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This is a collection of perspective pieces contributed by the participants of the Institute of Nuclear Theory's Program on Nuclear Physics for Precision Nuclear Physics which was held virtually from April 19 to May 7, 2021. The collection represents the reflections of a vibrant and engaged community of researchers on the status of theoretical research in low-energy nuclear physics, the challenges ahead, and new ideas and strategies to make progress in nuclear structure and reaction physics, effective field theory, lattice QCD, quantum information, and quantum computing. The contributed pieces solely reflect the perspectives of the respective authors and do not represent the viewpoints of the Institute for Nuclear theory or the organizers of the program., Perspective pieces of the virtual INT program 21-1b "Nuclear Forces for Precision Nuclear Physics", 107 pages

The authors analyze a proposed measurement of a high-energy reaction on the neutron-rich nucleus ${}^{6}$He. After the sudden knockout of the $\ensuremath{\alpha}$ particle (${}^{4}$He) by a proton in inverse kinematics all final-state particles are detected. This gives access to the final-state interaction between the two neutrons, thereby allowing extraction of the $n\phantom{\rule{0}{0ex}}n$ scattering length, which pertains to charge-symmetry breaking in the nucleon-nucleon interaction. The focus is on the theoretical uncertainties in the extraction of the $n\phantom{\rule{0}{0ex}}n$ scattering length from the relative-energy distribution of the two neutrons.

We assess the accuracy of Bayesian polynomial extrapolations from small parameter values, x, to large values of x. We consider a set of polynomials of fixed order, intended as a proxy for a fixed-order effective field theory (EFT) description of data. We employ Bayesian Model Averaging (BMA) to combine results from different order polynomials (EFT orders). Our study considers two "toy problems" where the underlying function used to generate data sets is known. We use Bayesian parameter estimation to extract the polynomial coefficients that describe these data at low x. A "naturalness" prior is imposed on the coefficients, so that they are O(1). We Bayesian-Model-Average different polynomial degrees by weighting each according to its Bayesian evidence and compare the predictive performance of this Bayesian Model Average with that of the individual polynomials. The credibility intervals on the BMA forecast have the stated coverage properties more consistently than does the highest evidence polynomial, though BMA does not necessarily outperform every polynomial., 19 pages, 5 figures, v2 corresponds to published version

We develop a method that uses truncation-order-dependent re-expansions constrained by generic strong-coupling information to extrapolate perturbation series to the nonperturbative regime. The method is first benchmarked against a zero-dimensional model field theory and then applied to the dilute Fermi gas in one and three dimensions. Overall, our method significantly outperforms Pad\'e and Borel extrapolations in these examples. The results for the ground-state energy of the three-dimensional Fermi gas are robust with respect to changes of the form of the re-expansion and compare well with quantum Monte Carlo simulations throughout the BCS regime and beyond., Comment: minor improvements, matches published version; 11 pages, 8 figures

We introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory ($\chi$EFT). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as $\chi$EFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $\chi$EFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density the predicted symmetry energy and its slope are consistent with experimental constraints., Comment: 7 pages, 2 figures, supplemental material; close to the published version; minor corrections and additional discussion of correlations in supplemental material; Jupyter notebooks for reproducing the results and figures can be found at https://buqeye.github.io/software/

Interpreting measurements requires a physical theory, but the theory's accuracy may vary across the experimental domain. To optimize experimental design, and so to ensure that the substantial resources necessary for modern experiments are focused on acquiring the most valuable data, both the theory uncertainty and the expected pattern of experimental errors must be considered. We develop a Bayesian approach to this problem, and apply it to the example of proton Compton scattering. Chiral Effective Field Theory ($\chi$EFT) predicts the functional form of the scattering amplitude for this reaction, so that the electromagnetic polarizabilities of the nucleon can be inferred from data. With increasing photon energy, both experimental rates and sensitivities to polarizabilities increase, but the accuracy of $\chi$EFT decreases. Our physics-based model of $\chi$EFT truncation errors is combined with present knowledge of the polarizabilities and reasonable assumptions about experimental capabilities at HI$\gamma$S and MAMI to assess the information gain from measuring specific observables at specific kinematics, \emph{i.e.}, to determine the relative amount by which new data are apt to shrink uncertainties. The strongest gains would likely come from new data on the spin observables $\Sigma_{2x}$ and $\Sigma_{2x^\prime}$ at $\omega\simeq140$ to $200$ MeV and $40^\circ$ to $120^\circ$. These would tightly constrain $\gamma_{E1E1}-\gamma_{E1M2}$. New data on the differential cross section between $100$ and $200$\,MeV and over a wide angle range will substantially improve constraints on $\alpha_{E1}-\beta_{M1}$, $\gamma_\pi$ and $\gamma_{M1M1}-\gamma_{M1E2}$. Good signals also exist around $160$ MeV for $\Sigma_3$ and $\Sigma_{2z^\prime}$. Such data will be pivotal in the continuing quest to pin down the scalar polarizabilities and refine understanding of the spin polarizabilities., Comment: 47 pages LaTeX2e (pdflatex) including 33 figures as .jpg files using includegraphics. Improved presentation with corrections do not affect the conclusions by details of the figures. Higher-resolution figures are available at https://home.gwu.edu/~hgrie/Compton/one-N-comprehensive-observables-delta4.v2.0.high-resolution-figures.tgz. Final version with minor corrections published in EPJA57(2021)81

