Universality in few-body systems with large scattering length

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.Comment: 11 pages, 10 ps figures, invited talk at the workshop on "Nuclei and Mesoscopic Physics", Michigan State University, October 200

Effective Field Theory for Cold Atoms

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms. Recent extensions of this approach to the four-body system and N-boson droplets in two spatial dimensions will also be discussed.Comment: Plenary talk at 19th European Few-Body Conference, Groningen, The Netherlands, August 23-27, 2004, 7 pages, 5 figures, uses aipproc.cls, aip-6s.clo, aipxfm.st

Universality in the triton charge form factor

We consider the three-nucleon system within an effective theory with contact interactions at leading order in the large scattering length. We calculate the charge form factor of the triton at low momentum transfer and extract the triton charge radius. At this order, no two-body currents contribute and the calculation can be performed in the impulse approximation. We also comment on the power counting for higher orders. The requirement of a three-body force for renormalization of the three-nucleon system explains the previously observed correlation between the triton binding energy and charge radius for different model potentials.Comment: 11 pages, 2 eps figures, revtex4, version to appear in Nucl. Phys.

Constraints on a possible dineutron state from pionless EFT

We investigate the sensitivity of the three-nucleon system to changes in the neutron-neutron scattering length to next-to-leading order in the pionless effective field theory, focusing on the the triton-3He binding energy difference and neutron-deuteron elastic scattering. Due to the appearance of an electromagnetic three-body counterterm at this order, the triton-3He binding energy difference remains consistent with the experimental value even for large positive neutron-neutron scattering lengths while the elastic neutron-deuteron scattering phase shifts are insensitive. We conclude that a bound dineutron cannot be excluded to next-to-leading order in pionless EFT.Comment: 11 pages, 5 figure

A renormalized equation for the three-body system with short-range interactions

We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of the three-body scattering length on the two-body scattering length can be obtained analytically using the asymptotic solution to the integral equation. An analogous formula for the three-body recombination coefficient is also obtained.Comment: 12 pages, RevTex, 2 ps figures, included with epsf.te