We calculate the electric dipole moments (EDMs) of three-nucleon systems at leading order in pionless effective field theory. The one-body contributions that arise from permanent proton and neutron EDMs and the two-body contributions that arise from CP-odd nucleon-nucleon interactions are taken into account. Neglecting the Coulomb interaction, we consider the triton and ${}^3$He, and also investigate them in the Wigner-SU(4) symmetric limit. We also calculate the electric dipole form factor and find numerically that the momentum dependence of the electric dipole form factor in the Wigner limit is, up to an overall constant (and numerical accuracy), the same as the momentum dependence of the charge form factor.
We analyze magnetic and axial two-nucleon contact terms in a combined large-$N_c$ and pionless effective field theory expansion. These terms play important roles in correctly describing, e.g., the low-energy cross section of radiative neutron capture and the deuteron magnetic moment. We show that the large-$N_c$ expansion hints towards a hierarchy between the two leading-order magnetic terms that matches that found in phenomenological fits. We also comment on the issue of naturalness in different Lagrangian bases.
We consider the two-nucleon weak interaction with a pionless effective field theory. Dibaryon fields are introduced to facilitate calculations and ensure precision in the initial and final state propagators. Weak interactions are accounted for with the parity-violating dibaryon-nucleon-nucleon vertices, which contain unknown weak dibaryon-nucleon-nucleon coupling constants. We apply the model to the calculation of a parity-violating observable in the neutron-proton capture at threshold. Result is obtained up to the linear order in the unknown dibaryon-nucleon-nucleon coupling constants. We com…
The symmetries of the Standard Model dictate that for very low energies, where nucleon dynamics can be described in terms of a pionless effective field theory, the leading-order parity-violating nucleon-nucleon Lagrangian contains five independent unknown low-energy constants (LECs). We find that imposing the approximate symmetry of QCD that appears when the number of colors N(c) becomes large reduces the number of independent LECs to two at leading order in the combined pionless effective field theory and large-N(c) expansions. We also find a relation between the two isoscalar LECs in the lar…
Recent proposals for the use of light nuclei as dark matter direct detection targets necessitate a strong theoretical understanding of the nuclear physics involved. We perform relevant calculations for dark matter-light nucleus scattering in a combined pionless effective field theory and large-$N_c$ expansion, where $N_c$ is the number of quark colors. We include a general set of one-nucleon currents that have been used in other effective theories, as well as novel two-nucleon contact currents. First, we obtain constraints for the relative sizes of the dark matter couplings to the one- and two…
We present results for two-body observables that are sensitive to the parity-violating component of nucleon-nucleon interactions. These interactions are studied using an effective field theory in which the only dynamic degrees of freedom are nucleon fields. The observables we study are cross-section asymmetries in nucleon-nucleon scattering and asymmetries and induced polarizations in the process np \to dγ.
We consider a pionless effective theory with dibaryon fields for the description of the weak process involving two nucleons. We construct leading order Lagrangians that contain nucleon-dibaryon weak coupling constants. We calculate the physical observable in the photodisintegration of the deuteron at threshold and obtain the result in terms of the nucleon-dibaryon weak coupling constants. Relation to existing calculations is discussed.
In this dissertation we apply the pionless effective field theory to low energy neutron deuteron elastic scattering process. We calculated some of the polarization observables in neutron deuteron scattering to next-to-next-to-next-to-leading-order, in particular the transverse asymmetry $A_y$. All of the previous calculations have the same characteristic feature of under-predicting this observable, this is known as the $A_y$-puzzle. At this order of the pionless EFT new two-body $P$-wave interaction terms enter into the Lagrangian. This interaction terms give crucial contributions to the $A_y$…
Pionless effective field theory in a finite volume (FVEFT$_{π\!/}$) is investigated as a framework for the analysis of multi-nucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT$_{π\!/}$ with the stochastic variational method, the spectra of nuclei with atomic number $A\in\{2,3\}$ are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass $m_π=806$ MeV, thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wave…
We investigate the sensitivity of the three-nucleon system to changes in the neutron-neutron scattering length to next-to-leading order in the pionless effective field theory, focusing on the the triton-3He binding energy difference and neutron-deuteron elastic scattering. Due to the appearance of an electromagnetic three-body counterterm at this order, the triton-3He binding energy difference remains consistent with the experimental value even for large positive neutron-neutron scattering lengths while the elastic neutron-deuteron scattering phase shifts are insensitive. We conclude that a bo…
We analyze two-derivative two-nucleon interactions in a combined pionless effective field theory and large-$N_c$ expansion. At leading order in the large-$N_c$ expansion, relationships among low-energy constants emerge. We find these to be consistent with experiment. However, it is critical to correctly address the subtraction-point dependence of the low-energy constants. These results provide additional confidence that the dual-expansion procedure is useful for analyzing low-energy few-body observables.