The lowest-lying resonance in the QCD spectrum is the $0^{++}$ isoscalar $\sigma$ meson, also known as the $f_0(500)$. We augment SU(2) chiral perturbation theory $\chi$PT) by including the $\sigma$ meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarr\'us and others. In this effective field theory, denoted $\chi$PT$_S$, the $\sigma$ meson's well-established mass and decay width are not sufficient to properly renormalize its self energy. At $\mathcal{O}(p^4)$ another low-energy constant appears in the dressed $\sigma$-meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the $\pi\pi\rightarrow\pi\pi$ and $\gamma\gamma\rightarrow\pi\pi$ reactions to data from threshold through the energies at which the $\sigma$-meson resonance affects observables. The leading-order (LO) $\pi \pi$ amplitude reproduces the $\sigma$-meson pole position, the isoscalar $\pi \pi$ scattering lengths and $\pi \pi$ scattering and $\gamma \gamma \rightarrow \pi \pi$ data up to $\sqrt{s} \approx 0.5$ GeV. It also yields a $\gamma \gamma\rightarrow\pi\pi$ amplitude that obeys the Ward identity. The value obtained for the $\pi^0$ polarizability is, however, only slightly larger than that obtained in standard $\chi$PT.

We describe the Bayesian Analysis of Nuclear Dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodology's ability to leverage insight from multiple models. In order to facilitate understanding of these tools we provide a simple and accessible example of the BAND framework's application. Four case studies are presented to highlight how elements of the framework will enable progress on complex, far-ranging problems in nuclear physics. By collecting notation and terminology, providing illustrative examples, and giving an overview of the associated techniques, this paper aims to open paths through which the nuclear physics and statistics communities can contribute to and build upon the BAND framework., Comment: 47 pages, 10 figures. Revised version includes minor corrections and changes in presentation. Matches journal version

We introduce the transition-density formalism, an efficient and general method for calculating the interaction of external probes with light nuclei. One- and two-body transition densities that encode the nuclear structure of the target are evaluated once and stored. They are then convoluted with an interaction kernel to produce amplitudes, and hence observables. By choosing different kernels, the same densities can be used for any reaction in which a probe interacts perturbatively with the target. The method therefore exploits the factorisation between nuclear structure and interaction kernel that occurs in such processes. We study in detail the convergence in the number of partial waves for matrix elements relevant in elastic Compton scattering on $^3$He. The results are fully consistent with our previous calculations in Chiral Effective Field Theory. But the new approach is markedly more computationally efficient, which facilitates the inclusion of more partial-wave channels in the calculation. We also discuss the usefulness of the transition-density method for other nuclei and reactions. Calculations of elastic Compton scattering on heavier targets like $^4$He are straightforward extensions of this study, since the same interaction kernels are used. And the generality of the formalism means that our $^3$He densities can be used to evaluate any $^3$He elastic-scattering observable with contributions from one- and two-body operators. They are available at https://datapub.fz-juelich.de/anogga., Comment: 44 pages LaTeX2e (pdflatex) including 4 figures as .pdf files using includegraphics. Improved proofs of symmetry relations and clarifications. Final version with minor changes and updates to reverences is text-identical with journal publication but more readable layout

We consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Pad\'{e} and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. We find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties., Comment: 19 pages, 3 figures. Paper prepared for the Festschrift in honor of the 60th birthday of Prof. D.A. Drabold. This version has minor changes in response to referee comments. Almost identical to version published in Physica Status Solidi B: Basic Solid State Physics

We consider the response of nucleons and light nuclei to electromagnetic fields to test the ability of chiral effective field theory to describe such systems in a consistent and systematically-improvable manner.

We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for \({}^{3}\mathrm {He}+{}^{4}\mathrm {He}\rightarrow {}^{7}\mathrm {Be}+ \gamma \) to perform the extrapolation of higher-energy data to solar energies. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic behavior of \({}^{7}\mathrm {Be}\) and its excited state, and short-distance contributions to the E1 capture amplitude. We use a Bayesian analysis to infer the multi-dimensional posterior of these parameters from capture data below 2 MeV. The total S factor \(S(0)= 0.578^{+0.015}_{-0.016}\) keV b at 68% degree of belief. We also find significant constraints on \({}^{3}\mathrm {He}\)–\({}^{4}\mathrm {He}\) scattering parameters.

