Nuclear Forces from Effective Field Theory

Chiral effective field theory allows for a systematic and model-independent derivation of the forces between nucleons in harmony with the symmetries of the quantum chromodynamics. After a brief review on the current status in the development of the chiral nuclear forces I will focus on the role of the ??-resonance contributions in the nuclear dynamics. We find improvement in the convergence of the chiral expansion of the nuclear forces if we explicitly take into account the ??-resonance degrees of freedom. The overall results for two-nucleon forces with and without explicit ??-resonance degrees of freedom are remarkably similar.     

Influence of Chiral Mean Field on Kaon In-plane Flow in Heavy Ion Collisions

The influence of the chiral mean field on the K⁺ in-plane flow in heavy ion collisions at SIS energy is investigated within covariant kaon dynamics. For the kaon mesons inside the nuclear medium a quasi-particle picture including scalar and vector fields is adopted and compared to the standard treatment with a static potential. It is confirmed that a Lorentz force from spatial component of the vector field provides an important contribution to the in-medium kaon dynamics and strongly counterbalances the influence of the vector potential on the K⁺ in-plane flow. The calculated results show that the new FOPI data can be reasonably described using the Brown & Rho parametrization, which partly takes into account the correction of higher order contributions in the chiral expansion. This indicates that one can abstract the information on the kaon potential in a nuclear medium from the analysis of the K⁺ in-plane flow.     

Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling (“BR scaling”) and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. It is suggested that BR scaling gives the background around which the fluctuations are weak. A simple model with BR-scaled parameters is constructed and reproduces the properties of the nuclear ground state at normal nuclear matter density successfully. It shows that the tree level in the model Lagrangian is enough to describe the fluctuations around BR-scaled background. The model Lagrangian is consistent thermodynamically and reproduces relativistic Landau Fermi-liquid properties. Such points are important for dealing with hadronic matter under extreme condition. On the other hand, it is shown that the vector current obtained from the chiral Lagrangian is the same as that obtained from Landau–Migdal approach. We can determine the Landau parameter in terms of BR-scaled parameter. However, these two approaches provide different results, when applied to the axial charge. The numerical difference is small. It shows that the axial response is not included properly in the Landau–Migdal approach.     

Chiral perturbation theory in a nuclear background

We propose a novel way to formulate chiral perturbation theory (ChPT) in a nuclear background, characterized by a static, non-uniform distribution of the baryon number that describes the finite nucleus. In the limiting case of a uniform distribution, the theory reduces to the well-known zero-temperature in-medium ChPT. The proposed approach is used to calculate the self-energy of the charged pion in the background of the heavy nucleus at O(p⁵) in the chiral expansion, and to derive the leading terms of the pion-nucleus optical potential.     

Effective field theories, Landau-Migdal Fermi liquid theory, and effective chiral Lagrangians for nuclear matter

We reinterpret Landau-Migdal Fermi liquid theory of nuclear matter as an effective chiral field theory with a Fermi surface. The effective field theory is formulated in terms of a chiral Lagrangian with its mass and coupling parameters scaling à la Brown-Rho and with the Landau-Migdal parameters identified as the fixed points of the field theory. We show how this mapping works out for response functions to the EM vector current and, then using the same reasoning, make a prediction on nuclear axial current, in particular on the enhanced axial-charge transitions in heavy nuclei. We speculate on how to extrapolate the resulting theory, which appears to be sound both theoretically and empirically up to normal nuclear-matter density r₀, to hitherto unexplored higher density regime relevant to relativistic heavy-ion processes and to cold compact (neutron) stars.     

Recent progress on the chiral unitary approach to meson meson and meson baryon interactions

We report on recent progress on the chiral unitary approach, analogous to the effective range expansion in Quantum Mechanics, which is shown to have a much larger convergence radius than ordinary chiral perturbation theory, allowing one to reproduce data for meson meson interaction up to 1.2 GeV. Applications to physical processes so far unsuited for a standard chiral perturbative approach are presented. Results for the extension of these ideas to the meson baryon sector are discussed, together with applications to kaons in a nuclear medium and K⁻ atoms.     

Second-quantization picture of the edge currents in the fractional quantum Hall effect

We study the quantum theory of two-dimensional electrons in a magnetic field and an electric field generated by a homogeneous background. The dynamics separates into a microscopic and a macroscopic mode. The latter is a circular Hall current which is described by a chiral quantum field theory. It is shown how in this second-quantized picture a Laughlin-type wave function emerges. Received: 30 January 2001 / Published online: 23 March 2001     

Nuclear mean field from chirally symmetric effective theory

The mean-field theory of the nuclear many-body problem proposed recently by Furnstahl, Serot, and Tang (FST) is discussed. The FST chiral Lagrangian is derived in terms of an effective field theory. This new approach allows one to construct in a controlled manner the universal nuclear Lagrangian consistent with symmetries of QCD. The FST Lagrangian is constructed by using power counting, i.e., the expansion in powers of the lowest lying hadronic fields and their derivatives. Terms in the Lagrangian are organized by applying Georgi’s naive dimensional analysis and “naturalness” condition. The relevant degrees of freedom are nucleons, pions, an isoscalar-vector field ω meson), an isoscalar-scalar field (σ meson), and an isovector-vector field (ρ meson). The chiral symmetry is realized nonlinearly using a standard WCCWZ procedure.     

