Search

We consider a possible resummation of subleading effects in two-body systems with a large scattering length as described by a short-range effective field theory (EFT). In particular, we investigate the consequences of a resummation of part of the range corrections. Explicit calculations of the two-body phase shifts and charge form factor indicate that, except for extreme choices, resummations do not alter the convergence of the EFT expansion and are often beneficial at lowest orders. We have considered the expansion when the regulator cutoff is removed as well as when it is finite, and find that the cutoff is not an important factor for resummations. Our results connect with other works where the partial resummation is induced by potentials with finite cutoffs or interaction ranges., Comment: 11 pages, 7 figures

Near two-body unitarity, the three-boson system is characterized by an approximate discrete scale invariance manifest in a geometric tower of bound states (the Efimov effect). In the absence of a strong four-body force, the four-boson system has two states associated with each Efimov state, one very nearly unstable, the other several times deeper. We study correlations between the excited- and ground-state properties, such as binding energies and radii, up to next-to-leading order in an effective field theory for short-range forces. We obtain the parameters in these correlations from similar correlations arising from existing precise calculations based on short-range potentials. We also derive correlations among excited-state properties that emerge from the proximity of the state to the break-up threshold into a boson and a three-boson bound state, using an effective field theory for "halo" states., Comment: 31 pages, 6 figures

We solve the Faddeev bound-state equations for three particles with simple two-body nonlocal, separable potentials that yield a scattering length twice as large as a positive effective range, as indicated by some lattice QCD simulations. Neglecting shape parameters, the two-body bound state is a double pole. For bosons we obtain a correlation between three- and two-body energies. For nucleons, this correlation depends additionally on the ratio of effective ranges in the two two-body $S$-wave channels. When this ratio takes the value suggested by lattice QCD, our three-body energy agrees well with a direct lattice determination. When this ratio takes the experimental value, we find a three-body bound state with energy close to that of the physical triton. We suggest that results could be improved systematically with distorted-wave perturbation theory around a separable potential whose form factor is an inverse square root of momentum squared., Comment: 12 pages, 1 figure

Weinberg's contributions to the power counting and derivation of few-nucleon forces in Chiral EFT are briefly recalled. Subsequent improvements are reviewed, concluding with the recent suggestion of a combinatorial enhancement., Comment: 7 pages. Invited talk at the XLIV Reuniao de Trabalho sobre Fisica Nuclear no Brasil, November 2021

Nearly 60 years ago Weinberg suggested a criterion for particle "compositeness", which has acquired new life with the discovery of new, exotic hadrons. His idea resonates with model-based intuition. I discuss the role it plays in the context of another of Weinberg's creations, the model-independent framework of effective field theories., Comment: 19 pages, 1 figure. Prepared for Special Issue of Symmetry on Fundamental Aspects of Theoretical Physics -- Memorial Issue for S. Weinberg

The renormalization of iterated one-pion exchange (OPE) is studied in Chiral Effective Field Theory ($\chi$EFT) for the antinucleon-nucleon ($\overline{N}\!N$) system. The OPE potential is cut off at a certain distance and contact interactions are represented by a complex spherical well with the same radius. We investigate the dependence on the cutoff radius of the phase shifts, inelasticities, and mixing angles for the low partial waves in $\overline{N}\!N$ scattering. We show that renormalization requires additional contact interactions compared to the expectation based on naive dimensional analysis. Results after renormalization are compared with the state-of-the-art energy-dependent partial-wave analysis of $\overline{N}\!N$ data. We compare our conclusions with applications of $\chi$EFT to the nucleon-nucleon system., Comment: 33 pages, 22 figures and 3 tables

We study the importance of few-nucleon forces in chiral effective field theory for describing many-nucleon systems. A combinatorial argument suggests that three-nucleon forces -- which are conventionally regarded as next-to-next-to-leading order -- should accompany the two-nucleon force already at leading order (LO) starting with mass number $A\approx 10-20$. We find that this promotion enables the first realistic description of the $^{16}$O ground state based on a renormalization-group-invariant LO interaction. We also performed coupled-cluster calculations of the equation of state for symmetric nuclear matter and our results indicate that LO four-nucleon forces could play a crucial role for describing heavy-mass nuclei. The enhancement mechanism we found is very general and could be important also in other many-body problems., Comment: 6 pages, 4 figures