We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($\chi$EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $\chi$EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $\chi$EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks., Comment: 23 pages, 21 figures, 4 tables, supplemental material; close to the published version; minor corrections and additional table summarizing the main results; Jupyter notebooks for reproducing the results and figures can be found at https://buqeye.github.io/software/

Journal of physics / G 49(1), 010502 (2022). doi:10.1088/1361-6471/ac2827, Published by IOP Publ., Bristol

Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. We formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. We demonstrate that model-checking diagnostics---applied to the case of multiple curves---are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub., 24 pages, 13 figures

Previous studies of the reaction ${}^{3}\mathrm{He} +{}^{4}\mathrm{He} \rightarrow {}^{7}\mathrm{Be} + \gamma$ have focused on providing the best central value and error bar for the $S$ factor at solar energies. Measurements of this capture reaction, the ${}^{3}\mathrm{He}$-${}^{4}\mathrm{He}$ scattering phase shifts, as well as properties of ${}^{7}\mathrm{Be}$, have been used to constrain employed theoretical models. Here we show that much more information than was previously appreciated can be extracted from angle-integrated capture data alone. We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for the reaction to perform the extrapolation. At this order the EFT describes the reaction using an s-wave scattering length and effective range, the asymptotic properties of the final bound states, and short-distance contributions to the $E1$ capture amplitude. We extract the multi-dimensional posterior of all these parameters via a Bayesian analysis. We find that properties of the ${}^{7}\mathrm{Be}$ ground and excited states are well constrained. The total $S$ factor $S(0)= 0.578^{+0.015}_{-0.016}$ keV~b, while the branching ratio for excited- to ground-state capture at zero energy, $Br(0)=0.406^{+0.013}_{-0.011}$, both at 68\% degree of belief. This $S(0)$ is broadly consistent with other recent evaluations, including the previously recommended value $S(0)=0.56 \pm 0.03$ eV b, but has a smaller error bar. We also find significant constraints on the scattering parameters, and we obtain constraints on the $S(E)$'s angular dependence. The path forward seems to lie with better measurements of the scattering phase shift and $S(E)$'s angular dependence, together with better understanding of the asymptotic normalization coefficients of the ${}^7$Be bound states' wave functions. Data on these could further reduce $S(0)$'s uncertainty., Comment: 19 pages and 10 figures (including the supplemental materials)

We compute the momentum-space probability density of ${}^6$He at leading order in Halo EFT. In this framework, the ${}^6$He nucleus is treated as a three-body problem with a ${}^4$He core ($c$) and two valence neutrons ($n$). This requires the $nn$ and $nc$ t-matrices as well as a $cnn$ force as input in the Faddeev equations. Since the $nc$ t-matrix corresponds to an energy-dependent potential, we consider the consequent modifications to the standard normalization and orthogonality conditions. We find that these are small for momenta within the domain of validity of Halo EFT. In this regime, the ${}^6$He probability density is regulator independent, provided the cutoff is significantly above the EFT breakdown scale., Comment: 34 pages, 3 figures, version to appear in Few-Body Systems. Further explanations and discussions added, typos corrected, results unchanged

I discuss the use of chiral effective field theory (χEFT) to describe electromagnetic reactions in the two- and three-nucleon systems. I review the results of χEFT power counting for charge and current operators up to [Formula: see text] relative to leading order, before showing that renormalization-group arguments imply that short-distance electromagnetic operators play a larger role than suggested by this standard counting. A detailed examination of χEFT's predictions for the electromagnetic form factors of deuterium and the trinucleons, and for the threshold captures np→dγ and nd→tγ, enables a critical appraisal of the theory's performance in these contexts. Recent χEFT calculations using the [Formula: see text] chiral perturbation theory (χPT) potential yielded both form factors that agree with experimental data for Q22 and an excellent description of the challenging threshold captures. Short-distance M1 operators are essential to this success, and the addition of a short-distance part of the nucleon–nucleon charge operator produces precise predictions of the deuteron charge and quadrupole form factors in this kinematic domain.

