U. van Kolck

Renormalization of the Three-Body System with Short-Range Interactions

We discuss renormalization of the nonrelativistic three-body problem with short-range forces. The problem becomes nonperturbative at momenta of the order of the inverse of the two-body scattering length, and an infinite number of graphs must be summed. This summation leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in a single three-body counterterm and compute the running of the three-body force with the cutoff. We comment on the relevance of this result for the effective field theory program in nuclear and molecular physics. {copyright} {ital 1999} {ital The American Physical Society }

Two-nucleon potential from chiral Lagrangians.

Chiral symmetry is consistently implemented in the two-nucleon problem at low-energy through the general effective chiral Lagrangian. The potential is obtained up to a certain order in chiral perturbation theory both in momentum and coordinate space. Results of a fit to scattering phase shifts and bound state data are presented, where satisfactory agreement is found for laboratory energies up to about 100 MeV. {copyright} {ital 1996 The American Physical Society.}

Effective field theory of short-range forces

Abstract The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective range expansion, to a Schrodinger equation with a pseudo-potential, and to an energy expansion of a generic boundary condition at the origin. The roles of regulators and potentials are also discussed.

The three-boson system with short-range interactions

Abstract We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be summed, which leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in one local three-body force counterterm and compute the running of the three-body force with the cutoff. This allows a calculation of the scattering of a particle and the two-particle bound state if the corresponding scattering length is used as input. We also obtain a model-independent relation between binding energy of a shallow three-body bound state and this scattering length. We comment on the power counting that organizes higher-order corrections and on relevance of this result for the effective field theory program in nuclear and molecular physics.

Towards a Perturbative Theory of Nuclear Forces

NT@UW-01-06 LBNL 47692 RBRC-186 Towards a Perturbative Theory of Nuclear Forces S.R. Beane a , P.F. Bedaque b , M.J. Savage a,c , and U. van Kolck d,e arXiv:nucl-th/0104030 v1 9 Apr 2001 a Department of Physics, University of Washington, Seattle, WA 98195 b Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 c Jefferson Laboratory, 12000 Jefferson Avenue, Newport News, VA 23606 Department of Physics, University of Arizona, Tucson, AZ 85721 d e RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973 Abstract We show that an expansion of nuclear forces about the chiral limit is formally consistent and is equivalent to KSW power counting in the 1 S 0 channel and Weinberg power counting in the 3 S 1 − 3 D 1 coupled channels. Numerical evidence suggests that this expansion converges. The feasibility of making contact between nuclear physics and lattice-QCD simulations is discussed.

Electric dipole moments of nucleons, nuclei, and atoms: The Standard Model and beyond

Searches for the permanent electric dipole moments (EDMs) of molecules, atoms, nucleons and nuclei provide powerful probes of CP violation both within the Standard Model and beyond the Standard Model (BSM). The interpretation of experimental EDM limits requires careful delineation of physics at a wide range of scales, from the long-range atomic and molecular scales to the short-distance dynamics of physics at or beyond the Fermi scale. In this review, we provide a framework for disentangling contributions from physics at these disparate scales, building out from the set of dimension four and six effective operators that embody CP violation at the Fermi scale. We survey computations of hadronic and nuclear matrix elements associated with Fermi-scale CP violation in systems of experimental interest and quantify the present level of theoretical uncertainty in these calculations. Using representative BSM scenarios of current interest, we discuss ways in which the interplay of physics at various scales can generate EDMs at a potentially observable level.

Effective theory of the triton

Abstract We apply the effective field theory approach to the three-nucleon system. In particular, we consider S=1/2 neutron–deuteron scattering and the triton. We show that in this channel a unique nonperturbative renormalization takes place which requires the introduction of a single three-body force at leading order. With one fitted parameter we find a good description of low-energy data. Invariance under the renormalization group explains some universal features of the three-nucleon system — such as the Thomas and Efimov effects and the Phillips line — and the origin of SU(4) symmetry in nuclei.

Renormalization of one-pion exchange and power counting

The renormalization of the chiral nuclear interactions is studied. In leading order, the cutoff dependence is related to the singular tensor interaction of the one-pion exchange potential. In S waves and in higher partial waves where the tensor force is repulsive this cutoff dependence can be absorbed by counterterms expected at that order. In the other partial waves additional contact interactions are necessary. The implications of this finding for the effective field theory program in nuclear physics are discussed.

Nucleon-Deuteron Scattering from an Effective Field Theory

Abstract We use an effective field theory to compute low-energy nucleon-deuteron scattering. We obtain the quartet scattering length using low energy constants entirely determined from low-energy nucleon-nucleon scattering. We find a th =6.33 fm, to be compared to a exp =6.35±0.02 fm.

Effective field theory for halo nuclei: shallow p-wave states

Halo nuclei are a promising new arena for studies based on effective field theory (EFT). We develop an EFT for shallow p-wave states and discuss the application to elastic nα scattering. In contrast to the s-wave case, both the scattering length and effective range enter at leading order. We also discuss the prospects of using EFT in the description of other halos, such as the three-body halo nucleus 6 He.  2002 Elsevier Science B.V. All rights reserved.