Effective field theories are recognized nowadays as the framework to describe low-energy nuclear structure and reactions consistently with the underlying theory of the strong interactions, QCD. It was not always so. As we celebrate the 30 years of the first publications, I collect here some memories from those early days. I also discuss some of the key issues that were raised back then and, despite all progress, are still with us. Dedicated to the memory of Steven Weinberg, whose ideas will not die, wherever they may lead., Comment: Contribution to the special issue of Few-Body Syst., "Celebrating 30 years of Steven Weinberg's papers on nuclear forces from chiral Lagrangians"

We calculate the lifetime of the deuteron from dimension-six quark operators that violate baryon number by one unit. We construct an effective field theory for $|\Delta B|=1$ interactions that give rise to nucleon and $\Delta B=1$ deuteron decay in a systematic expansion. We show that up to and including next-to-leading order the deuteron decay rate is given by the sum of the decay rates of the free proton and neutron. The first nuclear correction is expected to contribute at the few-percent level and comes with an undetermined low-energy constant. We discuss its relation to earlier potential-model calculations.

We discuss shallow resonances in the nonrelativistic scattering of two particles using an effective field theory (EFT) that includes an auxiliary field with the quantum numbers of the resonance. We construct the manifestly renormalized scattering amplitude up to next-to-leading order in a systematic expansion. For a narrow resonance, the amplitude is perturbative except in the immediate vicinity of the resonance poles. It naturally has a zero in the low-energy region, analogous to the Ramsauer-Townsend effect. For a broad resonance, the leading-order amplitude is nonperturbative almost everywhere in the regime of validity of the EFT. We regain the results of an EFT without the auxiliary field, which is equivalent to the effective-range expansion with large scattering length and effective range. We also consider an additional fine tuning leading to a low-energy amplitude zero even for a broad resonance. We show that in all cases the requirement of renormalizability when the auxiliary field is not a ghost ensures the resonance poles are in the lower half of the complex momentum plane, as expected by other arguments. The systematic character of the EFT expansion is exemplified with a toy model serving as underlying theory., Comment: 19 pages, 14 figures

Resonances are of particular importance to the scattering of composite particles in quantum mechanics. We build an effective field theory for two-body scattering which includes a low-energy $S$-wave resonance. Our starting point is the most general Lagrangian with short-range interactions. We demonstrate that these interactions can be organized into various orders so as to generate a systematic expansion for an $S$ matrix with two low-energy poles. The pole positions are restricted by renormalization at leading order, where the common feature is a non-positive effective range. We carry out the expansion explicitly to next-to-leading order and illustrate how it systematically accounts for the results of a toy model -- a spherical well with a delta shell at its border., Comment: 23 pages, 12 figures

Nuclear effective field theories (EFTs) have been developed over the last quarter-century with considerable impact on the description of light and even medium-mass nuclei. At the core of any EFT is a systematic expansion of observables, which is usually obtained from a rule based on an assumption of naturalness. I discuss naturalness in the context of the relatively weak binding of nuclei, where discrete scale invariance plays a role in the emergence of complexity., Comment: 22 pages, contribution to EPJA's topical issue "The tower of effective (field) theories and the emergence of nuclear phenomena"

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., Comment: 40 pages, 9 figures, 3 tables, contribution to Frontiers in Physics' research topic "The Long-Lasting Quest for Nuclear Interactions: The Past, the Present and the Future"

Ab initio nuclear physics tackles the problem of strongly interacting four-component fermions. The same setting could foreseeably be probed experimentally in ultracold atomic systems, where two- and three-component experiments have led to major breakthroughs in recent years. Both due to the problem's inherent interest and as a pathway to nuclear physics, in this Letter we study four-component fermions at unitarity via the use of quantum Monte Carlo methods. We explore novel forms of the trial wave function and find one which leads to a ground state of the eight-particle system whose energy is almost equal to that of two four-particle systems. We investigate the clustering properties involved and also extrapolate to the zero-range limit. In addition to being experimentally testable, our results impact the prospects of developing nuclear physics as a perturbation around the unitary limit., Comment: 6+1 pages, 3+1 figures; v2 corresponds to published version

The process at the heart of neutrinoless double-beta decay, $nn \rightarrow p p\, e^- e^-$ 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 corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-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-beta decay for $^6$He and $^{12}$Be. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.