We employ an effective field theory (EFT) that exploits the separation of scales in the $p$-wave halo nucleus $^{8}\mathrm{B}$ to describe the process $^{7}\mathrm{Be}(p,\ensuremath{\gamma})^{8}\mathrm{B}$ up to a center-of-mass energy of 500 keV. The key leading-order (LO) and next-to-leading-order (NLO) results appeared in our earlier papers. Here we first present full details of the EFT calculation. We develop the lagrangian and power counting in terms of velocity scaling, thereby making manifest that the Coulomb force between $^{7}\mathrm{Be}$ and proton plays a major role in both scattering and radiative capture at these energies: Coulomb interactions must be included to all orders in ${\ensuremath{\alpha}}_{\mathrm{em}}$. The EFT calculation of the capture reaction is then carried out using Feynman diagrams computed in time-ordered perturbation theory, so we recover existing quantum-mechanical technology such as the Lippmann-Schwinger equation and the two-potential formalism for the treatment of the Coulomb-nuclear interference. Meanwhile, the strong interactions and the E1 operator are dealt with via EFT expansions in powers of momenta, with a breakdown scale set by the size of the $^{7}\mathrm{Be}$ core, $\mathrm{\ensuremath{\Lambda}}\ensuremath{\approx}70$ MeV/c. This is worked out up to NLO in the EFT expansion; at this order the relevant physics in the different channels that enter the radiative capture reaction is encoded in ten different EFT couplings. The result is a model-independent parametrization for the reaction amplitude in the energy regime of interest. In the second part of the paper we consider other approaches that have been used to describe $^{7}\mathrm{Be}{(p,\ensuremath{\gamma})}^{8}\mathrm{B}$ in this energy range. We discuss the relationship of EFT to each of these approaches in qualitative terms and then make the connection quantitative by determining what the ten NLO EFT coefficients are in five different calculations that we consider representative. The EFT parameters are of natural size in all five cases, which shows that each of these earlier calculations corresponds to a particular point in the EFT parameter space. This understanding of the relationship between EFT and other ways of computing $^{7}\mathrm{Be}{(p,\ensuremath{\gamma})}^{8}\mathrm{B}$ allows us to update earlier results for the dependence of $S(0)$ on asymptotic normalization coefficients and scattering lengths, since EFT separates dependence on these asymptotic quantities from dependence on shorter-distance contributions to the matrix element. We also summarize the fit to experimental capture data presented in our earlier work and explain why we obtain an extrapolated $S(0)$ with a markedly smaller error bar than that of the previous standard evaluation. Finally, we demonstrate that the only ${\mathrm{N}}^{2}\mathrm{LO}$ corrections in $^{7}\mathrm{Be}(p,\ensuremath{\gamma})^{8}\mathrm{B}$ come from an inelasticity that is practically of $\mathrm{N}^{3}\mathrm{LO}$ size in the energy range of interest, and so the truncation error in our calculation is effectively $\mathrm{N}^{3}\mathrm{LO}$.

We present a description of the breakup of halo nuclei in peripheral nuclear reactions by coupling a model of the projectile motivated by halo effective field theory with a fully dynamical treatment of the reaction using the dynamical eikonal approximation. Our description of the halo system reproduces its long-range properties, i.e., binding energy and asymptotic normalization coefficients of bound states and phase shifts of continuum states. As an application we consider the breakup of $^{11}\mathrm{Be}$ in collisions on Pb and C targets. Taking the input for our halo-EFT-inspired description of $^{11}\mathrm{Be}$ from a recent ab initio calculation of that system yields a good description of the Coulomb-dominated breakup on Pb at energies up to about 2 MeV, with the result essentially independent of the short-distance part of the halo wave function. However, the nuclear dominated breakup on C is more sensitive to short-range physics. The role of spectroscopic factors and possible extensions of our approach to include additional short-range mechanisms are also discussed.

We recently developed a Bayesian framework for parameter estimation in general effective field theories. Here we present selected results from using that framework to estimate parameters with a nucleon-nucleon (NN) potential derived using chiral effective field theory ($\chi$EFT): the semi-local NN potential of Epelbaum, Krebs, and Mei{\ss}ner (EKM). There are many NN scattering data, up to high energies, and with rather small errors, so imposing a penalty for unnatural low-energy constants (LECs) usually has a small effect on the fits. In contrast, we have found that including an estimate of higher orders in $\chi$EFT plays an important role in robust parameter estimation.We present two case studies where our Bayesian machinery illuminates physics issues. The first involves the EKM potential at fourth order in the $\chi$EFT expansion: the two-dimensional posterior probability density function (pdf) for the fourth-order $s$-wave LECs obtained from the Nijmegen PWA93 phase shifts indicates these parameters in the NN potential are degenerate. We trace this feature of the pdf to the presence of an operator in the fourth-order NN potential that vanishes on-shell. The second case study examines the stability of LEC extractions as more data at higher energies are included in the fit. We show that as long as $\chi$EFT truncation errors are properly accounted for in the parameter estimation, the LEC values extracted using our Bayesian approach are not sensitive to the maximum energy chosen for the fit.Uncorrelated and fully correlated models for the truncation errors are compared, pointing the way to the use of Gaussian processes to more generally model the correlation structure., Comment: 42 pages, 14 figures

This corrects the article DOI: 10.1103/PhysRevLett.98.232303.

We report observables for elastic Compton scattering from $^3$He in Chiral Effective Field Theory with an explicit $\Delta(1232)$ degree of freedom ($\chi$EFT) for energies between 50 and 120 MeV. The $\gamma\,{}^3$He amplitude is complete at N3LO, $\mathcal{O}(e^2\delta^3)$, and in general converges well order by order. It includes the dominant pion-loop and two-body currents, as well as the Delta excitation in the single-nucleon amplitude. Since the cross section is two to three times that for deuterium and the spin of polarised $^3$He is predominantly carried by its constituent neutron, elastic Compton scattering promises information on both the scalar and spin polarisabilities of the neutron. We study in detail the sensitivities of 4 observables to the neutron polarisabilities: the cross section, the beam asymmetry and two double asymmetries resulting from circularly polarised photons and a longitudinally or transversely polarised target. Including the Delta enhances those asymmetries from which neutron spin polarisabilities could be extracted. We also correct previous, erroneous results at N2LO, i.e.~without an explicit Delta, and compare to the same observables on proton, neutron and deuterium targets. An interactive Mathematica notebook of our results is available from hgrie@gwu.edu., Comment: 37 pages LaTeX2e (pdflatex) including 16 figures as .pdf files using includegraphics; minor corrections, triggered by referee comments, plus typographical errors; text-identical to version published as EPJA 54 (2018) 125

