Abstract: We study the appearance of structures in the decay of the B- into K-pi D--(s0)+ (2317) and K-pi D--(s1)+ (2460) final states by forming invariant mass distributions of pi D--(s0)+ and pi D--(s1)+ pairs, respectively. The structure in the distribution is associated to the kinematical triangle singularity that appears when the B- -> K- K*(0) D-0 (B- -> K- K*(0) D*(0)) decay process is followed by the decay of the K*(0) into pi(-) K+ and the subsequent rescattering of the K+ D-0 (K+ D*(0)) pair forming the D-s0(+) (2317) (D-s1(+) (2460)) resonance. We find this type of non-resonant peaks at 2850MeV in the invariant mass of pi D--(s0) pairs from B- -> K- pi(-) D-s0(+) (2317) decays and around 3000MeV in the invariant mass of pi D--(s1)+ pairs from B- -> K- pi(-) D-s1(+)(2460) decays. By employing the measured branching ratios of the B- -> K- K*(0) D-0 and B- -> K- K*(0) D*(0) decays, we predict the branching ratios for the processes B- into K-pi D--(s0)+ (2317) K-pi D--(s1)+ (2460), in the vicinity of the triangle singularity peak, to be about 8 x 10(-6) and 1 x 10(-6), respectively. The observation of this reaction would also give extra support to the molecular picture of the D-s0(+)(2317) and D-s1(+)(2460).

Abstract: Analyses of the pion valence-quark distribution function (DF), u(pi) (x; sigma), which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict u(pi) (x similar or equal to 1; sigma) similar to (1 – x)(beta(sigma)), beta(sigma greater than or similar to m(p)) > 2, where mp is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the x similar or equal to 1 behaviour of up, the empirical status remains uncertain because some methods used to fit existing data return a result for up that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz. there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated.

Abstract: We present a full Bayesian analysis of the combination of current neutrino oscillation, neutrinoless double beta decay and Cosmic Microwave Background observations. Our major goal is to carefully investigate the possibility to single out one neutrino mass ordering, namely Normal Ordering or Inverted Ordering, with current data. Two possible parametrizations (three neutrino masses versus the lightest neutrino mass plus the two oscillation mass splittings) and priors (linear versus logarithmic) are exhaustively examined. We find that the preference for NO is only driven by neutrino oscillation data. Moreover, the values of the Bayes factor indicate that the evidence for NO is strong only when the scan is performed over the three neutrino masses with logarithmic priors; for every other combination of parameterization and prior, the preference for NO is only weak. As a by-product of our Bayesian analyses, we are able to (a) compare the Bayesian bounds on the neutrino mixing parameters to those obtained by means of frequentist approaches, finding a very good agreement; (b) determine that the lightest neutrino mass plus the two mass splittings parametrization, motivated by the physical observables, is strongly preferred over the three neutrino mass eigenstates scan and (c) find that logarithmic priors guarantee a weakly-to-moderately more efficient sampling of the parameter space. These results establish the optimal strategy to successfully explore the neutrino parameter space, based on the use of the oscillation mass splittings and a logarithmic prior on the lightest neutrino mass, when combining neutrino oscillation data with cosmology and neutrinoless double beta decay. We also show that the limits on the total neutrino mass Sigma m(nu) can change dramatically when moving from one prior to the other. These results have profound implications for future studies on the neutrino mass ordering, as they crucially state the need for self-consistent analyses which explore the best parametrization and priors, without combining results that involve different assumptions.