Density-functional theory for fermions in the unitary regime

In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the free Fermi gas with a proportionality constant $\xi$. We use a simple density functional parametrized by an effective mass and the universal constant $\xi$, and employ Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields $\xi=0.42$ and a rather large effective mass. Our approach is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.Comment: 5 pages, 2 figure

Octet Baryon Charge Radii, Chiral Symmetry and Decuplet Intermediate States

We compute the octet baryon charge radii to O(1/Heavy^3) in heavy baryon chiral perturbation theory. We examine the effect of including the decuplet of spin-3/2 baryons explicitly. We find that it does no t improve the level of agreement between the HBchiPT and experimental values for the Sigma^- charge radius.Comment: 9 pages, 2 figures. Uses axodraw.sty, include

Chiral Symmetry and the Parity-Violating NNπNN\pi Yukawa Coupling

We construct the complete SU(2) parity-violating (PV) $\pi, N, \Delta$ interaction Lagrangian with one derivative, and calculate the chiral corrections to the PV Yukawa $NN\pi$ coupling constant $h_\pi$ through ${\cal O}(1/\Lambda_\chi^3)$ in the leading order of heavy baryon expansion. We discuss the relationship between the renormalized \hpi, the measured value of \hpi, and the corresponding quantity calculated microscopically from the Standard Model four-quark PV interaction.Comment: RevTex, 26 pages + 5 PS figure

Subleading corrections to parity-violating pion photoproduction

We compute the photon asymmetry Bγ for near threshold parity-violating (PV) pion photoproduction through subleading order. We show that subleading contributions involve a new combination of PV couplings not included in previous analyses of hadronic PV. We argue that existing constraints on the leading order contribution to Bγ—obtained from the PV γ-decay of 18F—suggest that the impact of the subleading contributions may be more significant than expected from naturalness arguments

Anomalous Chiral Action from the Path-Integral

By generalizing the Fujikawa approach, we show in the path-integral formalism: (1) how the infinitesimal variation of the fermion measure can be integrated to obtain the full anomalous chiral action; (2) how the action derived in this way can be identified as the Chern-Simons term in five dimensions, if the anomaly is consistent; (3) how the regularization can be carried out, so as to lead to the consistent anomaly and not to the covariant anomaly. Our method uses Schwinger's ``proper-time'' representation of the Green's function and the gauge invariant point-splitting technique. We find that the consistency requirement and the point-splitting technique allow both an anomalous and a non-anomalous action. In the end, the nature of the vacuum determines whether we have an anomalous theory, or, a non-anomalous theoryComment: 28 page

Density Functional Theory: Methods and Problems

The application of density functional theory to nuclear structure is discussed, highlighting the current status of the effective action approach using effective field theory, and outlining future challenges.Comment: 10 pages, 14 figures, invited talk at INT workshop on Nuclear Forces and the Quantum Many-Body Problem, Seattle, October 200

Recoil Order Chiral Corrections to Baryon Octet Axial Currents

We calculate chiral corrections to the octet axial currents through ${\cal O}(p^3)$ using baryon chiral perturbation theory (BCPT). The relativistic BCPT framework allows one to sum an infinite series of recoil corrections at a given order in the chiral expansion. We also include SU(3)-breaking operators occuring at ${\cal O}(p^2)$ not previously considered. We determine the corresponding low-energy constants (LEC's) from hyperon semileptonic decay data using a variety of infrared regularization schemes. We find that the chiral expansion of the axial currents does not display the proper convergence behavior, regardless of which scheme is chosen. We explore the implications of our analysis for determinations of the strange quark contribution to the nucleon spin, $\Delta s$.Comment: RevTex, 19 pages + 2 PS figure

Baryon magnetic moments and sigma terms in lattice-regularized chiral perturbation theory

An SU(3) chiral Lagrangian for the lightest decuplet of baryons is constructed on a discrete lattice of spacetime points, and is added to an existing lattice Lagrangian for the lightest octets of mesons and baryons. A nonzero lattice spacing renders all loop integrations finite, and the continuum limit of any physical observable is identical to the result obtained from dimensional regularization. Chiral symmetry and gauge invariance are preserved even at nonzero lattice spacing. Specific calculations discussed here include the non-renormalization of a conserved vector current, the magnetic moments of octet baryons, and the pi N and KN sigma terms that relate to the nucleon's strangeness content. The quantitative difference between physics at a nonzero lattice spacing and physics in the continuum limit is easily computed, and it represents an expectation for the size of discretization errors in corresponding lattice QCD simulations.Comment: 19 pages, 5 figures, one paragraph added to introduction, to appear in Phys Rev

Time-Dependent Density-Functional Theory for Trapped Strongly-Interacting Fermionic Atoms

The dynamics of strongly interacting trapped dilute Fermi gases (dilute in the sense that the range of interatomic potential is small compared with inter-particle spacing) is investigated in a single-equation approach to the time-dependent density-functional theory. Our results are in good agreement with recent experimental data in the BCS-BEC crossover regime. It is also shown that the calculated corrections to the hydrodynamic approximation may be important even for systems with a rather large number of atoms.Comment: Resubmitted to PRA in response to referee's comments. Abstract is changed. Added new figure