Session DJ: Mini-Symposium: Nuclear Physics from Effective Field Theory and Lattice Field Theory I

Status and perspectives of nuclear effective field theories

The nuclear physics landscape appears today as a sequence of effective field theories (EFTs) that are connected to the Standard Model through symmetries and lattice simulations of Quantum Chromodynamics (QCD). EFTs in this sequence are expansions around different low-energy limits of QCD, each with its own characteristics, scales, and ranges of applicability regarding energy and number of nucleons. This talk gives an overview of the three main EFTs formulated in terms of nucleons and clusters thereof: Chiral EFT, Pionless EFT, and Halo/Cluster EFT. Covering both their history as well as recent developments, it will elucidate the similarities and differences of these theories, focusing in particular on their connections to each other and to lattice field theory.   

An effective field theory approach to two particles in a spherical box

We develop an effective field theory approach for two particles interacting via short-range interactions confined to a spherical box. We use the three-dimensional delta potential and its derivatives to simulate the short-range interactions and solve the problem in a truncated model space restricted by an ultraviolet regulator. Renormalization methods are used to remove regulator dependence and obtain meaningful predictions. The leading-order (LO) interaction is solved for exactly while higher-order contributions are treated in perturbation theory. It is shown explicitly that going to next-to-LO systematically improves convergence as the model space increases. In the large-box limit, we recover the known result that the potential produces level shifts proportional to the scattering phase shift at the unperturbed energy. Our approach provides a basis for further study of many-body systems in restricted model spaces that do not break spherical symmetry.   

Symmetries of Nucleon-Nucleon Scattering

The $S$-matrix for low-energy nucleon-nucleon scattering shows many properties that are not transparent in the effective action. Parameterized by momenta, the $S$-matrix can be viewed as flowing inside a region bounded by unitarity constraints. At the corners of this region, the $S$-matrix is at a fixed point of the RG and furnishes a representation of the Klein four-group. At leading order in the effective range expansion, the path that the $S$-matrix traces out has an isometry corresponding to a conformal (M\"obius) transformation. It is found that the curvature of this trajectory is related to the entanglement power of the $S$-matrix, a state-independent measure of operator entanglement. This is a new, more geometrical, way to think about entanglement.   

Finite volume relations for two hadron matrix elements and form factors

Recently, a framework has been developed to study form factors of two hadron states probed by an external current. The method is based on relating two hadron finite-volume matrix elements, computed using lattice QCD, to the corresponding infinite-volume generalized form-factors. We review the formalism, as well as the analytic properties of the generalized form-factors. As a consistency check, we study the formalism in two limits: The limit where the interaction between the two hadrons is perturbative, and the limit where the system forms a bound state. These checks allow us to verify that the formalism yields the expected finite volume scaling relations.   

A New Approach to the Effective Field Theory of the Two-Nucleon System with Perturbative Pions

By using symmetries and separation of scales, effective field theory (EFT) offers model-independent results and systematic error estimation. However, understanding the physics of the two-nucleon system at low energies is still one of the major challenges for EFT, because inclusion of the pion as a degree of freedom makes renormalization complicated. Specifically for the $^{1}S_{0}$ channel, we will show how pions can be treated perturbatively for momenta even higher than the pion mass, by accounting for the zero of the scattering amplitude at the leading order of the EFT expansion. In the light of a new power counting and with the help of an auxiliary dimer field we obtain results in good agreement with the partial wave analysis of two-nucleon data. Possible lessons for the extension of these ideas to other channels will be discussed as well.   

Lattice QCD input for baryon-baryon scattering and interactions in effective field theory

Our understanding of the physics of baryonic systems containing strangeness is limited by the scarcity of experimental data. Aiming at alleviating this deficit is Lattice QCD (LQCD), a numerical approach to solve the complex dynamics of strongly interacting systems of hadrons and nuclei. In this talk, I will present the results obtained by the NPLQCD collaboration for two octet-baryon systems, with strangeness ranging from 0 to -4, at two sets of quark masses that are heavier than those in nature. In particular, I will present their binding energies and scattering parameters, as well as the low-energy coefficients appearing in the effective field theory Lagrangian describing the interaction of two non-relativistic octet baryons. The findings point to interesting symmetries observed in hypernuclear forces as predicted in the limit of QCD with a large number of colors.