath{'}}{p}^{\ensuremath{'}}\ensuremath{\gamma}$ reaction, charge-conjugation symmetry in combination with nucleon crossing generates four relations among the ten originally proposed generalized polarizabilities of the nucleon.

Coherent η photoproduction on 4He and 12C in the near-threshold region

Coherent η meson photoproduction on 4He and 12C is considered in the near-threshold region. The elementary η photoproduction operator includes contributions from the S 11 (1535) and D 13 (1520) resonances as well as t-channel vector meson exchange and the nucleon pole terms. Due to the suppression of the dominant S 11 (1535) resonance for spin and isospin saturated nuclei, the reaction is mainly governed by ω exchange. Furthermore, the influence of Fermi motion and of different prescriptions for the choice of the invariant reaction energy W γN in the elementary amplitude is studied.

Coherent eta photoproduction on the deuteron in the S11 resonance region

Coherent eta photoproduction on the deuteron is studied in the S 11 resonance region neglecting eta rescattering and two-body processes. For the elementary reaction on the nucleon, we have considered the dominant S 11(1535) resonance and as background the nucleon pole terms as well as ϱ and ω meson exchange. We have studied the influence of different choices for the neutron resonance amplitude, different prescriptions for fixing the invariant mass of the resonance amplitude and different methods for deriving the elementary production amplitude for an arbitrary reference frame.

πNNand πNΔ form factors determined from a microscopic model for πNscattering

We determine the \ensuremath{\pi}NN and \ensuremath{\pi}N\ensuremath{\Delta} form factors from the ${\mathit{P}}_{11}$ (${\mathit{P}}_{33}$) partial wave of \ensuremath{\pi}N scattering by dressing corresponding bare vertices with the help of \ensuremath{\pi}N non-s-pole contributions. The underlying model is based on meson exchange, and involves nucleon and delta-isobar pole and crossed-pole terms together with correlated \ensuremath{\pi}\ensuremath{\pi} exchange in the ${\mathit{J}}^{\mathit{P}}$=${0}^{+}$ (\ensuremath{\sigma}) and ${1}^{\mathrm{\ensuremath{-}}}$ (\ensuremath{\rho}) channel. As a whole our results for the \ensuremath{\pi}NN form factor are somewhat less soft than (i) those determined recently quite analogously by Saito and Afnan and (ii) our results for the \ensuremath{\pi}N\ensuremath{\Delta} form factor. The results for the \ensuremath{\pi}NN form factor depend, due to trival kinematical factors, on the type of bare \ensuremath{\pi}NN coupling (ps or pv); namely for ps coupling it is less soft. \textcopyright{} 1996 The American Physical Society.

Microscopic approach to pion-nucleus dynamics.

Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum-space first-order optical potential combined with microscopic estimates of second-order corrections. The calculation of the first-order potential includes (1) full Fermi-averaging integration including the \ensuremath{\Delta} propagation and the intrinsic nonlocalities in the \ensuremath{\pi}-N amplitude, (2) covariant kinematics, (3) invariant amplitudes, and (4) a finite-range off-shell pion-nucleon model which contains the nucleon-pole term. The \ensuremath{\Delta} nucleus interaction is included via the mean spectral-energy approximation. This approach produces a convergent perturbation theory in which the Pauli corrections (treated as a second-order term) cancel remarkably against the pion true-absorption terms. Parameter-free results, including the \ensuremath{\Delta}-nucleus shell-model potential, Pauli corrections, pion true absorption, and short-range correlations, are presented.

Threshold pion photoproduction in the Skyrme model

Threshold photoproduction of pions on the nucleon is studied in the Skyrme model. Both the rotational and translational degrees of freedom of the Skyrmion are included in the calculations. It is found that in the case of neutral pion production there is a sizeable cancellation between the nucleon pole term and the anomalous contact term. This cancellation is a unique feature of the model and provides an important test of the validity of the model. A definitive conclusion must await a resolution of the existing controversies about the experimental data.

On the P11 problem in π-deuteron scattering

In the study of the π-deuteron system the proper treatment of the P 11 π-nucleon channel has remained a problem. When the P 11 channel is broken up into the nucleon pole term and a background term the nucleon pole term is Pauli blocked leading to a poorer fit to the data. In this work it is shown that there is a diagram which largely cancels the diagram responsible for the Pauli blocking. It is expected that the inclusion of this diagram will lead to better agreement with the data and cure the P 11 problem.