We treat $^{6}\mathrm{Li}$ as an effective three-body $(n\text{\ensuremath{-}}p\text{\ensuremath{-}}\ensuremath{\alpha})$ system and compute the $d\text{\ensuremath{-}}\ensuremath{\alpha}\phantom{\rule{4pt}{0ex}}S$-wave scattering length and three-body separation energy of $^{6}\mathrm{Li}$ for a wide variety of nucleon-nucleon and $\ensuremath{\alpha}$-nucleon potentials which have the same (or nearly the same) phase shifts. The Coulomb interaction in the $p\text{\ensuremath{-}}\ensuremath{\alpha}$ subsystem is omitted. The results of all calculations lie on a one-parameter curve in the plane defined by the $d\text{\ensuremath{-}}\ensuremath{\alpha}\phantom{\rule{4pt}{0ex}}S$-wave scattering length and the amount by which $^{6}\mathrm{Li}$ is bound with respect to the $n\text{\ensuremath{-}}p\text{\ensuremath{-}}\ensuremath{\alpha}$ threshold. We argue that these aspects of the $n\text{\ensuremath{-}}p\text{\ensuremath{-}}\ensuremath{\alpha}$ system can be understood using few-body universality and that $^{6}\mathrm{Li}$ can thus usefully be thought of as a two-nucleon halo nucleus.

We report an improved low-energy extrapolation of the cross section for the process Be 7 ( p , γ ) B 8 , which determines the 8B neutrino flux from the Sun. Our extrapolant is derived from Halo Effective Field Theory (EFT) at next-to-leading order. We apply Bayesian methods to determine the EFT parameters and the low-energy S-factor, using measured cross sections and scattering lengths as inputs. Asymptotic normalization coefficients of 8B are tightly constrained by existing radiative capture data, and contributions to the cross section beyond external direct capture are detected in the data at E 0.5 MeV . Most importantly, the S-factor at zero energy is constrained to be S ( 0 ) = 21.3 ± 0.7 eV b , which is an uncertainty smaller by a factor of two than previously recommended. That recommendation was based on the full range for S ( 0 ) obtained among a discrete set of models judged to be reasonable. In contrast, Halo EFT subsumes all models into a controlled low-energy approximant, where they are characterized by nine parameters at next-to-leading order. These are fit to data, and marginalized over via Monte Carlo integration to produce the improved prediction for S ( E ) .

The lowest-lying resonance in the QCD spectrum is the $ 0^{++}$ isoscalar $ \sigma$ -meson, also known as the $ f_{0}(500)$ . We augment SU(2) chiral perturbation theory ( $ \chi$ PT) by including the $ \sigma$ -meson as an additional explicit degree of freedom, as proposed by Soto, Talavera, and Tarrus and others. In this effective field theory, denoted $ \chi$ PTS, the $ \sigma$ -meson’s well-established mass and decay width are not sufficient to properly renormalize its self energy. At $ O(p^{4})$ another low-energy constant appears in the dressed $ \sigma$ -meson propagator; we adjust it so that the isoscalar pion-pion scattering length is also reproduced. We compare the resulting amplitudes for the $ \pi\pi\rightarrow\pi\pi$ and $ \gamma\gamma\rightarrow\pi\pi$ reactions to data from threshold through the energies at which the $ \sigma$ -meson resonance affects observables. The leading-order (LO) $ \pi \pi$ amplitude reproduces the $ \sigma$ -meson pole position, the isoscalar $ \pi \pi$ scattering lengths and $ \pi \pi$ scattering and $ \gamma\gamma\rightarrow\pi\pi$ data up to $ \sqrt{s} \approx 0.5$ GeV. It also yields a $ \gamma\gamma\rightarrow\pi\pi$ amplitude that obeys the Ward identity. The value obtained for the $ \pi^{0}$ polarizability is, however, only slightly larger than that obtained in standard $ \chi$ PT.

Nuclear halos emerge as new degrees of freedom near the neutron and proton driplines. They consist of a core and one or a few nucleons which spend most of their time in the classically-forbidden region outside the range of the interaction. Individual nucleons inside the core are thus unresolved in the halo configuration, and the low-energy effective interactions are short-range forces between the core and the valence nucleons. Similar phenomena occur in clusters of $^4$He atoms, cold atomic gases near a Feshbach resonance, and some exotic hadrons. In these weakly-bound quantum systems universal scaling laws for s-wave binding emerge that are independent of the details of the interaction. Effective field theory (EFT) exposes these correlations and permits the calculation of non-universal corrections to them due to short-distance effects, as well as the extension of these ideas to systems involving the Coulomb interaction and/or binding in higher angular-momentum channels. Halo nuclei exhibit all these features. Halo EFT, the EFT for halo nuclei, has been used to compute the properties of single-neutron, two-neutron, and single-proton halos of s-wave and p-wave type. This review summarizes these results for halo binding energies, radii, Coulomb dissociation, and radiative capture, as well as the connection of these properties to scattering parameters, thereby elucidating the universal correlations between all these observables. We also discuss how Halo EFT's encoding of the long-distance physics of halo nuclei can be used to check and extend ab initio calculations that include detailed modeling of their short-distance dynamics., Comment: 104 pages, 31 figures. Topical Review for Journal of Physics G. v2 incorporates several modifications, particularly to the Introduction, in response to referee reports. It also corrects multiple typos in the original submission. It corresponds to the published version

