PCAC and the non-relativistic pion-nucleon vertex

The Foldy-Wouthuysen reduction technique is applied to the sigma model and pseudovector coupling pion-nucleon Lagrangians. In contrast to electrodynamics the requirement that the non-relativistic pion-nucleon Lagrangian have an approximate symmetry under the same global transformation as the relativistic theory does not uniquely fix the Foldy-Wouthuysen transformation. It is shown that the partially conserved axial-vector current relation is satisfied by the non-relativistic theory and the implications of this on the form of the effective pion-nucleon vertex are discussed.     

The nucleon axial form factor and the pion-nucleon vertex function

The nucleon axial current and related form factors are investigated in a model of relativistic quarks confined by a scalar potential of the formM(r)=c r ⁿ , with special emphasis on center-of-mass corrections and pionic effects. Pionic contributions to the axial form factorG _A (q ²) from af _π?_μφ term with constantf _π are demonstrated to vanish. The pion-nucleon form factorG _πNN (q ²) is derived and turns out to be longer ranged thanG _A (q ²). The induced pseudo-scalar form factorG _p (q ²) is shown to be connected toG _πNN (q ²) by the standard PCAC relation, contributions from the quark core toG _p (q ²) being negligibly small.     

The ’t Hooft vertex revisited

In 1976 ’t Hooft introduced an elegant approach towards understanding the physical consequences of the topological structures that appear in non-Abelian gauge theories. These effects are concisely summarized in terms of an effective multi-fermion interaction. These old arguments provide a link between a variety of recent and sometimes controversial ideas including discrete chiral symmetries appearing in some models for unification, ambiguities in the definition of quark masses, and flaws with some simulation algorithms in lattice gauge theory.     

Pole expansion of the deuteron vertex functions revisited

New fits to the deuteronS andD state vertex functions are presented using a standard relativistic pole expansion. The new data from electron scattering admit two solutions which should be distinguishable by measuring the tensor polarization ined scattering.This note has been stimulated by discussions with Barbara Badelek. We thank S. Platchkov for providing the Saclay data in numerical form.     

The pion-nucleon forward scattering amplitude

The pion-nucleon forward scattering amplitude has been calculated from new data of the total cross sections, using several assumptions on the energy dependence above 20 GeV. The results are presented as complex diagrams of the forward amplitude, which are of interest for the discussion of the nucleonic resonances and the non-resonant background scattering. In addition the predictions for the elastic forward cross sections are given as well as the contributions of the real parts to this quantity. A comparison with the new Saclay data of the charge exchange forward cross section leads to the estimate αρ≈0.6, if a Regge behaviour is assumed above 20 GeV. There are indications in favour of a new\(T = \tfrac{1}{2}\) resonance at the total c.m. energyW≈2.8 GeV.     

Electroweak pion-nucleon constant

The parity-violating pion-nucleon coupling constant for the neutral currents of electroweak interaction is calculated by the method of QCD sum rules. In doing this, operators up to dimension 5 are retained in the operator-product expansion for the correlation function in an external pion field. That the value obtained for the pion-nucleon coupling constant is comparatively small stems from a partial cancellation between the leading perturbative and condensate contributions. This constant is compared with experimental data and with the results of calculations performed by other authors.     

Low-energy pion-nucleon scattering

Several topics in pion-nucleon scattering at low energies are addressed. First, we review the predictions of chiral symmetry for the near-threshold region. The pion-nucleon scattering lengths and the Cheng-Dashen theorem with the related issue of the strangeness content of the nucleon are discussed in some detail. Finally, the status of the scalar mesons and the relevance of the pomeron and the concept of duality for pion-nucleon dynamics is pointed out.Lecture given at the 8th Summer School on Intermediate Energy Physics: Hadron Dynamics at Low and Intermediate Energies, Prague, July 10–14, 1995.I would like to thank the organizers of the Praha Indian-summer school for inviting me to this beautiful city. I am indebted to Th. Rijken and J. J. de Swart for discussions about the pomeron, the scalar mesons, and partial-wave analysis, and to U. van Kolck and J. Friar for discussions about chiral symmetry. This work was included in the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM) with financial support from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO).     

Backward pion-nucleon scattering

A global analysis of the world data on differential cross-sections and polarization asymmetries of backward pion-nucleon scattering for invariant collision energies above 3GeV is performed in a Regge model. Including the N_a\ensuremath N_{\alpha} , N_g\ensuremath N_{\gamma} , D_d\ensuremath \Delta_{\delta} and D_b\ensuremath \Delta_{\beta} trajectories, we reproduce both angular distributions and polarization data for small values of the Mandelstam variable u , in contrast to previous analyses. The model amplitude is used to obtain evidence for baryon resonances with mass below 3GeV. Our analysis suggests a G₃₉\ensuremath G_{39} -resonance with a mass of 2.83GeV as member of the D_b\ensuremath \Delta_{\beta} -trajectory from the corresponding Chew-Frautschi plot.     

The pion-nucleon scattering lengths from pionic deuterium

We use the framework of effective field theories to discuss the determination of the S-wave scattering lengths from the recent high-precision measurements of pionic deuterium observables. The theoretical analysis proceeds in several steps. Initially, the precise value of the pion-deuteron scattering length is extracted from the data. Next, is related to the S-wave scattering lengths a ₊ and a _-. We discuss the use of this information for constraining the values of these scattering lengths in the full analysis, which also includes the input from the pionic hydrogen energy shift and width measurements, and thoroughly investigate the accuracy limits for this procedure. In this paper, we also give a detailed comparison to other effective field theory approaches, as well as to the earlier work on the subject, carried out within the potential model and multiple scattering framework. Received: 28 January 2005, Published online: 8 April 2005 PACS: 36.10.Gv, 12.39.Fe, 13.75.Cs, 13.75.Gx A. Rusetsky: On leave of absence from High Energy Physics Institute, Tbilisi State University, University St. 9, 380086 Tbilisi, Georgia. This research is part of the EU Integrated Infrastructure Initiative Hadron Physics Project under contract number RII3-CT-2004-506078. Work supported in part by DFG (SFB/TR 16, “Subnuclear Structure of Matter”). An erratum to this article is available at .     