This work implements pionless effective field theory with the two-nucleon system expanded around the unitarity limit at second order perturbation theory. The expansion is found to converge well. All Coulomb effects are treated in perturbation theory, including two-photon contributions at next-to-next-to-leading order. After fixing a three-nucleon force to the 3He binding energy at this order, proton-deuteron scattering in the doublet S-wave channel is calculated for moderate center-of-mass momenta.
Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wavefunctions optimised using differentiable programming and via solution of a generalised eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of…
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…
Deuteron Compton scattering is calculated to $\mathcal{O}(Q^2)$ in pionless effective field theory using a dibaryon approach. The vector amplitude, which was not included in the previous pionless calculations, contributes to the cross section at $\mathcal{O}(Q^2)$ and influences significantly the extracted values of nucleon electric polarizability at incident photon energy 49 MeV. We recommend future high precision deuteron compton scattering experiments being performed at 25-35 MeV photon energy where the nucleon polarizability effects are appreciable and the pionless effective field theory i…
In this article I summarize recent progress in the effective field theory approach to low energy nuclear systems, with a focus on the power counting issue. In the pionless sector, where the power counting is quite well understood at the nucleon-nucleon (NN) level, I discuss some recent developments toward few- and many-body calculations. In the pionful sector, I focus on the actively debated issue of power counting in the NN sector and some recent developments toward a model-independent NN interaction. Finally, the scenario that the power counting might depend on the number of particles is dis…
In this thesis, which is in the field of few-body systems, I am studying low-energy electro-weak interactions in light nuclear systems whose number of nucleons, $A$, is smaller than 4 ({\it i.e.,} $d$, $^3$H, $^3$He), where the main purpose of this work is to calculate the proton-proton ($pp$) fusion rate.
Nuclear parity violation is studied with polarized neutrons in the photodisintegration of the deuteron at low energies. A pionless effective field theory with di-baryon fields is used for the investigation. Hadronic weak interactions are treated by parity-violating di-baryon-nucleon-nucleon vertices, which have undetermined coupling contants. A parity-violating asymmetry in the process is calculated for the incident photon energy up to 30 MeV. If experimental data for the parity-violating asymmetry become available in the future, we will be able to determine the unknown coupling contants in th…
We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our ``pionless'' EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the 1S0 scattering length and effective range, the deuteron binding energy, the 3S1 effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse 3S1 and 1S0 scattering lengths vanishing at mpi_c=197.8577 MeV. A…
In this paper, we establish a general framework for calculating pionless matrix elements between $A=3$ bound-states up to next-to-leading-order. This framework is useful for pionless calculations of electroweak observables, such as $^3$H,$^3$He magnetic moments and $^3$H $β$ decay. Starting from a Bethe-Salpeter equation, we prove that for a bound-state, the three-nucleon wave-function normalization can be expressed diagrammatically in a way that is equivalent to the unit operator between two identical three-nucleon bound-states. This diagrammatic form of the identity matrix element is the fou…
We present a study of the two-photon-exchange ($2γ$-exchange) corrections to the $S$-levels in muonic ($μ$D) and ordinary (D) deuterium within the pionless effective field theory (pionless EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the pionless EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon-nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen-deuterium isotope sh…
A method to calculate the form factor for an external current with non-derivative coupling for the three-body system in an effective field theory (EFT) of short-range interactions is shown. Using this method the point charge radius of ${}^3\mathrm{He}$ is calculated to next-to-next-to-leading order (NNLO) in pionless EFT ($\mathrm{EFT}(\not{\!π})$), and the magnetic moment and magnetic radius of ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ are calculated to next-to-leading order (NLO). For the ${}^3\mathrm{He}$ charge and magnetic form factors Coulomb interactions are ignored. The ${}^3\mathrm{He}$ …
The s-wave nucleon-nucleon (NN) scattering matrix ($S$-matrix) exhibits UV/IR symmetries which are hidden in the effective field theory (EFT) action and scattering amplitudes, and which explain some generic features of the phase shifts. These symmetries offer clarifying interpretations of existing pionless EFT expansions, and suggest starting points for novel expansions. The leading-order (LO) $S$-matrix obtained in the pionless EFT with scattering lengths treated exactly is shown to have a UV/IR symmetry which leaves the sum of s-wave phase shifts invariant. A new scheme, which treats effecti…
We show that processes involving pions that remain very near their mass-shell can be reliably computed in the pionless effective field theory, with the pion integrated in as a heavy field. As an application, we compute the pion-deuteron scattering amplitude near threshold to next-to-leading order in the momentum expansion. This amplitude is formally dominated by an infrared logarithm of the form log(gamma/mpi), where gamma is the deuteron binding momentum, and mpi is the mass of the pion. The coefficient of this logarithm is determined by the S-wave pion-nucleon scattering lengths.
