Isovector axial form factors of the nucleon in two-flavor lattice QCD

We present a lattice calculation of the nucleon isovector axial and induced pseudoscalar form factors on the CLS ensembles using [Formula: see text] dynamical flavors of nonperturbatively [Formula: see text]-improved Wilson fermions and an [Formula: see text]-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective field theory (EFT) including axial vector mesons. Our results indicate that careful treatment of excited-state effects is important in order to obtain reliable results for the axial form factors of the nucleon, and that the main remaining error stems from the systematic uncertainties of the chiral extrapolation. As final results, we quote [Formula: see text], [Formula: see text], and [Formula: see text] for the axial charge, axial charge radius and induced pseudoscalar charge, respectively, where the first error is statistical and the second is systematic.

Beta-spectrum shapes of forbidden β decays

The neutrinoless [Formula: see text] decay of atomic nuclei continues to attract fervent interest due to its potential to confirm the possible Majorana nature of the neutrino, and thus the nonconservation of the lepton number. At the same time, the direct dark matter experiments are looking for weakly interacting massive particles (WIMPs) through their scattering on nuclei. The neutrino-oscillation experiments on reactor antineutrinos base their analyses on speculations of [Formula: see text]-spectrum shapes of nuclear decays, thus leading to the notorious “reactor antineutrino anomaly.” In all these experimental efforts, one encounters the problem of [Formula: see text]-spectrum shapes of forbidden [Formula: see text] decays, either as unwanted backgrounds or unknown components in the analyses of data. In this work, the problem of spectrum shapes is discussed and illustrated with a set of selected examples. The relation of the [Formula: see text]-spectrum shapes to the problem of the effective value of the weak axial-vector coupling strength [Formula: see text] and the enhancement of the axial-charge matrix element is also pointed out.