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.
1. EFFECTIVE FIELD THEORIES
I will remember GΓΆteborg as a clean and ordered town. INPC 2004 was certainly well organized. My talk, too, was about organization.
Nuclear structure involves energies that are much smaller than the typical QCD mass scale, M QCD βΌ 1 GeV. This is a common situation in physics: an "underlying" theory is valid at a mass scale M hi , but we want to study processes at momenta Q of the order of a lower scale M lo M hi . Typically, there is "more" at lower energies. How to organize the complexity brought in by the "effective" interactions that will ensure that low-energy observables are described correctly?
Effective Field Theory (EFT) is a framework to construct these interactions systematically, at the same time maintaining desirable general principles such as causality and cluster decomposition. Here I discuss the application of EFT to a class of nuclear systems: those that exhibit poles in the complex momentum plane at a scale much smaller than the pion mass, that is, M hi < βΌ m Ο . They include two-and three-nucleon systems, and other halo nuclei.
EFT starts with the observation that the effective interactions consist of the sum of all possible interaction terms in a Lagrangian that involves only the fields representing lowenergy degrees of freedom. Because of the uncertainty principle, each of these interaction terms can be taken as a local combination of derivatives of the fields. If the "integrating out" of the high-energy degrees of freedom is done appropriately, the effective Lagrangian will have the same symmetries as the underlying theory. The details of the underlying dynamics, on the other hand, are contained in the interaction strengths. The latter depend also on the details of how the low-and high-energy degrees of freedom are separated. This separation requires the introduction of a cutoff parameter Ξ with dimensions of energy. Both the interaction strengths and the quantum effects represented by loops depend on Ξ. However, the cutoff procedure is arbitrary, so by construction observables are independent of Ξ ("renormalization-group invariance"). The T matrix for any low-energy * Supported in part by the US Department of Energy and the Alfred P. Sloan Foundation.