Strong vertex corrections from weak disorder in 2D d-wave superconductors

We show that weak static random potentials have pronounced effects on the quasiparticle states of a 2Dd-wave superconductor close to a node. We prove that the vertex correction coming from the simplest crossed diagram is important even for a nonmagnetic potential. The leading frequency and momentum dependent logarithmic singularities in the self-energy are calculated exactly to second order in perturbation theory. The self-energy corrections lead to a modified low energy density of states which depends strongly on the type of random potential and which can be measured in experiments. There is an exceptional case for a potential with extremely local scatterers and opposite nodes separated by (, ) where an exact cancelation takes place eliminating the leading frequency dependent singularity in the simplest crossed diagram. A comparison of the perturbative results with a self-consistent CPA (coherent potential approximation) for the nonmagnetic disorder reveals qualitative differences in the self-energy at the smallest energies which are due to the neglectance of vertex corrections in CPA.     

Non-renormalization of the weak vertex in gauge theories with integrally charged quarks

We give current algebra arguments to show that toO(α) the colour octet vertices do not renormalize the effective weak vertex between colour singlet hadrons in models with broken colour symmetry. The result does not depend on the details of the mixing between colour gluons and electro-weak bosons.     

The nucleon-nucleon-deuteron vertex

The definition of a “dispersion theoretical nucleon-nucleon-deuteron vertex function” is given. This function is calculated with the help of the one boson exchange model.     

The charge-dependent Bonn potentials with pseudovector pion-nucleon coupling

In order to use high-precision realistic nucleon-nucleon(NN) potentials in relativistic many-body problems,new versions of the charge-dependent Bonn(CD-Bonn) NN potential are constructed with pseudovector pionnucleon coupling,instead of pseudoscalar coupling used in the original CD-Bonn potential as given by Machleidt~(2)).To describe precisely the charge dependence in the NN scattering data,two effective scalar mesons are introduced,whose coupling constants with nucleons are independently determined for each partial wave and for the total angular momentum J≤4.The coupling constants between the vector and pseudovector mesons and a nucleon are identical in all channels.Three revised CD-Bonn potentials with the pseudovector pion-nucleon coupling(pvCD-Bonn) are generated by fitting the Nijmegen PWA phase shift data and the deuteron binding energy with different pion-nucleon coupling strengths.The potentials reproduce the phase shifts in the spin-single channels and the low-energy NN scattering parameters very well,but result in significantly different mixing parameters in the spin-triplet channels.The Dstate probabilities for the deuteron range from 4.22% to 6.05%,demonstrating that the potentials contain different components of the tensor force,which is useful when considering the role of the tensor force in nuclear few-and many-body systems.     

The isospin bounds and phase-contours in pion-nucleon scattering

In this paper we investigate the isospin constraints on differential and integrated (unpolarized and polarized) cross sections in pion-nucleon scattering. Defining$\text{Σ}{}^{\mathrm{(n)}}\text{-}\text{integrated}$ cross sections and using the classical Minkowski and Hölder inequalities we obtain a large class of isospin bounds. The saturation of the isospin bounds is investigated using dispersion relation predictions and a CERN theoretical solution for the phase shifts.     

On the colour contribution to effective weak vertex in broken colour gauge theories

Treating the breaking of colour symmetry via the mixing between the colour gluons and weak bosons (a la Rajasekaran and Roy) it is observed that the colour contribution to the effective weak vertex of a quark at zero momentum transfer is zero uptoO(α). An erratum to this article is available at .     

Peratization of the vertex in the theory of weak interactions with the W-meson

The integral equation for the vertex with crossed boson lines is solved by the known peratization technique. In the zero energy approach some numerical corrections to the simple vertex are obtained and it is shown that higher order corrections cannot be neglected. The influence of these corrections on the cross-section for the neutrino production of the W-meson in the nuclear field and on the W-mass is investigated.This work is a part of a thesis written in 1965 at the Faculty of Technical and Nuclear Physics of The Czech Technical University in Prague.     

Aspects of chiral pion-nucleon physics

The next-to-leading order chiral pion-nucleon Lagrangian contains seven finite low-energy constants. Two can be fixed from the nucleon anomalous magnetic moments and another one from the quark mass contribution to the neutron-proton mass splitting. We find a set of nine observables, which to one-loop order only depend on the remaining four dimension-two couplings. These are then determined from a best fit. We also show that their values can be understood in terms of resonance exchange related to Δ excitation as well as vector and scalar meson exchange. In particular, we discuss the role of the fictitious scalar-isoscalar meson. We also investigate the chiral expansion of the two P-wave scattering volumes P₁⁻ and P₂⁺ as well as the isovector S-wave effective range parameter b⁻. The one-loop calculation is in good agreement with the data. The difference P₁⁻ − P₂⁺ signals chiral loop effects in the πN P-waves. The calculated D- and F-wave threshold parameters compare well with the empirical values.     

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$\text{q}$-pairs inside a hadron. (2) The interaction of the q$\text{q}$-pair with the surrounding quark-gluon medium. An important consequence of these discussions is that meson emission takes place preferentially, if the primary q$\text{q}$-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$\text{q}$-pair to the pion. The resulting form and coupling strength of the πNN vertex is consistent with the phenomenological OPEP.