We use effective field theory to compute the influence of nuclear structure on precision calculations of atomic energy levels. As usual, the EFT's effective couplings correspond to the various nuclear properties (such as the charge radius, nuclear polarizabilities, Friar and Zemach moments {\it etc.}) that dominate its low-energy electromagnetic influence on its surroundings. By extending to spinning nuclei the arguments developed for spinless ones in {\tt arXiv:1708.09768}, we use the EFT to show -- to any fixed order in $Zα$ (where $Z$ is the atomic number and $α$ the fine-structure constant) and the ratio of nuclear to atomic size -- that nuclear properties actually contribute to electronic energies through fewer parameters than the number of these effective nuclear couplings naively suggests. Our result is derived using a position-space method for matching effective parameters to nuclear properties in the EFT, that more efficiently exploits the simplicity of the small-nucleus limit in atomic systems. By showing that precision calculations of atomic spectra depend on fewer nuclear uncertainties than naively expected, this observation allows the construction of many nucleus-independent combinations of atomic energy differences whose measurement can be used to test fundamental physics (such as the predictions of QED) because their theoretical uncertainties are not limited by the accuracy of nuclear calculations. We provide several simple examples of such nucleus-free predictions for Hydrogen-like atoms.
The closed-form Brükner $G$ matrix for nuclear matter is computed in the $^1S_0$ channel of EFT($\not\!\!π$) and renormalized in nonperturbative context. The nuclear medium environment yields additional constraints that are consistent with off-shell $T$ matrix renormalization, keeping the power counting intact and simplifying the running behaviors of the EFT couplings. With the $G$ obtained we computed the energy per particle for neutron and symmetric nuclear matter to demonstrate the physical relevance of certain 'physical' parameters that arise from nonperturbative renormalization. We also e…
I present results and highlight aspects of halo EFT to loosely bound systems composed of nucleons and alpha particles, with emphasis on Coulomb interactions.
The application of effective field theory (EFT) methods to nuclear systems provides the opportunity to rigorously estimate the uncertainties originating in the nuclear Hamiltonian. Yet this is just one source of uncertainty in the observables predicted by calculations based on nuclear EFTs. We discuss the goals of uncertainty quantification in such calculations and outline a recipe to obtain statistically meaningful error bars for their predictions. We argue that the different sources of theory error can be accounted for within a Bayesian framework, as we illustrate using a toy model.
The Legendre flow equation, a version of exact Wilsonian renormalization group (WRG) equation, is employed to consider the power counting issues in Nuclear Effective Field Theory. A WRG approach is an ideal framework because it is nonperturbative and does not require any prescribed power counting rule. The power counting is determined systematically from the scaling dimensions of the operators at the nontrivial fixed point. The phase structure is emphasized and the inverse of the scattering length, which is identified as a relevant coupling, is shown to play a role of the order parameter. The …
We review a new generation of nuclear forces derived in chiral effective field theory using the recently proposed semilocal regularization method. We outline the conceptual foundations of nuclear chiral effective field theory, discuss all steps needed to compute nuclear observables starting from the effective chiral Lagrangian and consider selected applications in the two- and few-nucleon sectors. We highlight key challenges in developing high-precision tree-body forces, such as the need to maintain consistency between two- and many-body interactions and constraints placed by the chiral and ga…
Chiral effective field theory has established itself as the method of choice to study nuclear forces and low-energy nuclear dynamics. I review the status and prospects of this approach and discuss ongoing efforts to advance the precision frontier for ab initio description of few-nucleon systems. Special emphasis is put on the precise determination of the two-nucleon force at fifth order in the chiral expansion, role of the chiral symmetry, the convergence pattern of the chiral expansion and the quantification of the theoretical uncertainties. The discussed topics are essential for ongoing stud…
