πNN Vertex Research Articles

A connection between the high energy-scale evolution of the P- and T-odd πNN coupling constant and the strong πNN interaction

The large energy-scale behaviour of the parity and time-reversal violating (PTV) pion–nucleon coupling constant is analysed in a model combining renormalization-group techniques and the dressing of the PTV vertex with a pion loop. With the strong πNN vertex as a mixture of the pseudovector and pseudoscalar couplings, we show that depending on the admixture parameter, two qualitatively distinct types of behaviour are obtained for the PTV coupling constant at high energy scales: an asymptotic freedom or a fixed point. We find a critical value of the admixture parameter which delineates these two scenarios. Several examples of the high-energy scale behaviour of the PTV πNN constant are considered, corresponding to realistic hadronic models of the strong pion–nucleon interaction.

P- and T-violating πNN form factor

The form factor of the parity and time-reversal violating (PTV) pion–nucleon interaction is calculated from one-loop vertex diagrams. The degrees of freedom included in the effective Lagrangian are nucleons, pions, η, ρ and ω mesons. We show that by studying the form factor one can constrain the PTV meson–nucleon coupling constants. We evaluate the mean square radius associated with the PTV πNN vertex. Using the mean square radius, we estimate the effect of the PTV πNN vertex on the neutron electric dipole moment, and find a very small correction. We also extract the renormalisation group β function and use it to discuss evolution of the PTV πNN coupling constant beyond the hadronic mass scale.

Relativistic field-theoretical representation of the Schrödinger equation and field-theoretical generalization of the inverse scattering method

The relativistic three-dimensional equation ( 2 E p ′ − 2 E p ) 〈 p ′ / Ψ p 〉 = − ∫ V ( t ) d 3 p ″ 〈 p ″ / Ψ p 〉 with E p = m 2 + p 2 and t = ( E p′ − E p″ ) 2−( p′− p″) 2 is transformed into Schrödinger equation (Δ r + k 2)〈 r|ϕ k 〉=− v( r)〈 r|ϕ k 〉 with E p = k 2/2 m+ m using the Fourier transformation. The potential v( r) and the wave function 〈 r|ϕ k 〉 differ from the corresponding Fourier images of the relativistic potential V( t) and the relativistic wave function 〈 p′| Ψ p 〉 with the kinematical factors only. In the framework of the standard field-theoretical approach the three-dimensional relativistic equations for the NN scattering amplitude with the total NN potential V tot = V( t)+ V nonl are derived. The nonlocal part of this NN potential V nonl is constructed from the πNN vertex functions which are determined from the πN phase shifts. The other part of the NN potential V( t) consists of the π-, σ-, ρ-, ω-, … meson exchange diagrams and for the NN contact (overlapping) terms. In the case of the renormalizable Lagrangians V( t) reproduces exactly the One Boson Exchange (OBE) Bonn model of the NN potential. The inverse scattering problem for this V( t) potential is reduced to the construction of the potential v( r) of the ordinary Schrödinger equation from the NN phase shifts.

NUCLEON ELECTROMAGNETIC FORM FACTORS AND CHIRAL SINGULARITIES

Chiral singularities in both nucleon isovector radii are calculated in closed form. Within a one-meson-loop approximation we implement in an explicitly gauge invariant manner quark substructure in the γ π π and πNN vertex functions. The coefficients of log mπ and [Formula: see text] terms are directly related to gA and to the threshold behaviour of the πN amplitude A(-)(ν,0) which are 1 and 0, respectively, if only the N pole is considered in the πN scattering amplitude. This result is remarkably independent of the cut-off procedure. If mesonic substructure at the γ π π vertex is included, however, gA becomes slightly smaller than 1 and [Formula: see text] becomes moderately negative. This hints at important contributions to both gA and [Formula: see text] from the Δ(1232) and possibly other N*, Δ* resonances in this approach.

