Ghost poles in the nucleon propagator in the linear sigma model approach and its role in pi N low-energy theorems

Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff and Wilets (BPW), These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions, Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous studies of pi N scattering using ''dressed'' nucleon propagator and bare vertices, did by Nutt and Wilets in the 70's (NW), it was found that if these poles are explicitly included, the value of the isospin-even amplitude A((+)) is satisfied within 20% at threshold. The absence of a theoretical explanation for the ghosts and the lack of chiral symmetry in these previous studies led us to re-investigate the subject using the approach of the linear sigma-model and study the interplay of low-energy theorems for pi N scattering and ghost poles. For bare interaction vertices we find that ghosts are present in this model as well and that the A((+)) value is badly described, As a first approach to remove these complex poles, we dress the vertices with phenomenological form factors and a reasonable agreement with experiment is achieved, In order to fix the two cutoff parameters, we use the A((+)) value for the chiral limit (m(pi) --> 0) and the experimental value of the isoscalar scattering length, Finally, we test our model by calculating the phase shifts for the S waves and we find a good agreement at threshold. (C) 1997 Elsevier B.V. B.V.

Pauli nonlocality in heavy-ion rainbow scattering: A further test of the folding model

Nonlocal interactions are an intrinsically quantum phenomenon. In this work we point out that, in the context of heavy ions, such interactions can be studied through the refractive elastic scattering of these systems at intermediate energies. We show that most of the observed energy dependence of the local equivalent bare potential arises from the exchange nonlocality. The nonlocality parameter extracted from the data was found to be very close to the one obtained from folding models. The effective mass of the colliding, heavy-ion, system was found to be close to the nucleon effective mass in nuclear matter.

Dispersion relations and the spin polarizabilities of the nucleon

A forward dispersion calculation is implemented for the spin polarizabilities γ1, ⋯, γ4 of the proton and the neutron. These polarizabilities are related to the spin structure of the nucleon at low energies and are structure-constants of the Compton scattering amplitude at script O sign(ω3). In the absence of a direct experimental measurement of these quantities, a dispersion calculation serves the purpose of constraining the model building, and of comparing with recent calculations in heavy baryon chiral perturbation theory. © 1998 Elsevier Science B.V.

NN scattering: Chiral predictions for asymptotic observables

We assume that the nuclear potential for distances larger than 2.5 fm is given just by the exchanges of one and two pions and, for the latter, we adopt a model based on chiral symmetry and subthreshold pion-nucleon amplitudes, which contains no free parameters. The predictions produced by this model for nucleon-nucleon observables are calculated and shown to agree well with both experiment and those due to phenomenological potentials.

Generalized polarizabilities and electroexcitation of the nucleon

Generalized nucleon polarizabilities for virtual photons can be defined in terms of electroproduction cross sections as function of the 4-momentum transfer Q2. In particular, the sum of the generalized electric and magnetic polarizabilities ∑ = α + β and the spin polarizability γ can be expressed by virtual photon absorption cross sections integrated over the excitation energy. These quantities have been calculated within the framework of the recently developed unitary isobar model for pion photo- and electroproduction on the proton, which describes the available experimental data up to an excitation energy of about 1 GeV. Our results have been compared to the predictions of chiral perturbation theory. © 1999 Elsevier Science B.V. All rights reserved.

Nucleon-nucleon interaction: Central potential and pion production

We show that the tail of the chiral two-pion exchange nucleon-nucleon potential is proportional to the pion-nucleon (πN) scalar form factor and discuss how it can be translated into effective scalar meson interactions. We then construct a kernel for the process NN → πNN, due to the exchange of two pions, which may be used in either three-body forces or pion production in NN scattering. Our final expression involves a partial cancellation among three terms, due to chiral symmetry, but the net result is still important. We also find that, at large internucleon distances, the kernel has the same spatial dependence as the central NN potential and we produce expressions relating these processes directly.

Heavy-light mesons scattering from nucleons: Quark-gluon and meson exchanges

We investigate the scattering of heavy-light K and D mesons by nucleons at low energies. The short-distance part of the interaction is described by quark-gluon interchange and the longdistance part is described by a one-meson-exchange model that includes the contributions of vector (ρ, ω) and scalar (σ) mesons. The microscopic quark model incorporates a confining Coulomb potential extracted from lattice QCD simulations and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The derived effective meson-nucleon potential is used in a Lippmann-Schwinger equation to obtain s-wave phase shifts. Our final aim is to set up a theoretical framework that can be extended to finite temperatures and baryon densities. © 2010 American Institute of Physics.

Problem of the statistical model in deep inelastic scattering phenomenology

Recent deep inelastic data leads to an up-down quark asymmetry of the nucleon sea. Explanations of the flavour asymmetry and the di-lepton production in proton-nucleus collisions call for a temperature T ≈ 100 MeV in a statistical model. This T may be conjectured as being due to the Fulling-Davies-Unruh effect. But it is not possible to fit the structure function itself.

Dispersion approach to real and virtual Compton scattering

In recent years, new precision experiments have become possible withthe high luminosity accelerator facilities at MAMIand JLab, supplyingphysicists with precision data sets for different hadronic reactions inthe intermediate energy region, such as pion photo- andelectroproduction and real and virtual Compton scattering.By means of the low energy theorem (LET), the global properties of thenucleon (its mass, charge, and magnetic moment) can be separated fromthe effects of the internal structure of the nucleon, which areeffectively described by polarizabilities. Thepolarizabilities quantify the deformation of the charge andmagnetization densities inside the nucleon in an applied quasistaticelectromagnetic field. The present work is dedicated to develop atool for theextraction of the polarizabilities from these precise Compton data withminimum model dependence, making use of the detailed knowledge of pionphotoproduction by means of dispersion relations (DR). Due to thepresence of t-channel poles, the dispersion integrals for two ofthe six Compton amplitudes diverge. Therefore, we have suggested to subtract the s-channel dispersion integrals at zero photon energy($nu=0$). The subtraction functions at $nu=0$ are calculated through DRin the momentum transfer t at fixed $nu=0$, subtracted at t=0. For this calculation, we use the information about the t-channel process, $gammagammatopipito Nbar{N}$. In this way, four of thepolarizabilities can be predicted using the unsubtracted DR in the $s$-channel. The other two, $alpha-beta$ and $gamma_pi$, are free parameters in ourformalism and can be obtained from a fit to the Compton data.We present the results for unpolarized and polarized RCS observables,%in the kinematics of the most recent experiments, and indicate anenhanced sensitivity to the nucleon polarizabilities in theenergy range between pion production threshold and the $Delta(1232)$-resonance.newlineindentFurthermore,we extend the DR formalism to virtual Compton scattering (radiativeelectron scattering off the nucleon), in which the concept of thepolarizabilities is generalized to the case of avirtual initial photon by introducing six generalizedpolarizabilities (GPs). Our formalism provides predictions for the fourspin GPs, while the two scalar GPs $alpha(Q^2)$ and $beta(Q^2)$ have to befitted to the experimental data at each value of $Q^2$.We show that at energies betweenpion threshold and the $Delta(1232)$-resonance position, thesensitivity to the GPs can be increased significantly, as compared tolow energies, where the LEX is applicable. Our DR formalism can be used for analysing VCS experiments over a widerange of energy and virtuality $Q^2$, which allows one to extract theGPs from VCS data in different kinematics with a minimum of model dependence.

Polarization observables in virtual compton scattering

Virtual Compton Scattering (VCS) is an important reaction for understanding nucleon structure at low energies. By studying this process, the generalized polarizabilities of the nucleon can be measured. These observables are a generalization of the already known polarizabilities and will permit theoretical models to be challenged on a new level. More specifically, there exist six generalized polarizabilities and in order to disentangle them all, a double polarization experiment must be performed. Within this work, the VCS reaction p(e,e p)gamma was measured at MAMI using the A1 Collaboration three spectrometer setup with Q2=0.33 (GeV/c)2. Using the highly polarized MAMI beam and a recoil proton polarimeter, it was possible to measure both the VCS cross section and the double polarization observables. Already in 2000, the unpolarized VCS cross section was measured at MAMI. In this new experiment, we could confirm the old data and furthermore the double polarization observables were measured for the first time. The data were taken in five periods between 2005 and 2006. In this work, the data were analyzed to extract the cross section and the proton polarization. For the analysis, a maximum likelihood algorithm was developed together with the full simulation of all the analysis steps. The experiment is limited by the low statistics due mainly to the focal plane proton polarimeter efficiency. To overcome this problem, a new determination and parameterization of the carbon analyzing power was performed. The main result of the experiment is the extraction of a new combination of the generalized polarizabilities using the double polarization observables.

