Low Energy Expansion in the Three Body System to All Orders and the Triton Channel

We extend and systematise the power counting for the three-body system, in the context of the ``pion-less'' Effective Field Theory approach, to all orders in the low-energy expansion. We show that a sub-leading part of the three-body force appears at the third order and delineate how the expansion proceeds at higher orders. After discussing the renormalisation issues in a simple bosonic model, we compute the phase shifts for neutron-deuteron scattering in the doublet S wave (triton) channel and compare our results with phase shift analysis and potential model calculations.Comment: 22 pages revtex4, 7 figures in 8 .eps files. Figures cosmetically changed, minor corrections. Version accepted for publication in Nucl Phys

Universality in the physics of cold atoms with large scattering length

Effective field theories exploit a separation of scales in physical systems in order to perform systematically improvable, model-independent calculations. They are ideally suited to describe universal aspects of a wide range of physical systems. I will discuss recent applications of effective field theory to cold atomic and molecular few-body systems with large scattering length.Comment: Invited talk at Few-Body 17, June 2003, Durham, NC, USA, 5 pages, 3 figures, uses espcrc1.st

Effective Field Theories of Light Nuclei

Effective field theories have been developed for the description of light, shallow nuclei. I review results for two- and three-nucleon systems, and discuss their extension to halo nuclei.Comment: 10 pages, invited talk at the International Nuclear Physics Conference, Goeteborg, June 27 - July 2 200

A complex path around the sign problem

We review recent attempts at dealing with the sign problem in Monte Carlo calculations by deforming the region of integration in the path integral from real to complex fields. We discuss the theoretical foundations, the algorithmic issues and present some results for low dimensional field theories in both imaginary and real time.Comment: Write up of the talk delivered al Lattice 201

Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice

We propose a method for the lattice QCD computation of nucleon-nucleon low-energy interactions. It consists in simulating QCD in the background of a ''electromagnetic" field whose potential is non-vanishing, but whose field strength is zero. By tuning the background field, phase-shifts at any (but small) momenta can be determined by measuring the shift of the ground state energy. Lattice sizes as small as 5 Fermi can be sufficient for the calculation of phase shifts up to momenta of order of $m_{\pi}/2$

Naive Dimensional Analysis for Three-Body Forces Without Pions

For systems of three identical particles in which short-range forces produce shallow two-particle bound states, and in particular for the ``pion-less'' Effective Field Theory of Nuclear Physics, I extend and systematise the power-counting of three-body forces to all partial-waves and orders, including external currents. With low-energy observables independent of the details of short-distance dynamics, the typical strength of a three-body force is determined from the superficial degree of divergence of the three-body diagrams which contain only two-body forces. This na\"ive dimensional analysis must be amended as the asymptotic solution to the leading-order Faddeev equation depends for large off-shell momenta crucially on the partial wave and spin-combination of the system. It is shown by analytic construction to be weaker in most channels with angular momentum smaller than 3 than expected. This demotes many three-nucleon forces to high orders. Observables like the quartet-S-scattering length are less sensitive to three-nucleon forces than guessed. I also comment on the Efimov effect and limit-cycle for non-zero angular momentum.Comment: 31 pages LaTeX2e, including 8 figures in 13 .eps files, embedded with includegraphicx; linguistic corrections only, version to appear in Nucl Phys

Quartet S Wave Neutron Deuteron Scattering in Effective Field Theory

The real and imaginary part of the quartet S wave phase shift in nd scattering (^4 S_{3/2}) for centre-of-mass momenta of up to 300 MeV (E_cm \approx 70 MeV) is presented in effective field theory, using both perturbative pions and a theory in which pions are integrated out. As available, the calculation agrees with both experimental data and potential model calculations, but extends to a higher, so far untested momentum r\'egime above the deuteron breakup point. A Lagrangean more feasible for numerical computations is derived.Comment: 27 pages LaTeX2e with 11 figures, uses packages includegraphicx (6 .eps files), color and feynmp (necessary Metapost files included). Corrections in bibliography and NNLO results added above breaku

On the correlation between the binding energies of the triton and the alpha-particle

We consider the correlation between the binding energies of the triton and the alpha-particle which is empirically observed in calculations employing different phenomenological nucleon-nucleon interactions. Using an effective quantum mechanics approach for short-range interactions with large scattering length |a| >> l, where l is the natural low-energy length scale, we construct the effective interaction potential at leading order in l/|a|. In order to renormalize the four-nucleon system, it is sufficient to include a SU(4)-symmetric one-parameter three-nucleon interaction in addition to the S-wave nucleon-nucleon interactions. The absence of a four-nucleon force at this order explains the empirically observed correlation between the binding energies of the triton and the alpha-particle. We calculate this correlation and obtain a prediction for the alpha-particle binding energy. Corrections to our results are suppressed by l/|a|.Comment: 4 pages, 1 ps figure, references update