We calculate the forward unpolarised doubly-virtual Compton scattering (VVCS) off the deuteron 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 unknown two-nucleon one-photon contact coupling that enters the longitudinal amplitude at N3LO. We also study the lowest spin-independent generalised polarisabilitie…
Thermal properties of low-density neutron matter are investigated by determinantal quantum Monte Carlo lattice calculations on 3+1 dimensional cubic lattices. Nuclear effective field theory (EFT) is applied using the pionless single- and two-parameter neutron-neutron interactions, determined from the $^1S_0$ scattering length and effective range. The determination of the interactions and the calculations of neutron matter are carried out consistently by applying EFT power counting rules. The thermodynamic limit is taken by the method of finite-size scaling, and the continuum limit is examined …
Nuclear electric dipole moments of $^{3}He$ and $^{3}H$ are calculated using Time Reversal Invariance Violating (TRIV) potentials based on the meson exchange theory, as well as the ones derived by using pionless and pionful effective field theories, with nuclear wave functions obtained by solving Faddeev equations in configuration space for the complete Hamiltonians comprising both TRIV and realistic strong interactions. The obtained results are compared with the previous calculations of $^{3}He$ EDM and with time reversal invariance violating effects in neutron-deuteron scattering.
A systematic description of low-energy observables in light nuclei is presented. The effective field theory formalism without pions is extended to: i) predictions with next-to-leading-order (non-perturbatively) accuracy for the 4-helium binding energy B(α), the triton charge radius, and the 3-helium-neutron scattering length; ii) phase shifts for neutron-deuteron scattering and α-neutron low-energy scattering at leading order; iii) the ground states of the 5-helium (with and without Coulomb interaction) and 6-helium isotopes up to next-to-leading order; The convergence from leading- to next-to…
We address the $Λ$-hypernuclear `overbinding problem' in light hypernuclei which stands for a 1--3 MeV excessive $Λ$ separation energy calculated in $_Λ^5$He. This problem arises in most few-body calculations that reproduce ground-state $Λ$ separation energies in the lighter $Λ$ hypernuclei within various hyperon-nucleon interaction models. Recent pionless effective field theory nuclear few-body calculations are extended in this work to $Λ$ hypernuclei. At leading order, the $ΛN$ low-energy constants are associated with $ΛN$ scattering lengths and the $ΛNN$ low-energy constants are fitted to $…
Weak interactions in two-nucleon system at low energies are explored in the framework of effective field theory. We review our recent calculations of parity-violating observables in radiative neutron capture on a proton at threshold where both pionful and pionless theories are employed.
In chiral effective field theory the leading order (LO) nucleon-nucleon potential includes two contact terms, in the two spin channels $S=0,1$, and the one-pion-exchange potential. When the pion degrees of freedom are integrated out, as in the pionless effective field theory, the LO potential includes two contact terms only. In the three-nucleon system, the pionless theory includes a three-nucleon contact term interaction at LO whereas the chiral effective theory does not. Accordingly arbitrary differences could be observed in the LO description of three- and four-nucleon binding energies. We …
Two-neutrino double-beta decay of certain nuclear isotopes is one of the rarest Standard Model processes observed in nature. Its neutrinoless counterpart is an exotic lepton-number nonconserving process that is widely searched for to determine if the neutrinos are Majorana fermions. In order to connect the rate of these processes to the Standard Model and beyond the Standard Model interactions, it is essential that the corresponding nuclear matrix elements are constrained reliably from theory. Lattice quantum chromodynamics (LQCD) and low-energy effective field theories (EFTs) are expected to …
Current models of inter-nucleon interactions are built within the frame of Effective Field Theories (EFTs). Contrary to traditional nuclear potentials, EFT interactions require a renormalization of their parameters in order to derive meaningful estimations of observable. In this paper, a renormalization procedure is designed in connection with many-body approximations applicable to large-A systems and formulated within the frame of many-body perturbation theory. The procedure is shown to generate counterterms that are independent of the targeted A-body sector. As an example, the procedure is a…
We study the $N_c$ scalings of pion-nucleon and nucleon-nucleon scatterings and find that a consistent large $N_c$ counting can be established if we assume Witten's counting rules are applied to matrix elements or scattering amplitudes which use the relativistic normalization for the nucleons. With the pionless effective field theory, we also find that the $S$-wave nucleon-nucleon interaction is so strong that it should be treated nonperturbatively at the leading order in the $1/N_c$ expansion. By summing all the leading order diagrams, we find that the deuteron binding energy is of order $1/N…
We provide a systematic assessment of the order-$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…
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.
