We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions summed to all orders. At low energies, an EFT with only contact allows a detailed analysis of renormalization non-perturbative context and uncovers novel asymptotic behavior. Manifestly model-independent calculations can be carried out high orders, leading precision. higher that includes pion fields justifies extends...

We discuss renormalization of the nonrelativistic three-body problem with short-range forces. The becomes nonperturbative at momenta order inverse two-body scattering length, and an infinite number graphs must be summed. This summation leads to a cutoff dependence that does not appear in any perturbation theory. argue this can absorbed single counterterm compute running force cutoff. comment on relevance result for effective field theory program nuclear molecular physics.

Chiral symmetry is consistently implemented in the two-nucleon problem at low-energy through general effective chiral lagrangian. The potential obtained up to a certain order perturbation theory both momentum and coordinate space. Results of fit scattering phase shifts bound state data are presented, where satisfactory agreement found for laboratory energies about 100 Mev.

Few-nucleon forces are considered from the point of view effective chiral Lagrangians. It is argued that such naturally arise at same order in perturbation theory as some important features two-nucleon force. In particular, leading few-nucleon cancel against recoil correction iteration two-body potential. The remaining three-body potential presented momentum and coordinate spaces. dominated by contributions delta isobar (i) two-pion range, which not new, (ii) shorter involve an undetermined...

Effective field theory has revolutionized the of nuclear forces by providing a systematic expansion for strong interactions at low energies based on symmetries quantum chromodynamics. This paper reviews layers effective theories used in description nuclei and their reactions, broader applications to hadron structure fundamental symmetries.

The nucleon-nucleon potential obtained from the most general effective chiral Lagrangian involving low momentum pions, nonrelativistic nucleons, and \ensuremath{\Delta} isobars was considered to third order in expansion. parameters of were adjusted reproduce energy scattering phase shifts as well properties deuteron. Reasonable fits are this first application a based on symemtry.

The renormalization of the chiral nuclear interactions is studied. In leading order, cutoff dependence related to singular tensor interaction one-pion exchange potential. S waves and in higher partial where force repulsive this can be absorbed by counterterms expected at that order. other additional contact are necessary. implications finding for effective-field-theory program physics discussed.

We consider pion interactions in an effective field theory of the narrow resonance $X(3872)$, assuming it is a weakly bound molecule charm mesons ${D}^{0}{\overline{D}}^{*0}$ and ${D}^{*0}{\overline{D}}^{0}$. Since hyperfine splitting ${D}^{0}$ ${D}^{*0}$ only 7 MeV greater than neutral mass, pions can be produced near threshold are nonrelativistic. show that exchange treated perturbation calculate next-to-leading-order correction to partial decay width...

Within the framework of chiral effective field theory, we discuss leading contributions to neutrinoless double-beta decay transition operator induced by light Majorana neutrinos. Based on renormalization arguments in both dimensional regularization with minimal subtraction and a coordinate-space cutoff scheme, show need introduce leading-order short-range operator, missing all current calculations. We strategies determine finite part coupling matching lattice QCD or relating it via symmetry...

We study recently proposed ultraviolet and infrared momentum regulators of the model spaces formed by construction a variational trial wave function which uses complete set many-body basis states based upon three-dimensional harmonic oscillator (HO) functions. These are defined truncation expansion characterized counting number ($\mathcal{N}$) intrinsic scale ($\ensuremath{\hbar}\ensuremath{\omega}$) HO basis---in short ordered pair ($\mathcal{N},\ensuremath{\hbar}\ensuremath{\omega}$). In...

We show how nuclear effective field theory (EFT) and ab initio nuclear-structure methods can turn input from lattice quantum chromodynamics (LQCD) into predictions for the properties of nuclei. argue that pionless EFT is appropriate to describe light nuclei obtained in LQCD simulations carried out at pion masses heavier than physical mass. solve using effective-interaction hyperspherical harmonics auxiliary-field diffusion Monte Carlo methods. Fitting three leading-order parameters deuteron,...

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 various regularization schemes need to introduce short-range lepton-number-violating operator leading order, confirming earlier findings. demonstrate that such only needed spin-singlet $S$-wave transitions, while...

We extend the prediction range of Pionless Effective Field Theory with an analysis ground state 16O in leading order. To renormalize theory, we use as input both experimental data and lattice QCD predictions nuclear observables, which probe sensitivity nuclei to increased quark masses. The many-body Schrödinger equation is solved Auxiliary Diffusion Monte Carlo method. For first time a quantum calculation, linear optimization procedure, allows us devise accurate trial wave function large...

After a brief review of the role three-nucleon forces play in few-nucleon systems, chiral-perturbation-theory approach to these is discussed. Construction (nominal) leading- and subleading-order Born terms pion-rescattering graphs contributing two-pion-exchange reviewed, comparisons are made types such that used today. It demonstrated short-range c term Tucson-Melbourne force unnatural power counting should be dropped. The class then becomes rather uniform.

We show that a central ${1/r}^{n}$ singular potential (with $n>~2)$ is renormalized by one-parameter square-well counterterm; low-energy observables are made independent of the width adjusting strength. find closed form expression for renormalization-group evolution counterterm.