W. Weise

Pions and Nuclei

The pion has emerges as the main feature of nuclear structure beyond the traditional description in terms of neutrons and protons. It manifests itself in a number of areas which are normally only loosely interlinked, but intimately related to the pion-nucleon and pion-nuclear interactions: the nucleon-nucleon force; the nuclear many-body problem; nuclear electromagnetic and weak interactions; nuclear spinisospin interactions; pion-nucleus scattering and reactions; etc. This book is a systematic introduction to and survey of nuclear pion physics, a major sub-field of nuclear pion physics. The theoretical foundations are padagogically developed and the physical picture is illustrated with supporting experimental examples.

The Nambu and Jona Lasinio model: Its implications for hadrons and nuclei

Abstract We review recent developments and applications of the Nambu and Jona-Lasinio model with three quark flavours, based on the SU(3)L ⊗ SU(3)R ⊗ U(1)V symmetry of QCD. The model describes dynamical quark mass generation and spontaneous chiral symmetry breaking and includes effects of the axial U(1) anomaly. Mesons emerge as quark-antiquark modes; their spectra and properties are discussed. Properties of constituent quarks as quasi-particles, dressed by their strong interactions, are summarized. The quark-diquark structure of baryons is developed, and a brief summary is given on baryonic solitons as they result from the NJL model. Finally, selected implications for nuclear physics are described, such as the change of hadron structure in a dense and hot nuclear medium.

Chiral dynamics and the low-energy kaon-nucleon interaction

Abstract We examine the meson-baryon interaction in the strangeness S = −1 sector using an effective chiral Lagrangian. Potentials are derived from this Lagrangian and used in a coupled-channel calculation of the low-energy observables. The potentials are constructed such that in the Born approximation the s-wave scattering length is the same as that given by the effective chiral Lagrangian, up to order q2. A comparison is made with the available low-energy hadronic data of the coupled K−p, Σπ, Λπ system, which includes the Λ(1405) resonance, K−p elastic and inelastic scattering, and the threshold branching ratios of the K−p decay. Good fits to the experimental data and estimates of previously unknown Lagrangian parameters are obtained.

Pionic modes of excitation in nuclei

Abstract A unified treatment of pionic nuclear excitations both at low energy (ω«m π ) and at scattering energies (mπ ≲ ω ≲ 3 m π) is presented. The description is based on a many-body picture of the nucleus consisting of nucleons and Δ(1232) isobars interacting through meson exchange. Pion-nucleus elastic scattering is reviewed. Scattering in the 3.3 resonance region as well as photon-induced excitations of the Δ(1232) in nuclei a re treated in the Δ-hole model. Pion-like nuclear excited states at low energy are discussed with special emphasis of their significance in extracting information about nuclear spin-isospin correlations. Critical opalescence effects related to the possible occurance of a pion condensate are so far shown to be absent. Finally, the role of the Δ(1232) in the quenching of low energy Gamow-Teller and isovector magnetic spin transitions in the long wavelength limit is investigated.

Phases of QCD: Lattice thermodynamics and a field theoretical model

We investigate three-color QCD thermodynamics at finite quark chemical potential. Lattice QCD results are compared with a generalized Nambu Jona-Lasinio model in which quarks couple simultaneously to the chiral condensate and to a background temporal gauge field representing Polyakov loop dynamics. This so-called PNJL model thus includes features of both deconfinement and chiral symmetry restoration. The parameters of the Polyakov loop effective potential are fixed in the pure-gauge sector. The chiral condensate and the Polyakov loop as functions of temperature and quark chemical potential are calculated by minimizing the thermodynamic potential of the system. The resulting equation of state, (scaled) pressure difference and quark number density at finite quark chemical potential are then confronted with corresponding Lattice QCD data.

Pion scattering and isobars in nuclei

Abstract General features of pion scattering by systems with equal numbers of neutrons and protons are discussed. To begin with, it is pointed out that most phenomena can be understood within the framework of a simple formalism in terms of an index of refraction for pions traversing nuclear matter. The pion-nucleon scattering amplitude is of resonance type, the resonance being identified with the Δ (1230 MeV) resonance. The Lorentz-Lorenz correction to the scattering, arising from short-range nucleon-nucleon correlations, is first discussed in classical terms, and then later in terms of isobar dynamics. It is found that there are only small differences in descriptions of pion-nucleon scattering in nucleon medium : a) in which the isobar is considered as a composite system of nucleon and pion, b) in which the isobar is considered to be an elementary particle. Self-energy interactions of the isobar with the nuclear medium are estimated, and found to be nearly as attractive as those of a nucleon. In the final section we outline a dynamical approach towards pion scattering from finite nuclei and give instruction on “How to know an isobar when you see one”.