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., Comment: 76 pages, 29 figures, version to appear in Rev. Mod. Phys

Halo/Cluster Effective Field Theory describes halo/cluster nuclei in an expansion in the small ratio of the size of the core(s) to the size of the system. Even in the point-particle limit, neutron halo nuclei have a finite charge radius, because their center of mass does not coincide with their center of charge. This point-particle contribution decreases as $1/A_c$, where $A_c$ is the mass number of the core, and diminishes in importance compared to other effects, e.g., the size of the core to which the neutrons are bound. Here we propose that for heavy cores the EFT expansion should account for the small factors of $1/A_c$. As a specific example, we discuss the implications of this organizational scheme for the inclusion of finite-size effects in expressions for the charge radii of halo nuclei. We show in particular that a short-range operator could be the dominant effect in the charge radius of one-neutron halos bound by a P-wave interaction. The point-particle contribution remains the leading piece of the charge radius for one-proton halos, and so Halo EFT has more predictive power in that case., Comment: Published version

We calculate the lifetime of the deuteron with dimension-nine quark operators that violate baryon number by two units. We construct an effective field theory for $|\Delta B|=2$ interactions that give rise to neutron-antineutron ($n$-$\bar{n}$) oscillations and dinucleon decay within a consistent power counting. We calculate the ratio of the deuteron lifetime to the square of the $n$-$\bar{n}$ oscillation time up to next-to-leading order. Our result, which is analytical and has a quantified uncertainty, is smaller by a factor $\simeq 2.5$ than earlier estimates based on nuclear models, which impacts the indirect bound on he $n$-$\bar{n}$ oscillation time and future experiments. We discuss how combined measurements of $n$-$\bar{n}$ oscillations and deuteron decay can help to identify the sources of baryon-number violation.

These lectures are a pedagogical -- not comprehensive -- introduction to the applications of effective field theory in the context of nuclear and atomic physics. A common feature of these applications is the interplay between nonperturbative physics (needed at leading order to produce nonrelativistic bound states and resonances) and controlled perturbative corrections (crucial for predictive power). The essential ideas are illustrated with the simplest nuclear EFT, Pionless EFT, which contains only contact interactions and, with minor changes, can be adapted to certain atomic systems. This EFT exploits the two-body unitarity limit, where renormalization leads to discrete scale invariance in systems of three and more bodies. Remarkably complex structures then arise from very simple leading-order interactions. Some of the challenges and rewards of including long-range forces -- pion exchange in Chiral EFT for nuclear systems or Van der Waals forces between atoms -- are briefly described., Comment: Contribution to the Proceedings of the 2017 Les Houches Summer School on Effective Field Theory in Particle Physics and Cosmology (Les Houches, France, July 31-August 25, 2017); 53 pages, 7 figures

Within the framework of chiral effective field theory we discuss the leading contributions to the 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, we show the need to introduce a leading-order short-range operator, missing in all current calculations. We discuss strategies to determine the finite part of the short-range coupling by matching to lattice QCD or by relating it via chiral symmetry to isospin-breaking observables in the two-nucleon sector. Finally, we speculate on the impact of this new contribution on nuclear matrix elements of relevance to experiment., Comment: 6 pages, 3 figures

The properties of cold Bose gases at unitarity have been extensively investigated in the last few years both theoretically and experimentally. In this paper we use a family of interactions tuned to two-body unitarity and very weak three-body binding to demonstrate the universal properties of both clusters and matter. We determine the universal properties of finite clusters up to 60 particles and, for the first time, explicitly demonstrate the saturation of energy and density with particle number and compare with bulk properties. At saturation in the bulk we determine the energy, density, two- and three-body contacts and the condensate fraction. We find that uniform matter is more bound than three-body clusters by nearly two orders of magnitude, the two-body contact is very large in absolute terms, and yet the condensate fraction is also very large, greater than 90%. Equilibrium properties of these systems may be experimentally accessible through rapid quenching of weakly-interacting boson superfluids., Comment: 5 pages, 4 figures

We present a new rearrangement of short-range interactions in the $^1S_0$ nucleon-nucleon channel within Chiral Effective Field Theory. This is intended to reproduce the amplitude zero (scattering momentum $\simeq$ 340 MeV) at leading order, and it includes subleading corrections perturbatively in a way that is consistent with renormalization-group invariance. Systematic improvement is shown at next-to-leading order, and we obtain results that fit empirical phase shifts remarkably well all the way up to the pion-production threshold. An approach in which pions have been integrated out is included, which allows us to derive analytic results that also fit phenomenology surprisingly well., Comment: 34 pages, 7 figures

