The nuclear physics landscape has been redesigned as a sequence of effective field theories (EFTs) 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. We review each of the three main nuclear EFTs---Chiral, Pionless, Halo/Cluster---highlighting their similarities, differences, and connections. In doing so, we survey the structural properties and reactions of nuclei that have been derived from the ab initio solution of the few- and many-body problem built upon EFT input.

Nuclear effective field theory: status and perspectives

The process at the heart of neutrinoless double-$\ensuremath{\beta}$ decay, $nn\ensuremath{\rightarrow}pp\phantom{\rule{0.16em}{0ex}}{e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading-order corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-$\ensuremath{\beta}$ decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leading-order short-range operator but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-$\ensuremath{\beta}$ decay for $^{6}\mathrm{He}$ and $^{12}\mathrm{Be}$. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.

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Renormalized approach to neutrinoless double- β decay

Ever since quantum field theory was first applied to the derivation of nuclear forces in the mid-20th century, the renormalization of pion exchange with realistic couplings has presented a challenge. The implementation of effective field theories (EFTs) in the 1990s promised a solution to this problem but unexpected obstacles were encountered. The response of the nuclear community has been to focus on "chiral potentials" with regulators chosen to produce a good description of data. Meanwhile, a successful EFT without explicit pion exchange --- Pionless EFT --- has been formulated where renormalization is achieved order by order in a systematic expansion of low-energy nuclear observables. I describe how lessons from Pionless EFT are being applied to the construction of a properly renormalized Chiral EFT.

/pdf/the-problem-of-renormalization-of-chiral-nuclear-forces-3suj8ip2zi.pdf

The Problem of Renormalization of Chiral Nuclear Forces

Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. In this review, the progress of lattice QCD studies of nuclear matrix elements of electroweak currents and beyond-Standard-Model operators is summarized, and connections with effective field theories and nuclear models are outlined. 
Lattice QCD calculations of nuclear matrix elements can provide guidance for low-energy nuclear reactions in astrophysics, dark matter direct detection experiments, and experimental searches for violations of the symmetries of the Standard Model, including searches for additional CP violation in the hadronic and leptonic sectors, baryon-number violation, and lepton-number or flavor violation. Similarly, important inputs to neutrino experiments seeking to determine the neutrino-mass hierarchy and oscillation parameters, as well as other electroweak and beyond-Standard-Model processes can be determined. The phenomenological implications of existing studies of electroweak and beyond-Standard-Model matrix elements in light nuclear systems are discussed, and future prospects for the field toward precision studies of these matrix elements are outlined.

Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes

Chiral effective field theory $(\ensuremath{\chi}\mathrm{EFT})$, as originally proposed by Weinberg, promises a theoretical connection between low-energy nuclear interactions and quantum chromodynamics (QCD). However, the important property of renormalization-group (RG) invariance is not fulfilled in current implementations and its consequences for predicting atomic nuclei beyond two- and three-nucleon systems has remained unknown. In this work we present a systematic study of recent RG-invariant formulations of $\ensuremath{\chi}\mathrm{EFT}$ and their predictions for the binding energies and other observables of selected nuclear systems with mass numbers up to $A=16$. Specifically, we have carried out ab initio no-core shell-model and coupled cluster calculations of the ground-state energy of $^{3}\mathrm{H}$, $^{3,4}\mathrm{He}$, $^{6}\mathrm{Li}$, and $^{16}\mathrm{O}$ using several recent power-counting (PC) schemes at leading order (LO) and next-to-leading order, where the subleading interactions are treated in perturbation theory. Our calculations indicate that RG-invariant and realistic predictions can be obtained for nuclei with mass number $A\ensuremath{\le}4$. We find, however, that $^{16}\mathrm{O}$ is either unbound with respect to the four $\ensuremath{\alpha}$-particle threshold, or deformed, or both. Similarly, we find that the $^{6}\mathrm{Li}$ ground-state resides above the $\ensuremath{\alpha}$-deuteron separation threshold. These results are in stark contrast with experimental data and point to either necessary fine-tuning of all relevant counterterms, or that current state-of-the-art RG-invariant PC schemes at LO in $\ensuremath{\chi}\mathrm{EFT}$ lack necessary diagrams---such as three-nucleon forces---to realistically describe nuclei with mass number $Ag4$.

/pdf/power-counting-in-chiral-effective-field-theory-and-nuclear-2drdudpoji.pdf

Power counting in chiral effective field theory and nuclear binding

Within the framework of chiral effective field theory, perturbative calculation for $NN$ scattering is carried out in partial waves with orbital angular momentum $L \geqslant 1$. The primary goal is to identify the lowest angular momenta at which perturbative treatment of chiral forces can apply. Results up to the order where the subleading two-pion exchange appears are shown. It is concluded that perturbation theory applies to all partial waves but ${}^1S_0$, ${}^3S_1 - {}^3D_1$, and ${}^3P_0$. Where it is applicable, perturbation theory with the delta-less chiral forces produces good agreement with the empirical phase shifts up to $k_\text{c.m.} \simeq 300$ MeV.

Perturbative $NN$ scattering in chiral effective field theory

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Perturbative $NN$ scattering in chiral effective field theory