Backward elastic pd scattering at intermediate energies

The theoretical approaches to the description of backward elastic pd scattering at energies 0.5–2 GeV are reviewed. In addition to the mechanisms of neutron exchange and single pN scattering, the role of N * -isobar exchange is studied using the six-quark model for the dNN * vertex. Relativistic effects are taken into account within the Hamiltonian dynamics of systems with a fixed number of particles. The important role of Glauber rescatterings in the initial and final states in the neutron-transfer mechanism is displayed. Special attention is paid to the mechanism of Δ-isobar excitation, which, despite the large momentum transfer, is rather weakly sensitive to the high-momentum components of the deuteron wave function and dominates at incident protonenergies T p =0.5–1 GeV . The reaction pp→pnπ + is studied in the Δ-resonance region in order to determine the parameters of the amplitudes for NN↔NΔ transitions needed to calculate the Δ-isobar contribution to the process pd→dp. It is shown that the amplitude of the Δ-resonance mechanism for the process pd→dp is very sensitive to the parameters of the πNN, πNΔ, ρNN, and ρNΔ vertex form factors. The role of more exotic mechanisms is briefly discussed.

A meson-exchange isobar model for the π+d↔pp reaction

We calculated a broad set of observables for the π+d ↔ pp reaction with a relatively simple meson-exchange isobar model. The comparison between the calculated results and experimental data (including spin observables) shows that the model gives an overall phenomenologically acceptable description of the reaction around the Δ resonance. We also take into account the effects due to the inclusion of the Galilei invariant (pseudovector) recoil term in the πNN vertex, of relativistic corrections to the ρ-exchange component of the ΔN transition potential, and of NN final state interaction in the π+d → p + p process. Rescatterings via pion-nucleon interaction in the S–wave have also been included. The model is sufficiently simple to be extended to the case of pion absorption on other light nuclei, in particular 3He (or tritium).

Baryons as solitons in effective chiral field theories

This lecture comprises some recent developments concerning the description of baryons as topological solitons in effective chiral meson theories. In the first part one-loop corrections to the classical tree approximation are discussed. This involves renormalization of low-energy coupling constants and evaluation of the finite next-to-leading-order terms in the 1 N c expansion. In contrast to the corresponding procedure in the meson sector the magnitude of the chiral gradients involved in the soliton profile requires that counter terms and finite loop contributions be calculated to all chiral orders. Recent results for various nucleon observables are presented. They show that the 1 N c expansion essentially works as expected. In the second part electro-magnetic nucleon form factors (FFs) with relativistic corrections are evaluated in a chiral soliton model including vector mesons. The magnetic FF G M p is shown to agree well with new SLAC data for spacelike Q 2 up to 30 (GeV/c) 2 if superconvergence is enforced. The electric FF G E p is dominated by a zero in the few (GeV/c) 2 region due to a low-lying zero in the non-relativistic electric FF in tree approximation. The third part describes how to extract the strong πNN form factor from chiral soliton models, taking due care of the local metric created by the presence of the soliton. When used in a one-boson-exchange model for the nucleon-nucleon (NN) interaction, deuteron properties and phase parameters of NN scattering are reproduced as well as in conventional NN models that apply a hard monopole form factor at the πNN vertex.

Pion-Nucleon Interaction and Two-Pion-Exchange Three-Nucleon Forces

We compare the πN scattering amplitudes that underlie 2π-exchange three-nucleon forces (TBFs) with the experimental πN amplitudes in the form of partial-wave phase shifts and subthreshold invariant amplitudes. The amplitudes of the Tucson-Melbourne and Brazil TBFs when taken on-pion-mass-shell predict scattering lengths at threshold and phase shifts (slightly) above threshold which are in good agreement with the experimental amplitudes, except for the S-waves. Partial wave amplitudes from separable potentials, recently employed in a 2π-TBF calculation, were continued below threshold, summed into invariant amplitudes, and compared with the experimental amplitudes in this kinematic region, which is most relevant to the kinematics of TBFs. The separable-potential invariant amplitudes, in contrast to those of TM and Brazil TBFs, do not compare well quantitatively with the experimental amplitudes in this region but have a similar qualitative behaviour. The very small TBF effect in the triton of the separable-potential amplitude appears to be due to the πNN vertex function rather than the πN amplitude itself.

