The Power Of Effective Field Theories In Nuclei: The Deuteron, NN Scattering and Electroweak Processes

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.

Recently we have proposed a new cut-off scheme for pion loop integrals in the two-pion exchange potential. This method allows for a consistent implementation of constraints from pion-nucleon scattering and has been successfully applied to peripheral nucleon-nucleon partial waves. We now consider low partial waves in the non-perturbative regime, where the regularized Lippmann-Schwinger equation has to be solved in order to generate the bound and scattering states. We observe a...

The S wave pion deuteron scattering length is presented at NLO in the Effective Field Theory formulation of the two nucleon system with perturbative pions. At this order, this observable is determined by the iso-scalar S wave pion nucleon scattering length a^+, by pion re-scattering contributions inside the deuteron and by two nucleon two pion contact interactions that involve two unknown parameters which renormalise the appearing divergences. By choosing their values accordi...

I discuss the dynamics of the two-nucleon system as obtained from a chiral nucleon-nucleon potential. This potential is based on a modified Weinberg power counting and contains chiral one- and two-pion exchange as well as four-nucleon contact interactions. The description of the S-waves is very precise. Higher partial waves are also well reproduced. We also find a good description of most of the deuteron properties.

Effective field theory provides a powerful framework to exploit a separation of scales in physical systems. In these lectures, we discuss some general aspects of effective field theories and their application to few-body physics. In particular, we consider an effective field theory for non-relativistic particles with resonant short-range interactions where certain parts of the interaction need to be treated nonperturbatively. As an application, we discuss the so-called pionle...

Interactions from chiral effective field theory have been successfully employed in a broad range of \textit{ab initio} calculations of nuclei and nuclear matter, but it has been observed that most results of few- and many-body calculations experience a substantial residual regulator and cutoff dependence. In this work, we investigate the behavior of local chiral potentials at leading order under variation of the cutoff scale for different local regulators. When varying the cu...

An effective field theory treatment of nucleon-nucleon scattering at low energy shows much promise and could prove a useful tool in the study of nuclear matter at both ordinary and extreme densities. The analysis is complicated by the existence a large length scale --- the scattering length --- which arises due to couplings in the short distance theory being near critical values. I show how this can be dealt with by introducing an explicit s-channel state in the effective fie...

Attempts to apply effective field theory (EFT) methods to nonrelativistic nucleon-nucleon (NN) scattering have raised questions about the nature and limitations of an EFT expansion when used nonperturbatively. We discuss the characteristics of a meaningful EFT analysis and compare them with traditional approaches to NN scattering. A key feature of an EFT treatment is a systematic expansion in powers of momentum, which we demonstrate using an error analysis introduced by Lepag...

We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only be eliminated up to the order the calculations are performed. We further consider an effective theory for an exactly solvable quantum mechanical model which possesses a long- and short-range interaction to simulate pionful effective field t...

We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed to all orders. At low energies, an EFT with only contact interactions allows a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behavior. Manifestly model-independent calculations can be carried out to high orders, leading to high precision. At hig...