International Journal of Modern Physics E

The emergence of complex macroscopic phenomena from a small set of parameters and microscopic concepts demonstrates the power and beauty of physical theories. A theory which relates the wealth of data and peculiarities found in nuclei to the small number of parameters and symmetries of quantum chromodynamics is by that standard of exceptional beauty.

Decade-long research on computational physics and on effective field theories facilitate the assessment of the presumption that quark masses and strong and electromagnetic coupling constants suffice to parametrize the nuclear chart. By presenting the current status of that enterprise, this article touches the methodology of predicting nuclei by simulating the constituting quarks and gluons and the development of effective field theories as appropriate representations of the fundamental theory.

While the nuclear spectra and electromagnetic responses analyzed computationally so far with lattice QCD are in close resemblance to those which intrigued experimentalists a century ago, they also test the theoretical understanding which was unavailable to guide the nuclear pioneers but developed since then. This understanding is shown to be deficient in terms of correlations amongst nuclear observables and their sensitivity to fundamental parameters. By reviewing the transition from one effective field theory to another, from QCD to pionful chiral theories to pionless and eventually to cluster theories, we identify some of those deficiencies and conceptual problems awaiting a solution before QCD can be identified as the high-energy theory from which the nuclear landscape emerges.

Investigations of three-body nuclear systems using pionless effective field theory (${\mathrm{\text{EFT}}}_{\mathrm{\pi ̸}}$) are reviewed. The history of ${\mathrm{\text{EFT}}}_{\mathrm{\pi ̸}}$ in $nd$ and $pd$ scattering is briefly discussed and emphasis put on the use of strict perturbative techniques. In addition renormalization issues appearing in $pd$ scattering are also presented. Bound state calculations are addressed and new perturbative techniques for describing them are highlighted. Three-body breakup observables in $nd$ scattering are also considered and the utility of ${\mathrm{\text{EFT}}}_{\mathrm{\pi ̸}}$ for addressing them.

Few-body systems, such as cold atoms and halo nuclei, share universal features at low energies, which are insensitive to the underlying inter-particle interactions at short ranges. These low-energy properties can be investigated in the framework of effective field theory with two-body and three-body contact interactions. I review the effective-field-theory studies of universal physics in three-body systems, focusing on the application in cold atoms and halo nuclei.

In this article we review the recent progress in radiative reaction calculations in halo effective field theory. We look at radiative capture and breakup processes that involve a halo nucleus with a single valence neutron or proton. Looking at ${}^7\mathrm{\text{Li}}(n,\gamma )$ ${}^8\mathrm{\text{Li}}$,${}^{14}\mathrm{\text{C}}($n$,\gamma {)}^{15}\mathrm{\text{C}}$ and related reactions, the dominant source of theoretical uncertainty in $s$- and $p$-wave halo nuclei reaction calculations is quantified in a model-independent framework. The analysis for neutron halos is extended to proton halo systems. The effective field theory results quantify which observable parameters of the strong interaction at low energy need to be determined more precisely for accurate cross-section calculations.

The light double $\mathrm{\Lambda }$ hypernuclei, ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^4\mathrm{\text{H}}$ and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6\mathrm{\text{He}}$, are studied as three-body $\mathrm{\Lambda }\mathrm{\Lambda }d$ and $\mathrm{\Lambda }\mathrm{\Lambda }\alpha$ cluster systems in halo/cluster effective field theory at leading order. We find that the $\mathrm{\Lambda }\mathrm{\Lambda }d$ system in spin-0 channel does not exhibit a limit cycle whereas the $\mathrm{\Lambda }\mathrm{\Lambda }d$ system in spin-1 channel and the $\mathrm{\Lambda }\mathrm{\Lambda }\alpha$ system in spin-0 channel do. The limit cycle is associated with the formation of bound states, known as Efimov states, in the unitary limit. For the $\mathrm{\Lambda }\mathrm{\Lambda }d$ system in the spin-0 channel we estimate the scattering length $a_0$ for $S$-wave $\mathrm{\Lambda }$ hyperon–hypertriton scattering as $a_0=16.0\pm 3.0$fm. We also discuss that studying the cutoff dependences in the $\mathrm{\Lambda }\mathrm{\Lambda }d$ and $\mathrm{\Lambda }\mathrm{\Lambda }\alpha$ systems, the bound state of ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^4\mathrm{\text{H}}$ is not an Efimov state but formed due to a high energy mechanism whereas that of ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^6\mathrm{\text{He}}$ may be regarded as an Efimov state.

The present note summarizes the discourse on power counting issues of chiral nuclear forces, with an emphasis on renormalization-group invariance. Given its introductory nature, I will lean toward narrating a coherent point of view on the concepts, rather than covering comprehensively the development of chiral nuclear forces in different approaches.

Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.

We review recent progress in the theoretical description of the violation of discrete space–time symmetries in hadronic and nuclear systems. We focus on parity-violating and time-reversal-conserving interactions which are induced by the Standard Model weak interaction, and on parity- and time-reversal-violating interactions which can be caused by a nonzero QCD $\bar{\theta }$ term or by beyond-the-Standard Model physics. We discuss the origins of such interactions and review the development of the chiral effective field theory extension that includes discrete symmetry violations. We discuss the construction of symmetry-violating chiral Lagrangians and nucleon–nucleon potentials and their applications in few-body systems.

We give a brief review on the development of phenomenological NN interactions and the corresponding quantification of statistical uncertainties. We look into the uncertainty of effective interactions broadly used in mean field calculations through the Skyrme parameters and effective field theory counterterms by estimating both statistical and systematic uncertainties stemming from the NN interaction. We also comment on the role played by different fitting strategies on the light of recent developments.

We discuss the theory and computational algorithms involved in nuclear lattice simulations using chiral effective field theory. We elucidate the role of Wigner’s SU(4) symmetry and the role it plays in alpha clustering and rendering the auxiliary-field projection Monte Carlo simulations tractable.

The success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological $NN$ and $NNN$ interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as $r^2$, considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods.