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

Few-Body Effects in Cold Atoms and Limit Cycles

Physical systems with a large scattering length have universal properties independent of the details of the interaction at short distances. Such systems can be realized in experiments with cold atoms close to a Feshbach resonance. They also occur in many other areas of physics such as nuclear and particle physics. The universal properties include a geometric spectrum of three-body bound states (so-called Efimov states) and log-periodic dependence of low-energy observables on the physical parameters of the system. This behavior is characteristic of a renormalization group limit cycle. We discuss universality in the three- and four-body sectors and give an overview of applications in cold atoms.Comment: 7 pages, 3 figures, plenary talk at the 18th International IUPAP Conference on Few-Body Problems in Physics (FB18), Santos, Brazil, August 200

The Dilute Bose-Einstein Condensate with Large Scattering Length

We study a dilute Bose gas of atoms whose scattering length a is large compared to the range of their interaction. We calculate the energy density of the homogeneous Bose-Einstein condensate to second order in the low-density expansion, expressing it in terms of a and a second parameter Lambda_* that determines the low-energy observables in the 3-body sector. The second-order correction to the energy density has a small imaginary part that reflects the instability due to 3-body recombination. In the case of a trapped Bose-Einstein condensate with large negative scattering length, we calculate the coefficient of the 3-body mean-field term in the energy density in terms of a and Lambda_*. It can be very large if there is an Efimov state near threshold.Comment: 8 pages, RevTex, 1 ps figure, uses epsf.tex, minor changes, references adde

Scattering of an Ultrasoft Pion and the X(3872)

The identification of the X(3872) as a loosely-bound charm-meson molecule allows it to be described by an effective field theory, called XEFT, for the D^* Dbar, D Dbar^* and D Dbar pi sector of QCD at energies small compared to the pion mass. We point out that this effective field theory can be extended to the sector that includes an additional pion and used to calculate cross sections for the scattering of a pion and the X(3872). If the collision energy is much smaller than the pion mass, the cross sections are completely calculable at leading order in terms of the masses and widths of the charm mesons, pion masses, and the binding energy of the X(3872). We carry out an explicit calculation of the cross section for the breakup of the X(3872) into D^{*+} Dbar^{*0} by the scattering of a very low energy pi^+.Comment: 10 pages, 3 figure

An Infrared Renormalization Group Limit Cycle in QCD

Small increases in the up and down quark masses of QCD would tune the theory to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At critical values of the quark masses, the deuteron binding energy goes to zero and the triton has infinitely many excited states with an accumulation point at the 3-nucleon threshold. The ratio of the binding energies of successive states approaches a universal constant that is close to 515. The proximity of physical QCD to the critical trajectory for this limit cycle explains the success of an effective field theory of nucleons with contact interactions only in describing the low-energy 3-nucleon system.Comment: 4 pages, revtex4, 2 ps figure