Effects of the final-state interaction in (γ, pn) and (γ, pp) processes

A model is presented to describe electromagnetically induced two-nucleon emission processes in a shell-model picture. Distortions in the outgoing nucleon waves are accounted for by performing a partial-wave expansion in a real mean-field potential. The antisymmetry condition for the A-body wave functions is shown to be naturally preserved. The model is used to calculate (γ, pn) and (γ, pp) cross sections off the target nuclei 16O and 12C for photon energies ranging from 50 MeV up to the Δ(1232) isobar threshold. Effects due to the pionic currents and intermediate Δ creation are implemented. The impact of the distortions due to the interaction of the outgoing nucleon waves with the A — 2 core is examined. Hadronic form factors are introduced to regularize the πNN vertices and the sensitivity of the cross section to the pion cutoff mass is examined. The relative contribution of the (γ, pp) and the (γ, pn) channel to the total photoabsorption strength is discussed. Further, the photon energy dependence of the (γ, pp)/(γ, pn) ratio is investigated.

An analysis of parity-violating pion-nucleon couplings

We construct to all orders in the pion field and to one power of pion momentum the most general lagrangian for parity-violating pion-nucleon interactions that can arise from weak interactions. In particular, we show that in addition to the previously discussed P-violating πNN vertex, there are independent ππNN, and πγNN interactions. All three may be relevant for nuclear and atomic parity-violation experiments, as well as P-violating elastic nucleon scattering. We give numerical estimates for the interactions, and show that there is reason to believe that the Z°-induced strange-quark operator ( sγ μγ 5s)( uγ μu− dγ μd) contributes significantly in the ΔI = 1 channel.

Hadron structure and gauge invariance in photo- and electroproduction of pions

Abstract We give a detailed account of the constraints on the general operator for pion photo- and electroproduction provided by the Ward-Takahashi identities. We investigate the role of off-shell effects in electromagnetic and strong interaction from factors. Special attention is paid to the “internal insertions”, the coupling of the photon into the dressed πNN vertex. To be able to do this consistently, we use a simple field-theoretical model where the nucleon gets dressed by a neutral scalar meson. In the framework of this model we compare the exact production amplitude with that obtained from ad hoc prescriptions which have recently been proposed. Finally the discussion is extended to exchange currents in electron scattering.

Rescattering effects and the constant of weak pion-nucleon coupling

Renormalization of the weak pion-nucleon coupling constant ƒ π NN due to rescattering of the emitted π-meson is considered. The mechanism controlling this renormalization involves strong emission of the π-meson followed by its P-odd rescattering on the nucleon. This mechanism is shown to suppress the ƒ π NN value. The suppression factor depends upon the form factor in the strong πNN vertex. For realistic values of the cut-off parameter in this vertex the ƒ π NN coupling constant proves to be diminished by a factor of ∼4. The resulting value of ƒ π NN calculated in the quark model with current quark masses is compatible with experimental bounds. So the rescattering mechanism removes the disagreement between the (large) theoretical value of ƒ π NN and the (small) experimental limit without deteriorating the dynamic enhancement of the ΔT = 1 2 amplitude in nonleptonic hyperon decays.

Pion-nucleon interaction model for the P 11 and P 33 channels and the unitary three-body calculation of nn scattering

We extend the isobar-dominated model for the πN P 33 channel in such a manner as to incorporate a background (non-pole) interaction. The pion-nucleon potential has two driving terms, a pole part generated by the πNΔ vertex and a background part. The πrN P 11 interaction is constructed in a similar way by including a pole part generated by the πNN vertex and a non-pole part. Motivated by a quark-model picture for baryons, we choose the common cut-off form factor for the πNN and πNΔ vertices. The parameters of the model are determined by the fit to the empirical πN phase shifts. Using this πN interaction model as an input, we calculate nucleon-nucleon elastic-scattering phase parameters based on a unitary, relativistic, pion-exchange model. We find that our model adequately reproduces the 1D 2 phase parameters as well as those of peripheral partial waves. We also find that the longitudinal total cross section difference Δσ L(pp → NNπ) comes closer to the data. We discuss the different choice of the irN relative momentum, the backward pion propagation, and the Pauli-principle violating states for the background P 11 interaction.

Deuteron photodisintegration up to 140 MeV: (I). The theoretical model

We give details of a theoretical model for deuteron photodisintegration below the pion production threshold, which includes contributions to the current and charge densities from the impulse approximation (including relativistic corrections) and from the exchange of one meson. Contributions from the exchange of two or more mesons are systematically neglected. For one-meson exchange, we consider the exchange of a pion, both without and with a Δ (1231) intermediate state, and the exchange of ρ and ω. Form factors are included at the strong vertices, with a cut-off mass for the πNΔ vertex which is smaller than that for the πNN vertex. We use current conservation in calculating the electric multipole amplitudes and give expressions for the multipole amplitudes used in the calculation.