Virtual Compton scattering in baryon chiral perturbation theory

This thesis is concerned with the calculation of virtual Compton scattering (VCS) in manifestly Lorentz-invariant baryon chiral perturbation theory to fourth order in the momentum and quark-mass expansion. In the one-photon-exchange approximation, the VCS process is experimentally accessible in photon electro-production and has been measured at the MAMI facility in Mainz, at MIT-Bates, and at Jefferson Lab. Through VCS one gains new information on the nucleon structure beyond its static properties, such as charge, magnetic moments, or form factors. The nucleon response to an incident electromagnetic field is parameterized in terms of 2 spin-independent (scalar) and 4 spin-dependent (vector) generalized polarizabilities (GP). In analogy to classical electrodynamics the two scalar GPs represent the induced electric and magnetic dipole polarizability of a medium. For the vector GPs, a classical interpretation is less straightforward. They are derived from a multipole expansion of the VCS amplitude. This thesis describes the first calculation of all GPs within the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. Because of the comparatively large number of diagrams - 100 one-loop diagrams need to be calculated - several computer programs were developed dealing with different aspects of Feynman diagram calculations. One can distinguish between two areas of development, the first concerning the algebraic manipulations of large expressions, and the second dealing with numerical instabilities in the calculation of one-loop integrals. In this thesis we describe our approach using Mathematica and FORM for algebraic tasks, and C for the numerical evaluations. We use our results for real Compton scattering to fix the two unknown low-energy constants emerging at fourth order. Furthermore, we present the results for the differential cross sections and the generalized polarizabilities of VCS off the proton.

Nucleon electromagnetic structure studies in the spacelike and timelike regions

The thesis investigates the nucleon structure probed by the electromagnetic interaction. One of the most basic observables, reflecting the electromagnetic structure of the nucleon, are the form factors, which have been studied by means of elastic electron-proton scattering with ever increasing precision for several decades. In the timelike region, corresponding with the proton-antiproton annihilation into a electron-positron pair, the present experimental information is much less accurate. However, in the near future high-precision form factor measurements are planned. About 50 years after the first pioneering measurements of the electromagnetic form factors, polarization experiments stirred up the field since the results were found to be in striking contradiction to the findings of previous form factor investigations from unpolarized measurements. Triggered by the conflicting results, a whole new field studying the influence of two-photon exchange corrections to elastic electron-proton scattering emerged, which appeared as the most likely explanation of the discrepancy. The main part of this thesis deals with theoretical studies of two-photon exchange, which is investigated particularly with regard to form factor measurements in the spacelike as well as in the timelike region. An extraction of the two-photon amplitudes in the spacelike region through a combined analysis using the results of unpolarized cross section measurements and polarization experiments is presented. Furthermore, predictions of the two-photon exchange effects on the e+p/e-p cross section ratio are given for several new experiments, which are currently ongoing. The two-photon exchange corrections are also investigated in the timelike region in the process pbar{p} -> e+ e- by means of two factorization approaches. These corrections are found to be smaller than those obtained for the spacelike scattering process. The influence of the two-photon exchange corrections on cross section measurements as well as asymmetries, which allow a direct access of the two-photon exchange contribution, is discussed. Furthermore, one of the factorization approaches is applied for investigating the two-boson exchange effects in parity-violating electron-proton scattering. In the last part of the underlying work, the process pbar{p} -> pi0 e+e- is analyzed with the aim of determining the form factors in the so-called unphysical, timelike region below the two-nucleon production threshold. For this purpose, a phenomenological model is used, which provides a good description of the available data of the real photoproduction process pbar{p} -> pi0 gamma.

Improved dispersive analysis of the scalar form factor of the nucleon

We present a coupled system of integral equations for the pp → ¯NN and ¯K K → ¯N N S-waves derived from Roy–Steiner equations for pion–nucleon scattering. We discuss the solution of the corresponding two-channel Muskhelishvili–Omnès problem and apply the results to a dispersive analysis of the scalar form factor of the nucleon fully including ¯KK intermediate states. In particular, we determine the corrections Ds and DD, which are needed for the extraction of the pion– nucleon s term from pN scattering, and show that the difference DD −Ds = (−1.8±0.2)MeV is insensitive to the input pN parameters.

Isospin breaking in pion–deuteron scattering and the pion–nucleon scattering lengths

In recent years, high-accuracy data for pionic hydrogen and deuterium have become the primary source of information on the pion–nucleon scattering lengths. Matching the experimental precision requires, in particular, the study of isospin-breaking corrections both in pion– nucleon and pion–deuteron scattering. We review the mechanisms that lead to the cancellation of potentially enhanced virtual-photon corrections in the pion–deuteron system, and discuss the subtleties regarding the definition of the pion–nucleon scattering lengths in the presence of electromagnetic interactions by comparing to nucleon–nucleon scattering. Based on the p±p channels we find for the virtual-photon-subtracted scattering lengths in the isospin basis a1/2/ g= (170.5±2.0) · 10−3M−1p and a3/2/ g= (−86.5±1.8) · 10−3M−1p .

Effects of nuclear ground state correlations on pion scattering /

"LA-UR-76-1844."