We present an analysis of $13$ observables in Compton scattering on the proton. Cross sections, asymmetries with polarised beam and/or targets, and polarisation-transfer observables are investigated for energies up to the $\Delta(1232)$ resonance to determine their sensitivity to the proton's dipole scalar and spin polarisabilities. The Chiral Effective Field Theory Compton amplitude we use is complete at N$^4$LO, $\mathcal{O(}e^2\delta^4)$, for photon energies $\omega\sim m_\pi$, and so has an accuracy of a few per cent there. At photon energies in the resonance region it is complete at NLO, $\mathcal{O}(e^2\delta^0)$, and so its accuracy there is about $20$\%. We find that for energies from pion-production threshold to about $250\;\mathrm{MeV}$, multiple asymmetries have significant sensitivity to presently ill-determined combinations of proton spin polarisabilities. We also argue that the broad outcomes of this analysis will be replicated in complementary theoretical approaches, e.g., dispersion relations. Finally, we show that below the pion-production threshold, $6$ observables suffice to reconstruct the Compton amplitude, and above it $11$ are required. Although not necessary for polarisability extractions, this opens the possibility to perform "complete" Compton-scattering experiments. An interactive Mathematica notebook, including results for the neutron, is available from judith.mcgovern@manchester.ac.uk ., Comment: 75 pages LaTeX2e (pdflatex) including 37 figures as .pdf files using includegraphics; minor corrections. Text-identical to published version but including the Online Supplement. Higher-resolution figures are available at http://home.gwu.edu/~hgrie/Compton/one-N-comprehensive-observables-delta4.v2.0.high-resolution-figures.tgz

In this paper, the recent work our group has undertaken on effective field theory (EFT) analyses of experimental data pertaining to one- and two-neutron halo nuclei is discussed. The cases of 19C and 8Li (one-neutron halos) and 22C (two-neutron halo) are considered. For 19C and 8Li electromagnetic processes, such as Coulomb dissociation and radiative capture are considered. In the 22C system the way in which the measured matter radius can be used to derive constraints on the two-neutron separation energy of this very neutron-rich system is shown. In each case the ‘Halo EFT’ ability to correlate different experimental observables with one another, in a model-independent manner, and up to an accuracy that is determined by the separation of scales in the halo system is shown.

We study Borromean 2n-halo nuclei using effective field theory. We compute the universal scaling function that relates the mean-square matter radius of the 2n halo to dimensionless ratios of two- and three-body energies. We use the experimental value of the rms matter radius of 22C measured by Tanaka et al. to put constraints on its 2n separation energy and the 20C-n virtual energy. We also explore the consequences of these constraints for the existence of excited Efimov states in this nucleus. We find that, for 22C to have an rms matter radius within 1-sigma of the experimental value, the two-neutron separation energy of 22C needs to be below 100 keV. Consequently, this three-body halo system can have an excited Efimov state only if the 20C-n system has a resonance within 1 keV of the scattering threshold., Comment: 6 pages, 4 figures

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, $a$, which is large compared to the range of the interaction, $\ell$. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N$^2$LO) in the $\ell/a$ expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed $a$). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N$^2$LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N$^2$LO phase- shift predictions will receive higher-order corrections of $< 0.2$%. In contrast, the prediction of SREFT for the binding energy of the "deep" trimer of Helium-4 atoms displays poor convergence., 58 pages, 20 figures. Dedicated to Professor Henryk Witala at the occasion of his 60th birthday. Submitted in Few-Body Systems

We apply the large-${N}_{c}$ expansion to the time-reversal-invariance-violating (TV) nucleon-nucleon potential. The operator structures contributing to next-to-next-to-leading order in the large-${N}_{c}$ counting are constructed. For the TV and parity-violating case we find a single operator structure at leading order. The TV but parity-conserving potential contains two leading-order terms, which, however, are suppressed by $1/{N}_{c}$ compared to the parity-violating potential. Comparison with phenomenological potentials, including the chiral effective field theory potential in the TV parity-violating case, leads to large-${N}_{c}$ scaling relations for TV meson-nucleon and nucleon-nucleon couplings.

