Model Effective Field Theory Research Articles

Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern–Simons theory over the total configuration space CP3, or as a SU(2) Chern–Simons theory over S4. The new quantum Hall liquid supports various types of topological excitations, including the 0-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.

Density dependence of nucleon bag constant, radius and mass in an effective field theory model of QCD

With the global color symmetry model (GCM) being extended to finite chemical potential, the density dependence of the bag constant, the total energy and the radius of a nucleon, as well as the quark condensate in nuclear matter are investigated. A maximal nuclear matter density for the existence of the bag with three quarks confined within is obtained. The calculated results indicate that, before the maximal density is reached, the bag constant, the total energy of a nucleon and the quark condensate decrease gradually, and the radius of a nucleon increases, with the increasing of the nuclear matter density. Nevertheless no sudden change emerges. As the maximal nuclear matter density is reached, a phase transition from nucleons to quarks takes place and the chiral symmetry is restored.

Aspects of duality and confining strings

We inspect the energy spectrum of a confining string, at the classical level in an effective field theory model. The spectrum can be characterized by a spectral function, and twisting and bending of the string is manifested by the invariance of this function under a duality transformation. Both general considerations and numerical simulations reveal that the spectral function can be approximated by a simple rational form.

Effective field theory and nuclear mean-field models

The implications of an effective field theory (EFT) interpretation of nuclear mean-field phenomenology are reviewed.

An Effective Field Theory Model to Describe Nuclear Matter in Heavy-Ion Collisions

Relativistic mean field theory with mesons σ, ω, π and ρ mediating interactions and nucleons as basic fermions has been very successful in describing nuclear matter and finite nuclei. However, in heavy-ion collisions, where the c. m. energy of two colliding nucleons will be in the hundreds of GeV region, nucleons are not expected to behave as point-like particles. Analyses of elastic pp and ¯pp scattering data in the relevant c. m. energy range show that the nucleon is a composite object—a topological soliton or Skyrmion embedded in a condensed quark-antiquark ground state. Against this backdrop, we formulate an effective field theory model of nuclear matter based on the gauged linear σ-model where quarks are the basic fermions, but the mesons still mediate the interactions. The model describes the nucleon as a Skyrmion and produces a q¯q ground state analogous to a superconducting ground state. Quarks are quasi-particles in this ground state. When the temperature exceeds a critical value, the scalar field in the ground state vanishes, quarks become massless, and a chiral phase transition occurs leading to chiral symmetry restoration. We explore the possibility of a first order phase transition in this model by introducing suitable self-interactions of the scalar field. Internal structures of the Skyrmions are ignored, and they are treated as point-like fermions.

Compactification for a three-brane universe

A fully realistic and systematic effective field theory model of a 3-brane universe is constructed. It consists of a six-dimensional gravitating spacetime, containing several, approximately parallel (3+1)-dimensional defects, or ``3-branes''. The Standard Model particles are confined to live on one of the 3-branes while different four-dimensional field theories may inhabit the others, in literally a case of ``parallel universes''. The effective field theory is valid up to the six-dimensional Planck scale, where it must be replaced by a more fundamental theory of gravity and 3-brane structure. Each 3-brane induces a conical geometry in the two dimensions transverse to it. Collectively, the curvature induced by the 3-branes can compactify the extra dimensions into a space of spherical topology. It is possible to take the six-dimensional Planck scale to be not much larger than the weak scale, and the compact space not much smaller than a millimeter, thereby realizing the recent proposal by Arkani-Hamed, Dimopoulos and Dvali for eliminating the Gauge Hierearchy Problem. In this case, an extra force is required to stabilize the compact space against collapse. This is provided by a six-dimensional (compact) U(1) gauge field with a magnetic flux quantum trapped in the compact space. The nature of the Cosmological Constant Problem in this scenario is discussed.

Pion-nucleus scattering at medium energies with densities from chiral effective field theories

Abstract Recently developed chiral effective field theory models provide excellent descriptions of the bulk characteristics of finite nuclei, but have not been tested with other observables. In this work, densities from both relativistic point-coupling models and mean-field meson models are used in the analysis of meson-nucleus scattering at medium energies. Elastic scattering observables for 790 MeV/ c π ± on 208 Pb are calculated in a relativistic impulse approximation, using the Kemmer-Duffin-Petiau formalism to calculate the π ± nucleus optical potential.

Period doubling in the two-dimensional antiferromagnet: Gauge fields and their anomalies

We construct an effective gauge field theory model describing a 2D quantum antiferromagnet in the flux phase ground state. Due to period doubling the number of gauge fields is four rather than the naively expected single one. These additional gauge fields correspond to field configurations in which the flux is staggered, which should be taken into account to enforce single occupancy within the magnetic unit cell. We calculate a new type of quantum anomaly, present in such a model. In particular this leads to a generalized local flux hypothesis, which is tested numerically.

Pion loop contribution toρ-ωmixing and mass splitting

We study the self-energy amplitudes for the $\ensuremath{\rho}$-$\ensuremath{\omega}$ meson system produced by an effective field theory model at the quark level characterized by a finite range quark-quark interaction and an isospin breaking bare quark mass difference ${m}_{u}\ensuremath{-}{m}_{d}.$ Dynamical effects associated with confinement and dressing of quarks and the finite size of the produced $\mathrm{q\ifmmode\bar\else\textasciimacron\fi{}}q$ meson modes are treated. Parameters of this approach, previously constrained by soft pion physics, are here supplemented in a minimal way to reproduce ${m}_{\ensuremath{\omega}}$ and ${g}_{\ensuremath{\rho}\ensuremath{\pi}\ensuremath{\pi}}.$ Calculations are carried out up to the one-pion-loop level and the predictions for ${\ensuremath{\rho}}^{0}$-$\ensuremath{\omega}$ mixing, mass splitting, the $\ensuremath{\rho}$ width and the symmetry breaking $\ensuremath{\omega}\ensuremath{\pi}\ensuremath{\pi}$ coupling constant and form factor are presented. The contribution of the direct $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ process relative to the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ process is discussed within this model.

Quantum field-theory description of tunneling in the integer quantum Hall effect

We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field-theory model for the tunneling. It is shown that the phenomenon of fermion number fractionalization is expected to occur, either localized in conveniently modulated barriers or in the form of free excitations, once lattice effects are taken into account. This opens the experimental possibility of an observation of fractional charges with internal structure, close to the magnetic length scale. The coupling of the system to external gauge fields is performed, leading us to the exact quantization of the Hall conductivity at the interface. The field-theory approach is well supported by a numerical diagonalization of the microscopic hamiltonian.