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Register a new userElectric dipole moments of three-nucleon systems in the pionless effective field theory
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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.
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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({alpha}), the triton charge radius, and the 3-helium-neutron scattering length; ii) phase shifts for neutron-deuteron scattering and {alpha}-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-leading order of the theory is demonstrated for correlations between: i) the triton binding energy B(t) and the triton charge radius; ii) B(t) and the 4-helium binding energy B({alpha}); Furthermore, a correlation between B(t) and the scattering length in the singlet S-wave channel of neutron-helium-3 scattering is discovered, and a model-independent estimate for the trinucleon binding energy splitting is provided. The results provide evidence for the usefulness of the applied power-counting scheme, treating next-to-leading-order interactions nonperturbatively and four-nucleon interactions as, at least, one order higher. The 5- and 6-helium ground states are analyzed with a power-counting scheme which includes the momentum-dependent next-to-leading order vertices perturbatively. All calculations include a full treatment of the Coulomb interaction. The assessment of numerical uncertainties associated with the solution of the few-body equation of motion through the Resonating Group Method parallels the report of the results for light nuclei in order to establish this method as practical for the analysis of systems with up to six particles interacting via short-range interactions.
A nonzero electric dipole moment (EDM) of the neutron, proton, deuteron or helion, in fact, of any finite system necessarily involves the breaking of a symmetry, either by the presence of external fields (i.e. electric fields leading to the case of induced EDMs) or explicitly by the breaking of the discrete parity and time-reflection symmetries in the case of permanent EDMs. We discuss two theorems describing these phenomena and report about the cosmological motivation for an existence of CP breaking beyond what is generated by the Kobayashi-Maskawa mechanism in the Standard Model and what this might imply for the permanent electric dipole moments of the nucleon and light nuclei by estimating a window of opportunity for physics beyond what is currently known. Recent - and in the case of the deuteron even unpublished - results for the relevant matrix elements of nuclear EDM operators are presented and the relevance for disentangling underlying New Physics sources are discussed.
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.
Pionless effective field theory in a finite volume (FVEFT$_{pi!/}$) is investigated as a framework for the analysis of multi-nucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT$_{pi!/}$ with the stochastic variational method, the spectra of nuclei with atomic number $Ain{2,3}$ are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass $m_pi=806$ MeV, thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wavefunctions that are constructed in this approach, the finite-volume matrix elements of various local operators are computed in FVEFT$_{pi!/}$ and matched to LQCD calculations of the corresponding QCD operators in the same volume, thereby determining the relevant one and two-body EFT counterterms and enabling an extrapolation of the LQCD matrix elements to infinite volume. As examples, the scalar, tensor, and axial matrix elements are considered, as well as the magnetic moments and the isovector longitudinal momentum fraction.
We perform a model-independent analysis of the magnetic and electric dipole moments of the muon and electron. We give expressions for the dipole moments in terms of operator coefficients of the low-energy effective field theory (LEFT) and the Standard Model effective field theory (SMEFT). We use one-loop renormalization group improved perturbation theory, including the one-loop matching from SMEFT onto LEFT, and one-loop lepton matrix elements of the effective-theory operators. Semileptonic four-fermion operators involving light quarks give sizable non-perturbative contributions to the dipole moments, which are included in our analysis. We find that only a very limited set of the SMEFT operators is able to generate the current deviation of the magnetic moment of the muon from its Standard Model expectation.
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