We have recently completed a high-precision extraction of the proton spin-independent polarisabilities from the world database of low-energy Compton scattering experiments, within the framework of chiral effective field theory (ChEFT) with pions, nucleons, and the Delta(1232) as explicit degrees of freedom. Our Baldin-sum-rule-constrained results are, in units of $10^{-4}$~fm$^3$, alphae_p=10.65 \pm 0.35(stat)\pm 0.2(Baldin)\pm 0.3(theory) betam_p=3.15 \mp 0.35(stat)\pm 0.2(Baldin)\mp 0.3(theory).These were obtained in the heavy-baryon formulation, but almost identical results have been obtained ina covariant calculation.With the publication this year by Myers et al of the results of the deuteron Comptonscattering experiment using the Tagged-Photon Facility at the MAX IV Laboratory in Lund,Sweden, the world database has doubled in size, allowing the extraction of the isoscalar polarisabilities with unprecedented accuracy, and combined with the proton results we obtain alphae_n =11.65 \pm 1.25(stat) \pm 0.2(Baldin)\pm 0.8(theory), betam_n = 3.55 \mp 1.25(stat) \pm 0.2(Baldin) \mp 0.8(theory).A new generation of experiments with polarised beams have been performed at the Mainz Microtron, with the first results published this year by Martel et al, These experiments are sensitive to the spin polarisabilities, and we will discuss the predictions of ChEFT for the relevant cross sections and asymmetries.

The electric and magnetic polarizabilities of the proton are now well known, owing to Compton scattering measurements on hydrogen targets; however, the neutron polarizabilities are still relatively uncertain, compared to the proton values. To address this problem, a multiinstitutional collaboration has conducted a program of elastic Compton scattering experiments on deuterium at the MAX IV Laboratory in Lund, Sweden using tagged photons in the energy range Eγ= 65-115 MeV. We assembled at one laboratory, for the first time, three of the world's largest NaI detectors, each having better than ΔE/E ∼ 2% photon energy resolution. We have measured elastic Compton scattering cross sections at lab angles of θγ= 60°, 120° and 150° over this energy range in 8 MeV steps. This effectively doubles the world's set of elastic Compton scattering data from deuterium and provides valuable input for chiral effective field theory (χEFT) calculations. These new deuterium data overlap previous measurements and extend them by 20 MeV to higher energies. Based on χEFT fits to the expanded world data set, new values for the neutron electric and magnetic polarizabilities have been obtained with greater accuracy than previously achieved, decreasing the statistical error by more than 30%. (Less)

We examine the results of Chiral Effective Field Theory ($\chi$EFT) for the scalar- and spin-dipole polarisabilities of the proton and neutron, both for the physical pion mass and as a function of $m_\pi$. This provides chiral extrapolations for lattice-QCD polarisability computations. We include both the leading and sub-leading effects of the nucleon's pion cloud, as well as the leading ones of the $\Delta(1232)$ resonance and its pion cloud. The analytic results are complete at N$^2$LO in the $\delta$-counting for pion masses close to the physical value, and at leading order for pion masses similar to the Delta-nucleon mass splitting. In order to quantify the truncation error of our predictions and fits as $68$\% degree-of-belief intervals, we use a Bayesian procedure recently adapted to EFT expansions. At the physical point, our predictions for the spin polarisabilities are, within respective errors, in good agreement with alternative extractions using experiments and dispersion-relation theory. At larger pion masses we find that the chiral expansion of all polarisabilities becomes intrinsically unreliable as $m_\pi$ approaches about $300\;$MeV---as has already been seen in other observables. $\chi$EFT also predicts a substantial isospin splitting above the physical point for both the electric and magnetic scalar polarisabilities; and we speculate on the impact this has on the stability of nucleons. Our results agree very well with emerging lattice computations in the realm where $\chi$EFT converges. Curiously, for the central values of some of our predictions, this agreement persists to much higher pion masses. We speculate on whether this might be more than a fortuitous coincidence., Comment: 39 pages LaTeX2e (pdflatex) including 12 figures as 16 .pdf files using includegraphics. Version approved for publication in EPJA includes modifications, clarifications and removal of typographical errors in refereeing and publication process

6 He has a cluster structure with a tight 4 He ( α ) core surrounded by two loosely bound neutrons ( n ) making it a halo nucleus. The leading-order (LO) Halo Effective Field Theory (EFT) [1, 2] calculations using momentum-space Faddeev equations pertinent to a bound 6 He were carried out in [3]. In this work, we investigate 6 He up to next-to-leading order (NLO) within Halo EFT.

We examine the extent to which the properties of three-nucleon bound states are well-reproduced in the limit that nuclear forces satisfy Wigner's SU(4) (spin-isospin) symmetry. To do this we compute the charge radii up to next-to-leading order (NLO) in an effective field theory (EFT) that is an expansion in powers of $R/a$, with $R$ the range of the nuclear force and $a$ the nucleon-nucleon ($N\!N$) scattering lengths. In the Wigner-SU(4) limit, the triton and Helium-3 point charge radii are equal. At NLO in the range expansion both are $1.66$ fm. Adding the first-order corrections due to the breaking of Wigner symmetry in the $N\!N$ scattering lengths gives a ${}^3\mathrm{H}$ point charge radius of $1.58$ fm, which is remarkably close to the experimental number, $1.5978\pm0.040$ fm (Angeli and Marinova in At Data Nucl Data Tables 99:69-95, 2013). For the ${}^3\mathrm{He}$ point charge radius we find $1.70$ fm, about 4% away from the experimental value of $1.77527\pm0.0054$ fm (Angeli and Marinova 2013). We also examine the Faddeev components that enter the tri-nucleon wave function and find that an expansion of them in powers of the symmetry-breaking parameter converges rapidly. Wigner's SU(4) symmetry is thus a useful starting point for understanding tri-nucleon bound-state properties., Comment: v1: 22 pages, 6 figures, v2: 23 pages 6 figures