We calculate the muon capture rate on the deuteron to next-to-next-to-leading order in the pionless effective field theory. The result can be used to constrain the two-nucleon isovector axial coupling L_{1,A} to +/- 2 fm^3 if the muon capture rate is measured to 2% level. From this, one can determine the neutrino-deuteron break up reactions and the pp-fusion cross section in the sun to a same level of accuracy.
I present an exact relationship between the electric dipole moment and anomalous magnetic moment of the nucleon in the light-front formalism of QCD and consider its consequences.
We study the triton and three-nucleon force at lowest chiral order in pionless effective field theory both in the Hamiltonian and Euclidean nuclear lattice formalism. In the case of the Euclidean lattice formalism, we derive the exact few-body worldline amplitudes corresponding to the standard many-body lattice action. This will be useful for setting low-energy coefficients in future nuclear lattice simulations. We work in the Wigner SU(4)-symmetric limit where the S-wave scattering lengths {1}S{0} and {3}S{1} are equal. By comparing with continuum results, we demonstrate for the first time th…
The electric dipole form factor of the nucleon stemming from the QCD $\barθ$ term is calculated in chiral perturbation theory in leading order. To this order, the form factor originates from the pion cloud. Its momentum-dependence 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.
A partial screening of nucleon electric dipole moments (EDMs) in nuclear systems, which is related to the Schiff mechanism known for neutral atomic systems, is discussed. It is shown that the direct contribution from the neutron EDM to the deuteron EDM is partially screened by about 1% in a zero-range approximation calculation.
Spin observables in radiative neutron capture on a proton and its inverse process, photodisintegration of the deuteron are calculated using a pionless effective field theory with di-baryon fields. Good agreement with the results of existing standard nuclear physics approach is obtained at very low energies. As energy increases, however, the discrepancy between the effective field theory and the standard nuclear physics approach becomes substantial. We discuss the origin of the difference.
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) θe fm. The momentum dependence of the isovector EDFF is proportional to a non-derivative time-reversal-violating pion-nucleon coupling, and the scale for mom…
The Cabibbo-Kobayashi-Maskawa matrix in the Standard Model is currently the only experimentally-confirmed source of CP-violation. The intrinsic electric dipole moment of the nucleon induced by this CP-phase via hadronic loop and pole diagrams has been studied more than two decades ago, but the existing calculation is subject to various theoretical issues such as the breakdown of chiral power counting and uncertainties in the determination of low energy constants. We carry out an up-to-date re-analysis on both one-loop and pole diagram contributions to the nucleon electric dipole moment based o…
The application of effective field theories to hadronic parity violation in two- and three-nucleon systems is described. These methods provide several important advantages over the traditionally used meson-exchange models, e.g., model independence and the possibility to reliably estimate theoretical errors. We focus on the so-called "pionless" theory and describe calculations of various two- and three-nucleon observables. The role of parity-violating three-nucleon interactions is also discussed.
Machine learning the single-$Λ$ hypernuclei with neural-network quantum states
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Institute of Modern Physics, Fudan University（复旦大学现代物理研究所核物理与离子束应用教育部重点实验室）；State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与技术国家重点实验室）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生部）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（上海理论核物理研究中心（国家自然科学基金委与复旦大学））
The nuclear physics relevant to the electric dipole moment (EDM) of the deuteron is addressed. The general operator structure of the $P$- and $T$-odd nucleon-nucleon interaction is discussed and applied to the two-body contributions of the deuteron EDM, which can be calculated in terms of $P$- and $T$-odd meson-nucleon coupling constants with only small model dependence. The one-body contributions, the EDMs of the proton and the neutron, are evaluated within the same framework. Although the total theoretical uncertainties are sizable, we conclude that, compared to the neutron, the deuteron EDM…
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 …
Nucleon Energy Correlators as a Probe of Light-Quark Dipole Operators at the Electron-Ion Collider
Central South University（中南大学）；University of Utah（犹他大学）；University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；South China Normal University（华南师范大学）
We compare the subtractive renormalization and the Wilsonian renormalization group approaches in the context of an effective field theory for the two-nucleon system. Based on an exactly solvable model of contact interactions, we observe that the standard Wilsonian renormalization group approach with a single cutoff parameter does not cover the whole space spanned by the renormalization scale parameters of the subtractive formalism. In particular, renormalization schemes corresponding to Weinberg's power counting in the case of an unnaturally large scattering length are beyond the region covere…
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.
The isovector time-reversal- and parity-violating pion-nucleon coupling $\bar{g}_π^{(1)}$ is uniquely sensitive to dimension six interactions between right-handed light quarks and the Standard Model Higgs doublet that naturally arises in left-right symmetric models. Recent work has used the $\bar{g}_π^{(1)}$-induced one-loop contribution to the neutron electric dipole moment $d_n$, together with the present experimental $d_n$ bound, to constrain the CP-violating parameters of the left-right symmetric model. We show that this and related analyses are based on an earlier meson theory $d_n$ compu…