We extend the prediction range of Pionless Effective Field Theory with an analysis of the ground state of $^{16}$O in leading order. To renormalize the theory, we use as input both experimental data and lattice QCD predictions of nuclear observables, which probe the sensitivity of nuclei to increased quark masses. The nuclear many-body Schr\"odinger equation is solved with the Auxiliary Field Diffusion Monte Carlo method. For the first time in a nuclear quantum Monte Carlo calculation, a linear optimization procedure, which allows us to devise an accurate trial wave function with a large number of variational parameters, is adopted. The method yields a binding energy of $^{4}$He which is in good agreement with experiment at physical pion mass and with lattice calculations at larger pion masses. At leading order we do not find any evidence of a $^{16}$O state which is stable against breakup into four $^4$He, although higher-order terms could bind $^{16}$O., Comment: 11 pages, 4 figures

Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron scattering lengths and the triton binding energy) at the leading and next-to-leading orders of a power counting that ensures order-by-order renormalization in the two-nucleon system. Our results imply that three-body forces are not needed for renormalization of the three-nucleon system up to next-to-leading order, as usually assumed in the literature. (Erratum to the original article is included), Comment: 40 pages, 24 figures, (Erratum: 5 pages, 4 figures)

We analyze the power counting of the peripheral singlet partial waves in nucleon-nucleon scattering. In agreement with conventional wisdom, we find that pion exchanges are perturbative in the peripheral singlets. We quantify from the effective field theory perspective the well-known suppression induced by the centrifugal barrier in the pion-exchange interactions. By exploring perturbation theory up to fourth order, we find that the one-pion-exchange potential in these channels is demoted from leading to subleading order by a given power of the expansion parameter that grows with the orbital angular momentum. We discuss the implications of these demotions for few-body calculations: though higher partial waves have been known for a long time to be irrelevant in these calculations (and are hence ignored), here we explain how to systematize the procedure in a way that is compatible with the effective field theory expansion., Comment: 15 pages, 18 figures

We argue that many features of the structure of nuclei emerge from a strictly perturbative expansion around the unitarity limit, where the two-nucleon S waves have bound states at zero energy. In this limit, the gross features of states in the nuclear chart are correlated to only one dimensionful parameter, which is related to the breaking of scale invariance to a discrete scaling symmetry and set by the triton binding energy. Observables are moved to their physical values by small, perturbative corrections, much like in descriptions of the fine structure of atomic spectra. We provide evidence in favor of the conjecture that light, and possibly heavier, nuclei are bound weakly enough to be insensitive to the details of the interactions but strongly enough to be insensitive to the exact size of the two-nucleon system., Comment: 6 pages, 3 figures, published version, rewritten for clarity

We present a new perturbative expansion for pionless effective field theory with Coulomb interactions in which at leading order the spin-singlet nucleon-nucleon channels are taken in the unitarity limit. Presenting results up to next-to-leading order for the Phillips line and the neutron-deuteron doublet-channel phase shift, we find that a perturbative expansion in the inverse 1S0 scattering lengths converges rapidly. Using a new systematic treatment of the proton-proton sector that isolates the divergence due to one-photon exchange, we renormalize the corresponding contribution to the 3H-3He binding energy splitting and demonstrate that the Coulomb force in pionless EFT is a completely perturbative effect in the trinucleon bound-state regime. In our new expansion, the leading order is exactly isospin-symmetric. At next-to-leading order, we include isospin breaking via the Coulomb force and two-body scattering lengths, and find for the energy splitting (E_B(3He)-E_B(3H))^NLO = (-0.86 +/- 0.17) MeV., Comment: 37 pages, 14 figures, published version

I describe how nuclear structure can be predicted from lattice QCD through low-energy effective field theories, using as an example a world simulation with relatively heavy up and down quarks., Comment: 14 pages, to appear in Few-Body Syst

Thanks to the unnaturally small value of the QCD vacuum angle $\bar\theta < 10^{-10}$, time-reversal ($T$) violation offers a window into physics beyond the Standard Model (SM) of particle physics. We review the effective-field-theory framework that establishes a clean connection between $T$-violating mechanisms, which can be represented by higher-dimensional operators involving SM fields and symmetries, and hadronic interactions, which allow for controlled calculations of low-energy observables involving strong interactions. The chiral properties of $T$-violating mechanisms leads to a pattern that should be identifiable in measurements of the electric dipole moments of the nucleon and light nuclei., Comment: 35 pages. Accepted for publication in Ann. Rev. Nucl. Part. Sci. 65 (2015)

