Regularization, renormalization and "peratization" in effective field theory for two nucleons

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 theory. We discuss the meaning of low-energy theorems in this model and demonstrate their validity in calculations with a finite cutoff $\Lambda$ as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit $\Lambda \to \infty$ yields a finite result for the scattering amplitude but violates the low-energy theorems and is, therefore, not compatible with the effective field theory framework.Comment: 22 pages, 2 figures, to appear in Eur. Phys. J.

Wilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters

The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed.Comment: 6 pages, no figure

Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering

We compare the subtractive renormalization and the Wilsonian renormalization group approaches in the context of an effective field theory for the two-nucleon system. Based on an exactly solvable model of contact interactions, we observe that the standard Wilsonian renormalization group approach with a single cutoff parameter does not cover the whole space spanned by the renormalization scale parameters of the subtractive formalism. In particular, renormalization schemes corresponding to Weinberg's power counting in the case of an unnaturally large scattering length are beyond the region covered by the Wilsonian renormalization group approach. In the framework of pionless effective field theory, also extended by the inclusion of a long-range interaction of separable type, we demonstrate that Weinberg's power counting scheme is consistent in the sense that it leads to a systematic order-by-order expansion of the scattering amplitude.Comment: 23 pages, 2 figure

Two-Pion Exchange Currents in Photodisintegration of the Deuteron

Chiral effective field theory (ChEFT) is a modern framework to analyze the properties of few-nucleon systems at low energies. It is based on the most general effective Lagrangian for pions and nucleons consistent with the chiral symmetry of QCD. For energies below the pion-production threshold it is possible to eliminate the pionic degrees of freedom and derive nuclear potentials and nuclear current operators solely in terms of the nucleonic degrees of freedom. This is very important because, despite a lot of experience gained in the past, the consistency between two-nucleon forces, many-nucleon forces and the corresponding current operators has not been achieved yet. In this presentation we consider the recently derived long-range two-pion exchange (TPE) contributions to the nuclear current operator which appear at next-to leading order of the chiral expansion. These operators do not contain any free parameters. We study their role in the deuteron photodisintegration reaction and compare our predictions with experimental data. The bound and scattering states are calculated using five different chiral N2LO nucleon-nucleon (NN) potentials which allows to estimate the theoretical uncertainty at a given order in the chiral expansion. For some observables the results are very close to the reference predictions based on the AV18 NN potential and the current operator (partly) consistent with this force.Comment: Contribution to the 12th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2010), Williamsburg, USA, May 31-June 4, 201

The magnetic moment of the \rho-meson

The magnetic moment of the \rho-meson is calculated in the framework of a low-energy effective field theory of the strong interactions. We find that the complex-valued strong interaction corrections to the gyromagnetic ratio are small leading to a value close to the real leading tree level result, g_\rho = 2. This is in a reasonably good agreement with the available lattice QCD calculations for this quantity.Comment: 10 pages, 4 figure

Efficient calculation of chiral three-nucleon forces up to N3LO for ab initio studies

We present a novel framework to decompose three-nucleon forces in a momentum space partial-wave basis. The new approach is computationally much more efficient than previous methods and opens the way to ab initio studies of few-nucleon scattering processes, nuclei and nuclear matter based on higher-order chiral 3N forces. We use the new framework to calculate matrix elements of chiral three-nucleon forces at N2LO and N3LO in large basis spaces and carry out benchmark calculations for neutron matter and symmetric nuclear matter. We also study the size of the individual three-nucleon force contributions for $^3$H. For nonlocal regulators, we find that the sub-leading terms, which have been neglected in most calculations so far, provide important contributions. All matrix elements are calculated and stored in a user-friendly way, such that values of low-energy constants as well as the form of regulator functions can be chosen freely.Comment: 10 pages, 4 figure