A relation between nuclear forces derived using a phenomenological approach and nuclear effective field theory (NEFT) is proposed from a renormalization group point of view. A phenomenological nuclear force (V_ph) and an NEFT-based NN-potential (V_EFT) are satisfactorily related to each other through the Wilsonian renormalization group (WRG) method. It is clearly shown that use of the simple contact interactions in NEFT is adequate to simulate small scale phenomena, and that an NEFT-based NN-potential (V_EFT) is free from dependence on the model used to describe small scale phenomena. We study…
We study a relation between nuclear forces based on phenomenological approach (V_ph) and nuclear effective field theory (V_EFT) from a viewpoint of renormalization group. We find the relation between these two types of nuclear force using Wilsonian renormalization group equation. Considering the fact that V_EFT is defined in a certain small model space, we show that a simple contact interaction accurately simulates short-distance physics, and that V_EFT is free from dependence on modelling the details of the short-distance physics. Based on our result, we discuss some features of nuclear effec…
$ηNNN$ and $ηNNNN$ bound states are explored in stochastic variational method (SVM) calculations within a pionless effective field theory (EFT) approach at leading order. The theoretical input consists of regulated $NN$ and $NNN$ contact terms, and a regulated energy dependent $ηN$ contact term derived from coupled-channel models of the $N^{\ast}(1535)$ nucleon resonance plus a regulated $ηNN$ contact term. A self consistency procedure is applied to deal with the energy dependence of the $ηN$ subthreshold input, resulting in a weak dependence of the calculated $η$-nuclear binding energies on t…
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…
The pion contributions to the coupling $C_0$ of pionless EFT are studied via both non-relativistic and relativistic forms of chiral effective field theory for nuclear forces. A definite item in the $2N$-reducible component of the box diagram is shown to be dominant over the $2N$-irreducible (potential) ones due to the pinching of low-lying nucleon poles, and this anomalous mapping between pionless and pionfull EFT's occurs right within the non-relativistic regime. A natural strategy for renormalization of the pionfull theory emerges as a byproduct through the interactive analysis of the box di…
We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory so constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are "local flavor symmetry" of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden "quantum scale symmetry" with an IR fixed point with a "genuine dilaton (GD)" characterized …
Quantum Algorithms for Simulating Nuclear Effective Field Theories
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算联合中心，美国国家标准与技术研究院/马里兰大学）；Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland（马里兰大学计算机科学与高级计算研究所）；Joint Quantum Institute, NIST/University of Maryland（NIST/马里兰大学联合量子研究所）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Physics, University of Maryland（马里兰大学物理系）
Electron beams provide important probes and constraints for nuclear astrophysics. This is especially exciting at energies within the regime of chiral effective field theory (EFT), which provides a systematic expansion for nuclear forces and electroweak operators based on quantum chromodynamics. This talk discusses some recent highlights and future directions based on chiral EFT, including nuclear structure and reactions for astrophysics, the neutron skin and constraints for the properties of neutron-rich matter in neutron stars and core-collapse supernovae, and the dark matter response of nucl…
We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($χ$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 $χ$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 l…
We reformulate the analysis of nuclear parity-violation (PV) within the framework of effective field theory (EFT). To order Q, the PV nucleon-nucleon (NN) interaction depends on five a priori unknown constants that parameterize the leading-order, short-range four-nucleon operators. When pions are included as explicit degrees of freedom, the potential contains additional medium- and long-range components parameterized by PV piNN couplings. We derive the form of the corresponding one- and two-pion-exchange potentials. We apply these considerations to a set of existing and prospective PV few-body…
Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear s…
We present an overview of low-momentum two-nucleon and many-body interactions and their use in calculations of nuclei and infinite matter. The softening of phenomenological and effective field theory (EFT) potentials by renormalization group (RG) transformations that decouple low and high momenta leads to greatly enhanced convergence in few- and many-body systems while maintaining a decreasing hierarchy of many-body forces. This review surveys the RG-based technology and results, discusses the connections to chiral EFT, and clarifies various misconceptions.