Phenomenological effective interactions like Skyrme forces are currently used in mean--field calculations in nuclear physics. Mean--field models have strong analogies with the first order of the perturbative many--body problem and the currently used effective interactions are adjusted at the mean--field level. In this work, we analyze the renormalizability of the nuclear many--body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order., Comment: Revised version

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. We argue that pionless EFT is the appropriate theory to describe the light nuclei obtained in recent LQCD simulations carried out at pion masses much heavier than the physical pion mass. We solve the EFT using the effective-interaction hyperspherical harmonics and auxiliary-field diffusion Monte Carlo methods. Fitting the three leading-order EFT parameters to the deuteron, dineutron and triton LQCD energies at $m_{\pi}\approx 800$ MeV, we reproduce the corresponding alpha-particle binding and predict the binding energies of mass-5 and 6 ground states., Comment: 5 pages, 2 figures

We calculate the toroidal quadrupole moment and form factor of the deuteron, which violate time-reversal symmetry but conserve parity, at leading order in two-flavor chiral effective field theory with perturbative pion exchange. We take into account time-reversal and parity violation due to the QCD vacuum angle combined with parity violation resulting from the weak interaction in the Standard Model. We also consider time-reversal and parity violation that at the quark-gluon level results from effective dimension-six operators originating from physics beyond the Standard Model.

Searches for the permanent electric dipole moments (EDMs) of molecules, atoms, nucleons and nuclei provide powerful probes of CP violation both within and beyond the Standard Model (BSM). The interpretation of experimental EDM limits requires careful delineation of physics at a wide range of distance scales, from the long-range atomic and molecular scales to the short-distance dynamics of physics at or beyond the Fermi scale. In this review, we provide a framework for disentangling contributions from physics at these disparate scales, building out from the set of dimension four and six effective operators that embody CP violation at the Fermi scale. We survey existing computations of hadronic and nuclear matrix elements associated with Fermi-scale CP violation in systems of experimental interest, and quantify the present level of theoretical uncertainty in these calculations. Using representative BSM scenarios of current interest, we illustrate how the interplay of physics at various scales generates EDMs at a potentially observable level., Comment: To appear in Prog. Part. Nucl. Phys

We classify the parity- and time-reversal-violating operators involving quark and gluon fields that have effective dimension six: the quark electric dipole moment, the quark and gluon chromo-electric dipole moments, and four four-quark operators. We construct the effective chiral Lagrangian with hadronic and electromagnetic interactions that originate from them, which serves as the basis for calculations of low-energy observables. The form of the effective interactions depends on the chiral properties of these operators. We develop a power-counting scheme and calculate within this scheme, as an example, the parity- and time-reversal-violating pion-nucleon form factor. We also discuss the electric dipole moments of the nucleon and light nuclei., Comment: Matches published version

We calculate the magnetic quadrupole moment (MQM) of the deuteron at leading order in the systematic expansion provided by chiral effective field theory. We take into account parity and time-reversal violation which, at the quark-gluon level, results from the QCD vacuum angle and dimension-six operators that originate from physics beyond the Standard Model. We show that the deuteron MQM can be expressed in terms of five low-energy constants that appear in the parity- and time-reversal-violating nuclear potential and electromagnetic current, four of which also contribute to the electric dipole moments of light nuclei. We conclude that the deuteron MQM has an enhanced sensitivity to the QCD vacuum angle and that its measurement would be complementary to the proposed measurements of light-nuclear EDMs.

We combine Halo/Cluster Effective Field Theory (H/CEFT) and the Gamow Shell Model (GSM) to describe the $0^+$ ground state of $\rm{^6He}$ as a three-body halo system. We use two-body interactions for the neutron-alpha particle and two-neutron pairs obtained from H/CEFT at leading order, with parameters determined from scattering in the p$_{3/2}$ and s$_0$ channels, respectively. The three-body dynamics of the system is solved using the GSM formalism, where the continuum states are incorporated in the shell model valence space. We find that in the absence of three-body forces the system collapses, since the binding energy of the ground state diverges as cutoffs are increased. We show that addition at leading order of a three-body force with a single parameter is sufficient for proper renormalization and to fix the binding energy to its experimental value.

