Pionless EFT for Few-Body Systems

Christiane H. Schmickler, H.‐W. Hammer

Lucas Platter

The pionless effective field theory (EFT) is the appropriate low-energy EFT for short-range interactions that display a large scattering length. It has been successfully applied in atomic, nuclear and particle physics. We give an overview over recent calculations employing the pionless effective field theory and lay emphasis on applications in the three- and four-body sector where the most exciting developments have occurred.

Teck-kah Lim, Bao Cheng-guang, De-Peng Hou +1 more

Jacob Schach Møller, Dmitri Fedorov

M. Drissi

The current paradigm to describe the nuclear interaction is within the frame of Chiral Effective Field Theory (ₓEFT) which organizes contributions to observables in a serie of decreasing importance. It happens that the leading contribution already requires to solve exactly the Schrödinger equation with a particular Hamiltonian. The same requirement is at play in pionless EFT which considers only nucleonic degrees of freedom. Such calculations are numerically intractable for A-body observables with A >> 10. One must design an additional expansion and truncation for many-body observables. In this thesis, non-perturbative approximations on the basis self-consistent Green’s function (SCGF) and on many-body perturbation theory (MBPT) are considered together with a pionless EFT. The goal of the present thesis is to investigate, in such framework, the renormalization invariance of many-body observables computed in A-body sectors with A >> 10. Hopefully the lessons learnt can be extended to ₓEFT. Analysis of numerical calculations realized with a state-of-the-art SCGF code reveals a critical numerical approximation leading to renormalization dependent observables. A necessary fix is proposed and must be implemented before any calculations based on SCGF and EFT in the future. This emphasizes the criticality of numerical approximations for any calculation within a pionless EFT. At the same time, renormalization invariance of observables computed within MBPT is studied formally, opening the path to formulate the renormalization of a wide range of many-body truncation schemes in the future.

M. Drissi, T. Duguet, V. Somà

Abstract Current models of inter-nucleon interactions are built within the frame of Effective Field Theories (EFTs). Contrary to traditional nuclear potentials, EFT interactions require a renormalization of their parameters in order to derive meaningful estimations of the observables. In this paper, a renormalization procedure is designed in connection with many-body approximations applicable to large- $$\mathrm {A}$$ A systems and formulated within the frame of many-body perturbation theory. The procedure is shown to generate counterterms that are independent of the targeted $$\mathrm {A}$$ A -body sector. As an example, the procedure is applied to the random phase approximation. This work constitutes one step towards the design of a practical EFT for many-body systems.