The cross section for coherent elastic neutrino-nucleus scattering (CE$ν$NS) depends on the response of the target nucleus to the external current, in the Standard Model (SM) mediated by the exchange of a $Z$ boson. This is typically subsumed into an object called the weak form factor of the nucleus. Here, we provide results for this form factor calculated using the large-scale nuclear shell model for a wide range of nuclei of relevance for current CE$ν$NS experiments, including cesium, iodine, argon, fluorine, sodium, germanium, and xenon. In addition, we provide the responses needed to captu…
We present fully non-perturbative quantum Monte Carlo calculations with non-local chiral effective field theory (EFT) interactions for the ground state properties of neutron matter. The equation of state, the nucleon chemical potentials and the momentum distribution in pure neutron matter up to one and a half times the nuclear saturation density are computed with a newly optimized chiral EFT interaction at next-to-next-to-leading order. This work opens the way to systematic order by order benchmarking of chiral EFT interactions, and \emph{ab initio} prediction of nuclear properties while respe…
We study effective field theories (EFT) of nuclear structure based on spontaneously broken global $SU(2)_L\times SU(2)_R$ chiral symmetry of QCD with two massless quarks, i.e. $SU(2)χPT$. For ground-state nuclei, this EFT enables expansion and truncation in inverse powers of $Λ_{χSB}\simeq 1 GeV$, with analytic operators renormalized to all loop orders. We derive the EFT Lagrangian to order $Λ^0_{χSB}$. We show that $SU(2)χPT$ of protons, neutrons and pions admits a semi-classical "Static Chiral Nucleon Liquid" (Static$χ$NL) phase and that "Pion-less" $SU(2)χPT$ emerges in this liquid: far-inf…
Accurate nuclear matrix elements (NMEs) for neutrinoless double beta decays of candidate nuclei are important for the design and interpretation of future experiments. Significant progress has been made in the modeling of these NMEs from first principles. The NME for 48Ca shows a good agreement among three different ab initio calculations starting from the same nuclear interaction constructed within the chiral EFT and the same decay operator. These studies open the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as 76Ge, 130Te, and 136Xe. The ultimate …
In this whitepaper, I describe modern applications of effective field theory (EFT) techniques to classical and quantum gravity, with relevance to problems in astrophysics and cosmology. As in applications of EFT to high-energy, nuclear, or condensed matter physics, the Wilsonian paradigm based on decoupling of short distance scales via renormalization group evolution remains a powerful organizing principle in the context of gravity. However, the presence of spacetime geometry brings in new elements ( non-trivial time-dependence, cosmological or black hole event horizons) which necessitate the …
The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem. Recent developments are changing this situation. New experimental capabilities and theoretical approaches are opening windows into the richness of many-body phenomena in QCD. A common theme is the use of effective field theory (EFT) methods, which exploit the separation of scales in physical systems. At low energies, effective field theory can explain how existing phenomenology emerges from QCD and how to refine it sys…
Chiral effective field theory (EFT) provides a systematic expansion for the coupling of WIMPs to nucleons at the momentum transfers relevant to direct cold dark matter detection. We derive the currents for spin-dependent WIMP scattering off nuclei at the one-body level and include the leading long-range two-body currents, which are predicted in chiral EFT. As an application, we calculate the structure factor for spin-dependent WIMP scattering off 129,131Xe nuclei, using nuclear interactions that have been developed to study nuclear structure and double-beta decays in this region. We provide th…
We calculate the nuclear matrix element for the two-neutrino $ββ$ decay of $^{136}$Xe into the first excited $0^+$ state of $^{136}$Ba. We use different many-body methods: the quasiparticle random-phase approximation (QRPA) framework, the nuclear shell model, the interacting boson model (IBM-2), and an effective field theory (EFT) for $β$ and $ββ$ decays. While the QRPA suggests a decay rate at the edge of current experimental limits, the shell model points to a half-life about two orders of magnitude longer. The predictions of the IBM-2 and the EFT lie in between, and the latter provides syst…
Second order beta-decay processes with and without neutrinos in the final state are key probes of nuclear physics and of the nature of neutrinos. Neutrinoful double-beta decay is the rarest Standard Model process that has been observed and provides a unique test of the understanding of weak nuclear interactions. Observation of neutrinoless double-beta decay would reveal that neutrinos are Majorana fermions and that lepton number conservation is violated in nature. While significant progress has been made in phenomenological approaches to understanding these processes, establishing a connection…
We present our studies of the forward unpolarised doubly-virtual Compton scattering (VVCS) off the deuteron and the closely related two-photon-exchange ($2γ$-exchange) corrections to the Lamb shift of muonic deuterium. The deuteron VVCS amplitude is calculated in the framework of pionless effective field theory, up to next-to-next-to-next-to-leading order (N3LO) for the longitudinal and next-to-leading order (NLO) for the transverse amplitude. The charge elastic form factor of the deuteron, obtained from the residue of the longitudinal VVCS amplitude, is used to extract the value of the single…
