An update of muon capture on hydrogen

The successful precision measurement of the rate of muon capture on a proton by the MuCap Collaboration allows for a stringent test of the current theoretical understanding of this process. Chiral perturbation theory, which is a low-energy effective field theory that preserves the symmetries and the pattern of symmetry breaking in the underlying theory of QCD, offers a systematic framework for describing $\mu p$ capture and provides a basic test of QCD at the hadronic level. We describe how this effective theory with no free parameters reproduces the measured capture rate. A recent study has addressed new sources of uncertainties that were not considered in the previous works, and we review to what extent these uncertainties are now under control. Finally, the rationale for studying muon capture on the deuteron and some recent theoretical developments regarding this process are discussed.Comment: A mini-review article, 14 pages and 1 figur

The two-nucleon electromagnetic charge operator in chiral effective field theory (χ\chiEFT) up to one loop

The electromagnetic charge operator in a two-nucleon system is derived in chiral effective field theory ($\chi$EFT) up to order $e\, Q$ (or N4LO), where $Q$ denotes the low-momentum scale and $e$ is the electric charge. The specific form of the N3LO and N4LO corrections from, respectively, one-pion-exchange and two-pion-exchange depends on the off-the-energy-shell prescriptions adopted for the non-static terms in the corresponding potentials. We show that different prescriptions lead to unitarily equivalent potentials and accompanying charge operators. Thus, provided a consistent set is adopted, predictions for physical observables will remain unaffected by the non-uniqueness associated with these off-the-energy-shell effects.Comment: 16 pages, 10 figure

Neutrinoless double beta decay matrix elements in light nuclei

We present the first ab initio calculations of neutrinoless double beta decay matrix elements in $A=6$-$12$ nuclei using Variational Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon potential and Illinois-7 three-nucleon interaction. We study both light Majorana neutrino exchange and potentials arising from a large class of multi-TeV mechanisms of lepton number violation. Our results provide benchmarks to be used in testing many-body methods that can be extended to the heavy nuclei of experimental interest. In light nuclei we have also studied the impact of two-body short range correlations and the use of different forms for the transition operators, such as those corresponding to different orders in chiral effective theory.Comment: 15 pages, 6 figure

Quantum Monte Carlo calculations of weak transitions in A A\,= \,6--10 nuclei

Ab initio calculations of the Gamow-Teller (GT) matrix elements in the $\beta$ decays of $^6$He and $^{10}$C and electron captures in $^7$Be are carried out using both variational and Green's function Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon interactions, and axial many-body currents derived from either meson-exchange phenomenology or chiral effective field theory. The agreement with experimental data is excellent for the electron captures in $^7$Be, while theory overestimates the $^6$He and $^{10}$C data by $\sim 2\%$ and $\sim 10\%$, respectively. We show that for these systems correlations in the nuclear wave functions are crucial to explain the data, while many-body currents increase by $\sim 2$--$3\%$ the one-body GT contributions. These findings suggest that the longstanding $g_A$-problem, i.e., the systematic overprediction ($\sim 20 \%$ in $A\le 18$ nuclei) of GT matrix elements in shell-model calculations, may be resolved, at least partially, by correlation effects.Comment: 6 pages, 2 figure

Electromagnetic processes in a χ\chiEFT framework

Recently, we have derived a two--nucleon potential and consistent nuclear electromagnetic currents in chiral effective field theory with pions and nucleons as explicit degrees of freedom. The calculation of the currents has been carried out to include N$^3$LO corrections, consisting of two--pion exchange and contact contributions. The latter involve unknown low-energy constants (LECs), some of which have been fixed by fitting the $np$ S- and P-wave phase shifts up to 100 MeV lab energies. The remaining LECs entering the current operator are determined so as to reproduce the experimental deuteron and trinucleon magnetic moments, as well as the $np$ cross section. This electromagnetic current operator is utilized to study the $nd$ and $n^3$He radiative captures at thermal neutron energies. Here we discuss our results stressing on the important role played by the LECs in reproducing the experimental data.Comment: Invited talk at the 5th International Conference on Quarks and Nuclear Physics, to appear in Chinese Physics