Orthonormalization procedure for chiral effective nuclear field theory

We show that the -box expansion of nuclear many-body physics can be applied in nuclear effective field theory with explicit pions and external sources. We establish the corresponding power counting and give an algorithm for the construction of a hermitean and energy-independent potential for arbitrary scattering processes on nucleons and nuclei to a given order in the chiral expansion. Various examples are discussed in some detail.     

A chiral theory of nucleons

We present arguments that QCD at low momenta is reduced to a simple theory given by a path integral over pion fields and quarks which obtain dynamical mass owing to chiral symmetry breaking. The dimensional quantities of this low-momenta theory are fixed through the Λ_QCD parameter. The effective chiral lagrangian is given by a quark determinant in a background chiral field. Its properties are investigated both for slowly and rapidly varying pion fields. Though it satisfies requirements known from theory and phenomenology, it does not possess non-trivial soliton solutions. However we show that, at large N_c, nucleons correspond not to the local minimum of the effective chiral lagrangian but to a minimum of a more subtle quantity. In general, different functionals of the chiral field should be minimized, depending on the baryon charge of the system.We obtain a quantitative picture of nucleons as localized states of “constituent” quarks bound by a self-consistent pion field. Its properties, such as electromagnetic form factors, etc., are investigated in detail. We get very reasonable numerical values for the nucleon static properties.     

Chiral magnetism of the nucleona

We study the quark mass expansion of the magnetic moments of the nucleon in a chiral effective field theory including nucleons, pions and delta-resonances as explicit degrees of freedom. We point out that the usual power counting applied so far to this problem misses important quark mass structures generated via an intermediate isovector M1 nucleon-delta transition. We propose a modified power counting and compare the resulting chiral extrapolation function to available (quenched) lattice data. The extrapolation is found to work surprisingly well, given that the lattice data result from rather large quark masses. Our calculation raises the hope that extrapolations of lattice data utilizing chiral effective field theory might be applicable over a wider range in quark masses than previously thought, and we discuss some open questions in this context. Furthermore, we observe that within the current lattice data uncertainties the extrapolations presented here are consistent with the Padé fit ansatz introduced by the Adelaide group a few years ago. Received: 23 April 2002 / Accepted: 18 July 2002 / Published online: 17 December 2002 RID="c" ID="c"e-mail: themmert@physik.tu-muenchen.de RID="d" ID="d"e-mail: weise@ect.it Communicated by A. Sch?fer     

Recent developments in effective field theory

We will give a short introduction to the one-nucleon sector of chiral perturbation theory and will address the issue of a consistent power counting and renormalization. We will discuss the infrared regularization and the extended on-mass-shell scheme. Both allow for the inclusion of further degrees of freedom beyond pions and nucleons and the application to higher-loop calculations. As applications we consider the chiral expansion of the nucleon mass to order O(q⁶) and the inclusion of vector and axial-vector mesons in the calculation of nucleon form factors.     

Magnetic moment of the delta(1232) resonance in chiral effective-field theory

We perform a relativistic chiral effective-field theory calculation of the radiative pion photoproduction (gammap--> pi(0)pgamma(')) in the Delta-resonance region, to next-to-leading order in the "delta expansion." This work is aimed at a model-independent extraction of the Delta(+) magnetic moment from new precise measurements of this reaction. It also predicts the chiral behavior of Delta's magnetic moment, which can be used to extrapolate the recent lattice QCD results to the physical point.     

The derivative expansion of the fermion number current

The fermion number current is evaluated to leading order in the derivative expansion for chiral fermions in the background of arbitrary Higgs and chiral gauge fields. This current is given by the gauge topological current plus a total divergence term. The total divergence term is absent in Weinberg-Salam theory with one scalar Higgs doublet, even for an arbitrary mass matrix, but appears when several Higgs doublets are present.     

Recent developments in quark nuclear physics

We provide an overview of recent work exploring the quark-mass dependence of hadronic observables and the associated role of chiral non-analytic behavior due to the meson-cloud of hadrons. In particular, we address an issue of great current interest, namely the degree of model independence of results obtained through a controlled extrapolation of lattice QCD simulation results. Physical insights gained from this research are highlighted. We emphasize how chiral effective field theory formulated with a finite-range regulator provides a reliable and model-independent extrapolation to the physical world.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.Gc Lattice QCD calculations - 11.30.Rd Chiral symmetries - 24.85. + p Quarks, gluons, and QCD in nuclei and nuclear processes     

Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory

We discuss lattice simulations of the ground state of dilute neutron matter at next-to-leading order in chiral effective field theory. In a previous paper the coefficients of the next-to-leading-order lattice action were determined by matching nucleon-nucleon scattering data for momenta up to the pion mass. Here the same lattice action is used to simulate the ground state of up to 12 neutrons in a periodic cube using Monte Carlo simulations. We explore the density range from 2% to 8% of normal nuclear density and analyze the ground-state energy as an expansion about the unitarity limit with corrections due to finite scattering length, effective range, and P -wave interactions.     

Chiral dynamics of nuclear saturation

We apply the relativistic chiral Lagrangian to the nuclear equation of state. An effective chiral power expansion scheme, which is constructed to work around nuclear saturation density, is presented. The leading and subleading terms are evaluated and are shown to provide an excellent equation of state. Our saturation mechanism is found to probe in detail the underlying pion dynamics.