We have studied the 7 Be( p , γ ) 8 B reaction in the Halo effective field theory (EFT) framework. The leading order (LO) results were published in Ref. [1] after the isospin mirror process, 7 Li( n , γ ) 8 Li, was addressed in Ref. [2]. In both calculations, one key step was using the final shallow bound state asymptotic normalization coefficients (ANCs) computed by ab initio methods to fix the EFT couplings. Recently we have developed the next-to-LO (NLO) formalism [3], which could reproduce other model results by no worse than 1% when the 7 Be-p energy was between 0 and 0:5 MeV. In our recent report [4], a different approach from that in Ref. [1] was used. We applied Bayesian analysis to constrain all the NLO-EFT parameters based on measured S -factors, and found tight constraints on the S -factor at solar energies. Our S ( E = 0 MeV) = 21.3 ± 0.7 eV b. The uncertainty is half of that previously recommended. In this proceeding, we provide extra details of the Bayesian analysis, including the computed EFT parameters’ probability distribution functions (PDFs) and how the choice of input data impacts final results.

We study the $^{11}\mathrm{Li}$ and $^{22}\mathrm{C}$ nuclei at leading order (LO) in halo effective field theory (Halo EFT). Using the value of the $^{22}\mathrm{C}$ rms matter radius deduced in Ref. [1] as an input in a LO calculation, we simultaneously constrained the values of the two-neutron (2$n$) separation energy of $^{22}\mathrm{C}$ and the virtual-state energy of the $^{20}\mathrm{C}-$neutron system (hereafter denoted $^{21}$C). The 1$-\sigma$ uncertainty of the input rms matter radius datum, along with the theory error estimated from the anticipated size of the higher-order terms in the Halo EFT expansion, gave an upper bound of about 100 keV for the 2$n$ separation energy. We also study the electric dipole excitation of 2$n$ halo nuclei to a continuum state of two neutrons and the core at LO in Halo EFT. We first compare our results with the $^{11}\mathrm{Li}$ data from a Coulomb dissociation experiment and obtain good agreement within the theoretical uncertainty of a LO calculation. We then obtain the low-energy spectrum of $B(E1)$ of this transition at several different values of the 2$n$ separation energy of $^{22}\mathrm{C}$ and the virtual-state energy of $^{21}\mathrm{C}$. Our predictions can be compared to the outcome of an ongoing experiment on the Coulomb dissociation of $^{22}\mathrm{C}$ to obtain tighter constraints on the two- and three-body energies in the $^{22}\mathrm{C}$ system., Comment: 6 pages, 3 figures; Contribution to the 21st International Conference on Few-Body Problems in Physics

We review theoretical progress and prospects for determining the nucleon’s static dipole polarisabilities from Compton scattering on few-nucleon targets, including new values; see Refs. [1–5] for details and a more thorough bibliography.

We analyze how corrections linear in the effective range, r_0, affect quantities in the three-body sector within an effective field theory for short-range interactions. We demonstrate that observables can be obtained straightforwardly using a perturbative expansion in powers of r_0. In particular, we show that two linear-in-r_0 counterterms are needed for renormalization at this order if scattering-length-dependent observables are considered. We exemplify the implications of this result using various three-body observables. Analytic results for the running of the next-to-leading-order portion of the three-body force in this effective field theory are provided. Expressions which incorporate O(r_0) corrections and relate the positions of features observed in three-atom recombination near a Feshbach resonance are presented., Comment: revtex4, 30 pages, 6figures, version2 accepted for publication in Annals of Physics, section on universal relations at NLO rewritten

We present a calculation of the π − d scattering length with an accuracy of a few percent using chiral perturbation theory. For the first time isospin-violating corrections are included consistently. Using data on pionic deuterium and pionic hydrogen atoms, we extract the isoscalar and isovector pion–nucleon scattering lengths and obtain a + = ( 7.6 ± 3.1 ) ⋅ 10 − 3 M π − 1 and a − = ( 86.1 ± 0.9 ) ⋅ 10 − 3 M π − 1 . Via the Goldberger–Miyazawa–Oehme sum rule, this leads to a charged-pion–nucleon coupling constant g c 2 / 4 π = 13.69 ± 0.20 .

We study how EFT can improve the description of reactions used to study the structure of exotic nuclei. Using Halo EFT helps constraining the potential that simulates the interaction between the projectile constituents. It enables us to include ab initio results within the reaction model and to clearly identify the nuclear properties probed by the reaction. New local chiral EFT nucleon-nucleon interactions can also be used to derive nucleus-nucleus optical potentials from first principles, which can provide reliable inputs in reaction modelling., SCOPUS: cp.p, info:eu-repo/semantics/published