We describe systems of two and three nucleons trapped in a harmonic-oscillator potential with interactions from the pionless effective field theory up to next-to-leading order (NLO). We construct the two-nucleon interaction using two-nucleon scattering information. We calculate the trapped levels in the three-nucleon system with isospin $T=1/2$ and determine the three-nucleon force needed for stability of the triton. We extract neutron-deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data., Comment: 19 pages, 15 figures

We set up the framework for the calculation of electric dipole moments (EDMs) of light nuclei using the systematic expansion provided by chiral effective field theory (EFT). We take into account parity (P) and time-reversal (T) violation which, at the quark-gluon level, originates from the QCD vacuum angle and dimension-six operators capturing physics beyond the Standard Model. We argue that EDMs of light nuclei can be expressed in terms of six low-energy constants that appear in the P- and T-violating nuclear potential and electric current. As examples, we calculate the EDMs of the deuteron, the triton, and 3He in leading order in the EFT expansion.

We derive the parity- and time-reversal-violating nuclear interactions stemming from the QCD theta term and quark/gluon operators of effective dimension 6: quark electric dipole moments, quark and gluon chromo-electric dipole moments, and two four-quark operators. We work in the framework of two-flavor chiral perturbation theory, where a systematic expansion is possible. The different chiral-transformation properties of the sources of time-reversal violation lead to different hadronic interactions. For all sources considered the leading-order potential involves known one-pion exchange, but its specific form and the relative importance of short-range interactions depend on the source. For the theta term, the leading potential is solely given by one-pion exchange, which does not contribute to the deuteron electric dipole moment. In subleading order, a new two-pion-exchange potential is obtained. Its short-range component is indistinguishable from one of two undetermined contact interactions that appear at the same order and represent effects of heavier mesons and other short-range QCD dynamics. One-pion-exchange corrections at this order are discussed as well., Comment: 39 pages, 8 figures

We include the Roper excitation of the nucleon in a version of heavy-baryon chiral perturbation theory recently developed for energies around the delta resonance. We find significant improvement in the $P_{11}$ channel., Comment: Version to be published

We calculate the electric-dipole and magnetic-quadrupole form factors of the deuteron that arise as a low-energy manifestation of parity and time-reversal violation in quark-gluon interactions of effective dimension four and six: the QCD vacuum angle, the quark electric and chromo-electric dipole moments, and the gluon chromo-electric dipole moment. Within the framework of two-flavor chiral perturbation theory, we show that the relative sizes of the corresponding moments allow an identification of the symmetry-breaking source.

The electric dipole form factor (EDFF) of the nucleon stemming from the QCD theta term and from the quark color-electric dipole moments is calculated in chiral perturbation theory to sub-leading order. This is the lowest order in which the isoscalar EDFF receives a calculable, non-analytic contribution from the pion cloud. In the case of the theta term, the expected lower bound on the deuteron electric dipole moment is |d_d| > 1.4 10^(-4) \theta e fm. The momentum dependence of the isovector EDFF is proportional to a non-derivative time-reversal-violating pion-nucleon coupling, and the scale for momentum variation ---appearing, in particular, in the radius of the form factor--- is the pion mass., Comment: 14 pages, 3 figures

We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the No-Core Shell Model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by others methods (in the four-body case). We also present results for finite scattering lengths and non-zero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length., Comment: 18 pages, 10 figures

We calculate the electric dipole form factor of the nucleon that arises as a low-energy manifestation of time-reversal violation in quark-gluon interactions of effective dimension 6: the quark electric and chromoelectric dipole moments, and the gluon chromoelectric dipole moment. We use the framework of two-flavor chiral perturbation theory to one loop.

We construct the effective chiral Lagrangian involving hadronic and electromagnetic interactions originating from the QCD theta term. We impose vacuum alignment at both quark and hadronic levels, including field redefinitions to eliminate pion tadpoles. We show that leading time-reversal-violating (TV) hadronic interactions are related to isospin-violating interactions that can in principle be determined from charge-symmetry-breaking experiments. We discuss the complications that arise from TV electromagnetic interactions. Some implications of the expected sizes of various pion-nucleon TV interactions are presented, and the pion-nucleon form factor is used as an example., Comment: 57 pages

We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction., Comment: 27 pages, 12 figures

One of the central open problems in nuclear physics is the construction of effective interactions suitable for many-body calculations. We discuss a recently developed approach to this problem, where one starts with an effective field theory containing only fermion fields and formulated directly in a no-core shell-model space. We present applications to light nuclei and to systems of a few atoms in a harmonic-oscillator trap. Future applications and extensions, as well as challenges, are also considered.