Excitation of deformed skyrmions

The couplings of vibrational and deformed rotational excitations of the Skyrme soliton to the πN and γN system are investigated. Additionally features of the linear πNN vertex in the Skyrme model and constraints on the model parameters from soliton stability are discussed.

Relativistic study of the reaction pp → dπ: Formalism and comparison with experiment at Tp = 578 MeV

A detailed relativistic calculation of pp → πd is presented. The leading graph is the exchange of a nucleon and a pion. The πN amplitudes, including off-shell information, are input, together with relativistic dpn and πNN vertex functions. The dominant nucleon spectator term is calculated without uncontrolled approximations, and the relativistic pion antiparticle contribution is evaluated. The single nucleon exchange diagram is added. Higher order rescattering is treated by initial and final state distortion factors. All amplitudes and spin observables are calculated and a detailed comparison with the measured data at 578 MeV is made. The remaining observed discrepancies are traced to the pp spin-triplet waves.

Study of πNN Vertex from Hadron and Quark Point of View

We have identified the first-order mixing amplitude of πNN process described by the hadron model with the second-order mixing amplitude of the same process described by the quark model. Then the expression for the coupling constant fπ of the πNN vertex with different quark wave functions and gluon propagators in different approximations has been derived. The calculation results of fπ have been compared with experimental data.

Deuteron photodisintegration at high energies

The reaction γ + d → p + n is studied at photon energies in the range 0.1 to 0.7 GeV. The approach is based on a non-covariant description of the deuteron (d) (accounting for the pn S- and D-components as well as for the virtual ΔΔ component) and a plane-wave description of the final pn state. The scattering amplitude incorporates, in addition to the impulse term, all the relevant one-pion exchange current terms corresponding to the Born and the rescattering terms in the process γN → N + π. We discuss contributions to the latter process induced by the N 33 ∗(Δ) resonance as well as by the N 33 ∗(S 11, P 11, D 13) resonances in the second bump. We consider two treatments of the N 33 ∗ contribution based on the isobaric model and a dispersion theory model. Predictions are presented for differential cross sections and for proton polarizations. We assess the roles of the various terms in the scattering amplitude. Some refinements are considered occasionally, bearing on final-state interaction effects and the ρ-meson exchange terms. We also examine in detail the sensitivity of predictions to various inputs and approximations, the most relevant being the range parameters for the πNN vertex, the off-shell extrapolation of the amplitude γN → πN and the retardation corrections. Recognizing that the indefiniteness in certain inputs may be the cause of appreciable uncertainties, we are led to seek for plausible prescriptions for these inputs by referring to measurements. We find that instrumental items, in order to achieve acceptable fits to differential cross sections, are a range parameter for the πNN vertex around 700–900 MeV/ c and an energy-dependent N 33 ∗ width. The predictions for the proton polarizations feature a much stronger sensitivity. In particular, we fail to explain the large enhancement observed at around 500 MeV photon energy.

Quark dynamics and pion-nucleon coupling

In the framework of nonperturbative QCD phenomenology we discuss: (1) The elementary process for the creation of color-singlet q q -pairs inside a hadron. (2) The interaction of the q q -pair with the surrounding quark-gluon medium. An important consequence of these discussions is that meson emission takes place preferentially, if the primary q q -pair is created in the surface region of the hadron. For the case of pseudoscalar coupling we employ PCAC to obtain the coupling of the q q -pair to the pion. The resulting form and coupling strength of the πNN vertex is consistent with the phenomenological OPEP.

The πNN vertex function and off-mass-shell πN scattering

We have extended the dispersion relation calculation of the πNN vertex function to include off-shell terms in the πN scattering matrix. These off-shell terms are constrained by the current algebra and PCAC results, and contribute to the N N → ππ s-wave. As such, they add to the kinematic off-shell effects which Durso, Jackson and VerWest found in the p-terms. The off-shell terms increase the calculated Goldberger-Treiman discrepancy from 0.02 to 0.03, bringing it into agreement with the field theory value of Jones and Scadron (0.035). The calculated discrepancy remains smaller than the experimental value of 0.06±0.01.