We perform state-of-the-art large-scale shell-model calculations of the structure factors for elastic spin-dependent WIMP scattering off 129,131Xe, 127I, 73Ge, 19F, 23Na, 27Al, and 29Si. This comprehensive survey covers the non-zero-spin nuclei relevant to direct dark matter detection. We include a pedagogical presentation of the formalism necessary to describe elastic and inelastic WIMP-nucleus scattering. The valence spaces and nuclear interactions employed have been previously used in nuclear structure calculations for these mass regions and yield a good spectroscopic description of these i…
We perform a nonperturbative calculation of the 1S0 NN scattering amplitude using an effective field theory (EFT) expansion. The expansion we advocate is a modification of what has been used previously; it is no a chiral expansion in powers of the pion mass. We use dimensional regularization throughout and the MS-bar subtraction scheme; our final result depends only on physical observables. We show that the EFT expansion of the quantity |p|cot delta(p) converges at momenta much greater than the scale that characterizes the derivative expansion of the EFT Lagrangian. Our conclusions are optimis…
We introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory ($χ$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 $χ$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 $χ$EFT expansion. This produce…
We present the first quantum Monte Carlo (QMC) calculations with chiral effective field theory (EFT) interactions. To achieve this, we remove all sources of nonlocality, which hamper the inclusion in QMC calculations, in nuclear forces to next-to-next-to-leading order. We perform auxiliary-field diffusion Monte Carlo (AFDMC) calculations for the neutron matter energy up to saturation density based on local leading-order, next-to-leading order, and next-to-next-to-leading order nucleon-nucleon interactions. Our results exhibit a systematic order-by-order convergence in chiral EFT and provide no…
We provide a systematic assessment of the order-$α^5$ nuclear contributions to the Lamb shift of muonic deuterium, including the accompanying radiative corrections due to vacuum polarization, up to next-to-next-to-next-to-leading order (N3LO) within the pionless effective field theory (EFT). We also evaluate higher-order corrections due to the single-nucleon structure, which are expected to be the most important corrections beyond N3LO. We find a correlation between the deuteron charge and Friar radii, which can be useful to judge the quality of charge form factor parametrisations. We refine t…
I discuss how the axial current coupling constant $g_A$ renormalized in scale symmetric chiral EFT defined at a chiral matching scale impacts on the axial current matrix elements on beta decays in nuclei with and without neutrinos. The "quenched" $g_A$ observed in nuclear superallowed Gamow-Teller transitions, a long-standing puzzle in nuclear physics, is shown to encode the emergence of chiral-scale symmetry hidden in QCD in the vacuum. This enables one to explore how trace-anomaly-induced scale symmetry breaking enters in the renormalized $g_A$ in nuclei applicable to certain non-unique forb…
Using the volume coupling version of the cloudy bag model, the quark-meson coupling model is extended to study the role of pion field and the properties of nuclear matter. The extended model includes the effect of gluon exchange as well as the pion-cloud effect, and provides a good description of the nuclear matter properties. The relationship between the extended model and the EFT approach to nuclear matter is also discussed.
Distinguishing a dark matter interaction from an astrophysical neutrino-induced interaction will be major challenge for future direct dark matter searches. In this paper, we consider this issue within non-relativistic Effective Field Theory (EFT), which provides a well-motivated theoretical framework for determining nuclear responses to dark matter scattering events. We analyze the nuclear energy recoil spectra from the different dark matter-nucleon EFT operators, and compare to the nuclear recoil energy spectra that is predicted to be induced by astrophysical neutrino sources. We determine th…
Bulk nuclear observables such as charge radii and binding energies are well described by both nonrelativistic and covariant mean-field models. However, predictions of neutron radii, which are not tightly constrained by reliable data, vary significantly. The nature of this variation is investigated using correlations between basic properties of the models and the neutron skin thickness in lead. The results suggest that conventional covariant models are too limited. The study is guided by principles and insights of effective field theory (EFT), such as power counting, and the relation of mean-fi…
We investigate the sensitivity of the $Λ$ directed flow to the $Λ$ potential in mid-central Au + Au collisions at $\sqrt{s_{NN}}\approx3.0$--$30$ GeV. The $Λ$ potential obtained from the chiral effective field theory ($χ$EFT) is used in a microscopic transport model, a vector version of relativistic quantum molecular dynamics (RQMDv). We find that the density-dependent $Λ$ potentials, obtained from the $χ$EFT assuming weak momentum dependence of the potential, reproduce the rapidity and the beam-energy dependence of the $Λ$ directed flow measured by the STAR collaboration in the Beam Energy Sc…
Comprehensive effective field theory framework for coherent elastic neutrino-nucleus scattering
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-Sen University（中山大学广东省量子精密测量与传感重点实验室）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础科学与数学学院）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；International Centre for Theoretical Physics Asia-Pacific（亚太理论物理中心）
