Nuclear Forces from Chiral EFT: The Unresolved Issues

In recent years, there has been substantial progress in the derivation of nuclear forces from chiral effective field theory (EFT). Accurate two-nucleon forces have been constructed at next-to-next-to-next-to-leading order (N³LO) and applied (together with three-nucleon forces at NNLO) to nuclear few- and many-body systems??with a good deal of success. This may suggest that the 80-year old nuclear force problem has finally been cracked. Not so! Some pretty basic issues are still unresolved. In this talk, I focus on the two most pressing ones, namely, subleading many-body forces and the proper renormalization of the two-nucleon potential.     

An overview of quarks in nuclei

In this report, the relevance and possible manifestations of quark-gluon degrees of freedom in nuclear systems are discussed. An attempt is made to view the subject in the context of the modern theory of fundamental interactions based on the concept of local gauge invariance. How this gives rise to the quantum chromodynamics of colored quarks and gluons is recounted. An introduction is given to the concepts of asymptotic freedom, color confinement, lattice gauge theory, and chiral symmetry. The nature, the successes and limitations of phenomenological quark models of hadrons are described. The possible appearance of exotic hadrons, and of quark effects in nuclear forces, in high-energy nuclear reactions and in nuclear properties are discussed. The expected properties and possible production and detection of unusual quark-gluon phases of matter are reviewed. Both the experimental detection and the theoretical treatment of quark effects in nuclei appear difficult, but the question of how nuclear physics fits into the panorama which is the modern theory of fundamental interactions appears to represent a worthwhile intellectual challenge.     

A quantum Monte Carlo method for nucleon systems

We describe a quantum Monte Carlo method for Hamiltonians which include tensor and other spin interactions such as those that are commonly encountered in nuclear structure calculations. The main ingredients are a Hubbard-Stratonovich transformation to uncouple the spin degrees of freedom along with a fixed node approximation to maintain stability. We apply the method to neutron matter interacting with a central, spin-exchange, and tensor forces. The addition of isospin degrees of freedom is straightforward.     

Correlated charged pions from chiral dynamics in high-energy nuclear collisions

It is expected that chiral symmetry is approximately restored in the very excited matter produced in a high-energy nuclear collision and that the chiral order parameter will thereafter quickly relax towards its aligned vacuum value. This non-equilibrium evolution of the environment endows the pionic degrees of freedom with a time-dependent effective mass and this agency, in turn, may create correlated soft pions that could provide specific observable signatures of the chiral dynamics that are based solely on charged pions.     

On Kaon Condensation in Dense Nuclear,Matter

The properties of kaons and antikaons in dense nuclear matter are investigated within the framework of relativistic mean-field theory including delta degrees of freedom. The couplings of kaon-baryon interactions are determined by the chiral models. We find that the effective masses and energies of kaons and antikaons are reduced on account of the delta resonance in the nuclear matter. This mechanism may enhance the possibility of the existence of kaon condensation.     

Spontaneous P-violation in QCD in extreme conditions

We investigate the possibility of parity being spontaneously violated in QCD at finite baryon density and temperature. QCD is approximated by a generalized σ model with two isomultiplets of scalars and pseudoscalars. The interaction with the chemical potential is introduced via the coupling to constituent quark fields as nucleons are not considered as point-like degrees of freedom in our approach. This mechanism of parity violation is based on interplay between lightest and heavier degrees of freedom and it cannot be understood in simple models retaining the pion and nucleon sectors solely. We argue that, in the appropriate environment (dense and hot nuclear matter of a few normal densities and moderate temperatures), parity violation may be the rule rather than the exception and its occurrence is well compatible with the existence of stable bound state of normal nuclear matter. We prove that the so-called ‘chiral collapse’ never takes place for the parameter region supporting spontaneous parity violation.     

On the connection between quantum and classical descriptions

The review paper presents generalization of d??Alembert??s variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum force ?j, ??. Spatial attention is dedicated to the systems with (hidden) symmetries. It is shown how the symmetry reduces the number of quantum degrees of freedom down to the independent ones. The sin-Gordon model is considered as an example of such field theory with symmetry. It is shown why the particles S-matrix is trivial in that model.     

Chiral Kosterlitz-Thouless transition in the frustrated Heisenberg antiferromagnet on a pyrochlore slab

Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. In contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally noncoplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. Under certain conditions, the model exhibits a novel Kosterlitz-Thouless-type transition at a finite temperature associated with these chiral degrees of freedom.     