The Structure of the Nucleon

Introduction ELECTROMAGNETIC STRUCTURE OF THE NUCLEON Elastic Electron Scattering Electromagnetic Form Factors of the Nucleon Nucleon Resonances Compton Scattering WEAK PROBES OF NUCLEON STRUCTURE Matrix Elements of the Weak Currents The Axial Matrix Elements in Charged Current Neutrino Reactions Beta-Decay Myon Capture Near Threshold Pion Electroproduction Neutral Current Interactions DEEP-INELASTIC LEPTON SCATTERING ON THE NUCLEON The Parton Model Scaling Violations Sum Rules Neutrino Deep-Inelastic Scattering Experimental Results for Unpolarised Targets Spin Dependent Structure Functions Qualitative Understanding of Parton Distributions ELEMENTS OF QCD Basic Lagrangian Feynman Rules Renormalization The Renormalization Group Deep Inelastic Scattering: Parton Model Deep Inelastic Scattering within QCD ASPECTS OF NON-PERTUBATIVE QCD Symmetries, Currents and Anomalies Structure of the QCD Vacuum: Brief Survey QCD Sum Rules Lattice QCD and the Nucleon CHIRAL SYMMETRY AND NUCLEON STRUCTURE Chiral Effective Field Theory Baryon Masses and Sigma Terms Chiral Low Energy Theorems Summary: The Pion Cloud of the Nucleon MODELS OF THE NUCLEON Survey Non-relativistic Quark Models Soliton Models Bag Models Chiral Quark Models Chiral Solitons Final Remarks Appendix A: Notations and Conventions Appendix B: Cross Sections for Lepton and Photon Nucleon Scattering.

SU(3) chiral dynamics with coupled channels eta and kaon photoproduction

We identify the next-to-leading order s-wave amplitudes of the SU(3) chiral meson-baryon Lagrangian with a coupled-channel potential which is iterated in a Lippmann-Schwinger equation. The strangeness S = −1 resonance Λ(1405) and the S 11(1535) nucleon resonance emerge as quasi-bound states of anti-kaon/nucleon and kaon/Σ-hyperon. Our approach to meson photoproduction introduces no new parameters. By adjusting a few finite range parameters we are able to simultaneously describe a large amount of low energy data. These include the cross sections of K − p elastic and inelastic scattering, the cross sections of eta meson and kaon photoproduction from nucleons as well as those of pion induced production of etas and kaons (15 different reaction channels altogether).

Current correlation functions, QCD sum rules and vector mesons in baryonic matter

Abstract Based on an effective Lagrangian which combines chiral SU(3) dynamics with vector meson dominance, we have developed a model for the forward vector meson-nucleon scattering amplitudes. We use this as an input to calculate the low energy part of the current-current correlation function in nuclear matter. Its spectrum enters directly in the “left-hand side” of QCD sum rules. For the isovector channel we find a significant enhancement of the in-medium spectral density below the ϱ resonane while the ρ meson mass itself changes only slightly. The situation is different in the isoscalar channel, where the mass and peak position of the ω meson move downward while its width increases less drastically than in the ρ meson case. For the φ meson we find almost no mass shift; the width of the peak broadens moderately. We observe a remarkable degree of consistency with the operator product expansion of QCD sum rules in all three channels. We point out, however, that these results cannot simply be interpreted, as commonly done, in terms of a universal rescaling of vector meson masses in matter.

Chiral dynamics and the S11 (1535) nucleon resonance

Abstract The SU(3) chiral effective lagrangian at next-to-leading order is applied to the S-wave meson-baryon interaction in the energy range around the ηN threshold. A potential is derived from this lagrangian and used in a coupled channel calculation of the πN, ηN, KΛ, KΣ system in the isospin - 1 2 , l = 0 partial wave. Using the same parameters as obtained previously from a fit to the low energy K N data it is found that a quasi-bound KΣ-KΛ-state is formed, with properties remarkably similar to the S11(1535) nucleon resonance. In particular, we find a large partial decay width into ηN consistent with the empirical data.