Proton pole contribution in proton decay

We show that nucleon pole terms contribute significantly to proton decay, increasing the branching ratio for e + π 0 and ν R π + modes. The total lifetime is decreased to the point where keeping the SU(5) value of the lifetime below the experimental upper bound forces us to the choice of QCD scale parameter and proton radius parameter which are near the edge of the allowed region.

Nucleon recoil effect in the pion-nucleon interaction

We have studied the effect of nucleon recoil on pion-nucleon interaction in the $P$ wave using the dynamical model of Chew and Low which uses the nucleon pole terms as the driving mechanism. In general, the inclusion of recoil causes sizable reduction of the rescattering terms in every channel. In the $P33$ channel, this reduction is large enough to remove the resonance. This conclusion holds for any acceptable pion-nucleon coupling constant, and is independent of the choice of pion-nucleon form factor.

Simple model of pion-nucleon elastic scattering

A nonstatic model for elastic pion-nucleon scattering is developed using knowledge of the analytic structure of the scattering amplitude and partial wave $\frac{N}{D}$ dispersion techniques. In $S$, $D$, and $F$ partial wave channels the model is equivalent to a separable potential model which includes the coupling to inelastic channels. In $P$-wave channels the nucleon pole which arises from absorption and emission of the pion is included. A more general model which incorporates both a nucleon pole term and a separable potential term is developed for the ${P}_{11}$ channel. This model is capable of reproducing the change of sign which is present in the ${P}_{11}$ phase shifts. The necessary information concerning the coupling of the inelastic scattering to the elastic scattering is taken from the experimentally determined phase shifts as input. If simple kinematic factors are included explicitly, quite simple analytic functions for the form factors in the model are able to reproduce the experimental phase shifts for pion laboratory kinetic energies up to 1.2 GeV. The model produces off-shell behavior which is different from previous models. In particular, the inclusion of the nucleon pole alters substantially the range of the interaction in all $P$-wave channels.NUCLEAR REACTIONS Pion-nucleon elastic scattering; separable potential and Chew-Low models extended; $S$-, $P$-, $D$-, and $F$-wave phase shifts for $E<~1.2$ GeV.

Truncated pion-nucleon amplitudes and pion-nucleus interactions

It is pointed out that there are considerable structural differences among the various types of truncated pion-nucleon amplitudes which have been proposed in order to avoid overcounting ambiguities in pion-nucleus interactions. A previously proposed prescription is shown to yield truncated amplitudes which are free of the usual problems involved with the proper representation of the nucleon-pole term. It is shown that these truncated amplitudes can also possess ghost pole singularities arising from the ..pi..NN vertex function. Some problems caused by the appearance of such ghost poles in approximations to pion-nucleus amplitudes are discussed.

Soft-pion production ine+e−annihilations

We show that we can apply the soft-pion theorem to the high-energy ${e}^{+}{e}^{\ensuremath{-}}$ process, assuming the new extrapolation method, and point out that the nucleon-pole term plays an important role at PEP and PETRA energy.

Role of the Nucleon Exchange in the Diffraction Dissociation N-> (N )

Properties of the nucleon exchange and the direct nucleon pole terms are studied in the diffraction dissociation JrN~>r. (N7r). It is shown that contrary to the naive expectation, the nucleon exchange term with the s-channel helicity conserving 7rN scattering amplitude cannot give the maximum at ¢aJ=O in the ¢aJ distribution. The transverse momentum distributions in the lab. frame reflect well the cos eaJ but not the ¢aJ distributions. We need something besides the pion exchange term to enhance the backward side, cos !JaJ<O, bnt it is questionable whether the nucleon exchange term plays the role of something completely. Including cross-over phenomena, it is qualitatively examined that the resonance production term plays the role of the something.

Dual model with second-sheet resonances for pion-nucleon scattering

A crossing-symmetric pion-nucleon scattering amplitude with Regge behaviour and second-sheet resonance poles is constructed using suitable combinations of a representation proposed by Cohen-Tannoudji, Henyey, Kane and Zakrzewski (CHKZ). The Regge residues for high-energy scattering are obtained in terms of the functionf(t) which is used in construction of the CHKZ representation. An attempt is made to find the form off(t) which gives the best fit to the high-energy chargeexchange differential cross-section in the forward direction. It is also shown that the nucleon pole term imposes restrictions on the location of the branch point off(t), and that the fit at large |t| can be improved by modifying the π trajectory function so that it satisfies the bound |αρ (t)| < |C|t|1/2 log |t1|| fort→-∞.