Abstract: The next to leading order chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes- Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, delta(pi), the value delta(pi) = (6.2 +/- 1.6)%. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate < 0 vertical bar(u) over baru vertical bar 0 > similar or equal to < 0 vertical bar(d) over bard vertical bar 0 > < 0 vertical bar(q) over barq vertical bar 0 >vertical bar(2GeV) = (-267 +/- 5MeV)(3). As a byproduct, the chiral perturbation theory (unphysical) low energy constant H-2(r) is predicted to be H-2(r)(nu(X) = M-p) = -(5.1 +/- 1.8) x10(-3), or H-2(r) (nu(X) = M-eta) = -(5.7 +/- 2.0) x10(-3).

Abstract: As a result of a new improved fit to old bubble chamber data of the dominant axial C-5(A) nucleon-to-delta form factor, and due to the relevance of this form factor for neutrino induced coherent pion production, we reevaluate our model predictions in [Phys. Rev. D 79, 013002 ( 2009)] for different observables of the latter reaction. Central values for the total cross sections increase by 20%-30%, while differential cross sections do not change their shape appreciably. Furthermore, we also compute the uncertainties on total, differential, and flux-averaged cross sections induced by the errors in the determination of C-5(A). Our new results turn out to be compatible within about 1 sigma with the former ones. Finally, we stress the existing tension between the recent experimental determination of the sigma(CCcoh pi(+))/sigma(NCcoh pi(0)) ratio by the SciBooNE Collaboration and the theoretical predictions.

Abstract: The KamLAND and Borexino experiments have detected electron antineutrinos produced in the decay chains of natural thorium and uranium (Th and U geoneutrinos). We analyze the energy spectra of current geoneutrino data in combination with solar and long-baseline reactor neutrino data, with marginalized three-neutrino oscillation parameters. We consider the case with unconstrained Th and U event rates in KamLAND and Borexino, as well as cases with fewer degrees of freedom, as obtained by successively assuming for both experiments a common Th/U ratio, a common scaling of Th + U event rates, and a chondritic Th/U value. In combination, KamLAND and Borexino can reject the null hypothesis (no geoneutrino signal) at 5 sigma. Interesting bounds or indications emerge on the Th + U geoneutrino rates and on the Th/U ratio, in broad agreement with typical Earth model expectations. Conversely, the results disfavor the hypothesis of a georeactor in the Earth's core, if its power exceeds a few TW. The interplay of KamLAND and Borexino geoneutrino data is highlighted.