The objectives of the present work are twofold. The first is to address and resolve some of the differences present in independent, chiral-effective-field-theory (χEFT) derivations up to one loop, recently appeared in the literature, of the nuclear charge and current operators. The second objective is to provide a complete set of χEFT predictions for the structure functions and tensor polarization of the deuteron, for the charge and magnetic form factors of 3 He and 3 H, and for the charge and magnetic radii of these few-nucleon systems. The calculations use wave functions derived from high-order chiral two-and three-nucleon potentials and Monte Carlo methods to evaluate the relevant matrix elements. Predictions based on conventional potentials in combination with χEFT charge and current operators are also presented. There is excellent agreement between theory and experiment for all these observables for momentum transfers up to q 2.0-2.5 fm −1 ; for a subset of them, this agreement extends to momentum transfers as high as q ≃ 5-6 fm −1 . A complete analysis of the results is provided.

We construct a coordinate-space chiral potential, including ∆-isobar intermediate states in its two-pion-exchange component up to order Q 3 (Q denotes generically the low momentum scale). The contact interactions entering at next-to-leading and next-to-next-to-next-to-leading orders (Q 2 and Q 4 , respectively) are rearranged by Fierz transformations to yield terms at most quadratic in the relative momentum operator of the two nucleons. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database, consisting of 2309 pp and 2982 np data (including, respectively, 148 and 218 normalizations) in the laboratory-energy range 0-300 MeV. For the total 5291 pp and np data in this range, we obtain a χ 2 /datum of roughly 1.3 for a set of three models characterized by long-and short-range cutoffs, RL and RS respectively, ranging from (RL, RS) = (1.2, 0.8) fm down to (0.8, 0.6) fm. The long-range (short-range) cutoff regularizes the one-and two-pion exchange (contact) part of the potential.

We present fully local versions of the minimally non-local nucleon-nucleon potentials constructed in a previous paper [M. Piarulli et al., Phys. Rev. C 91, 024003 (2015)], and use them in hypersperical-harmonics and quantum Monte Carlo calculations of ground and excited states of 3 H, 3 He, 4 He, 6 He, and 6 Li nuclei. The long-range part of these local potentials includes oneand two-pion exchange contributions without and with ∆-isobars in the intermediate states up to order Q 3 (Q denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order Q 4 . The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0-125 MeV or 0-200 MeV, and to the deuteron binding energy and nn singlet scattering length. Fits to these data are performed for three models characterized by long-and short-range cutoffs, R L and R S respectively, ranging from (R L , R S ) = (1.2, 0.8) fm down to (0.8, 0.6) fm. The long-range (short-range) cutoff regularizes the one-and two-pion exchange (contact) part of the potential.

No abstract

The process at the heart of neutrinoless double-beta decay, nn → pp e − e − induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-numberviolating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet S-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-beta decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leadingorder short-range operator, but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-beta decay for 6 He and 12 Be. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.

The muon capture reactions 2 H(µ − , νµ)nn and 3 He(µ − , νµ) 3 H are studied with conventional or chiral realistic potentials and consistent weak currents. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v18 or chiral N3LO two-nucleon potential, in combination with, respectively, the Urbana IX or chiral N2LO three-nucleon potential in the case of A = 3. The weak current consists of polar-and axial-vector components. The former are related to the isovector piece of the electromagnetic current via the conserved-vector-current hypothesis. These and the axial currents are derived either in a meson-exchange or in a chiral effective field theory (χEFT) framework. There is one parameter (either the N -to-∆ axial coupling constant in the meson-exchange model, or the strength of a contact term in the χEFT model) which is fixed by reproducing the Gamow-Teller matrix element in tritium β-decay. The model dependence relative to the adopted interactions and currents (and cutoff sensitivity in the χEFT currents) is weak, resulting in total rates of 392.0 ± 2.3 s −1 for A = 2, and 1484 ± 13 s −1 for A = 3, where the spread accounts for this model dependence.

The Gamow-Teller (GT) matrix element contributing to tritium β decay is calculated with trinucleon wave functions obtained from hyperspherical-harmonics solutions of the Schrödinger equation with the chiral two-and three-nucleon interactions including ∆ intermediate states that have recently been constructed in configuration space. Predictions up to N3LO in the chiral expansion of the axial current (with ∆'s) overestimate the empirical value by 1-4 %. By exploiting the relation between the low-energy constant (LEC) in the contact three-nucleon interaction and two-body axial current, we provide new determinations of the LECs cD and cE that characterize this interaction by fitting the trinucleon binding energy and tritium GT matrix element. Some of the implications that the resulting models of three-nucleon interactions have on the spectra of light nuclei and the equation of state of neutron matter are briefly discussed. We also provide a partial analysis, which ignores ∆'s, of the contributions due to loop corrections in the axial current at N4LO. Finally, explicit expressions for the axial current up to N4LO have been derived in configuration space, which other researchers in the field may find useful.

Abstract. Experimental form factors of the hydrogen and helium isotopes, extracted from an up-to-date global analysis of cross sections and polarization observables measured in elastic electron scattering from these systems, are compared to predictions obtained in three different theoretical approaches: the first is based on realistic interactions and currents, including relativistic corrections (labeled as the conventional approach); the second relies on a chiral effective field theory description of the strong and electromagnetic interactions in nuclei (labeled χEFT); the third utilizes a fully relativistic treatment of nuclear dynamics as implemented in the covariant spectator theory (labeled CST). For momentum transfers below Q 5 fm −1 there is satisfactory agreement between experimental data and theoretical results in all three approaches. However, at Q 5 fm −1 , particularly in the case of the deuteron, a relativistic treatment of the dynamics, as is done in the CST, is necessary. The experimental data on the deuteron A structure function extend to Q ≃ 12 fm −1 , and the close agreement between these data and the CST results suggests that, even in this extreme kinematical regime, there is no evidence for new effects coming from quark and gluon degrees of freedom at short distances.