Purely transmitting defect field theories

We define an infinite class of integrable theories with a defect which are formulated as chiral defect perturbations of a conformal field theory. Such theories are massless in the bulk and are purely transmitting through the defect. The integrability of these theories requires the introduction of defect degrees of freedom. Such degrees of freedom lead to a novel set of Yang-Baxter equations. The defect degrees of freedom are identified through folding the chiral defect theories onto massless boundary field theories. The examples of the sine-Gordon theory and Ising model are worked out in some detail.     

Spin polarizabilities of the nucleon from polarized low-energy Compton scattering

As a guideline for forthcoming experiments, we present predictions from Chiral Effective Field Theory for polarized cross-sections in low-energy Compton scattering for photon energies below 170 MeV, both on the proton and on the neutron. Special interest is put on the role of the nucleon spin polarizabilities which can be examined especially well in polarized Compton scattering. We present a model-independent way to extract their energy dependence and static values from experiment, interpreting our findings also in terms of the low-energy effective degrees of freedom inside the nucleon: The polarizabilities are dominated by chiral dynamics from the pion cloud, except for resonant multipoles, where contributions of the -resonance turn out to be crucial. We therefore include it as an explicit degree of freedom. We also identify some experimental settings which are particularly sensitive to the spin polarizabilities.Received: 19 August 2003, Revised: 30 October 2003, Published online: 27 April 2004PACS: 13.40.-f Electromagnetic processes and properties - 13.60.Fz Elastic and Compton scattering - 14.20.Dh Protons and neutronsH.W. Grießhammer: Permanent address: Technische Universität MünchenT.R. Hemmert: Permanent address: Technische Universität München     

Monte Carlo study of long-range chiral structure in QCD

Results of a Monte Carlo study of long-range chiral structure is massless 4-dimensional QCD are presented. The algorithm employed integrates fermion degrees of freedom exactly. The behavior of chiral correlations in both abelian and SU(2) color theories is compared. We find strong evidence for chiral breakdown, with a solution of the U(1) problem, in lattice QCD at large β.     

Fluid dynamical description of the chiral transition

We investigate the dynamics of the chiral transition in an expanding quark-antiquark plasma. The calculations are made within a linear σ-model with explicit quark and antiquark degrees of freedom. We solve numerically the classical equations of motion for chiral fields coupled to the fluid dynamical equations for the plasma. Fast initial growth and strong oscillations of the chiral field and strong amplification of long wavelength modes of the pion field are observed in the course of the chiral transition.     

QCD aspects of hadron physics

Several topics in hadron physics at different scales of resolution are discussed. First, deep-inelastic scattering from nucleons and nuclei is viewed in a light-come coordinate space picture. Then the smooth transition from parton to hadron degrees of freedom is demonstrated by analysing generalized Q²-dependent polarizabilities of the nucleon. Turning to low energy QCD we summarize recent developments related to the role of strange quarks in Chiral SU(3) Dynamics, a non-perturbative coupled channel approach to hadronic processes. Finally we elaborate on a unification of QCD Sum Rules with aspects of spontaneous chiral symmetry breaking in the analysis of quark-antiquark excitations of the condensed QCD vacuum and in nuclear matter.     

An anomalous way to quantize solitons

We picture soliton solutions as collective modes. Their quantization is performed analogously to examples from many-body theory. In contrast to previous approaches we aim for effective actions of both type of degrees of freedom, collective as well as the non-collective ones, plus coupling terms. The procedure used is an adapted version of the Bohm-Pines method, originally developed for treating collective modes of the electron gas, later applied to nuclear transport theory. As one of the novel features we exploit chiral transformations to introduce the collective variables.Dedicated to Prof. Dr. H. J. Mang on the occasion of his 60th birthday     

Modern theory of nuclear forces A.D. 2006

I present and discuss recent results on nuclear forces and few-nucleon systems obtained in the framework of chiral effective nuclear field theory.     

Drinfeld-Sokolov Construction of Heterotic Toda Model

A free field representation for the left-right asymmetric conformal Toda theory based on simplf-laced even-rank Lie algebras is given. It is shown that the classical chiral exchange algebra for such theories can be reconstructed from free chiral bosons via Drinfeld-Sokolov linear systems, and is a bit more complicated than that of the standard Toda due to some additional δ-function terms and extra degrees of freedom.