Abstract: The study of pion production in nuclei is important for signal and background determinations in current and future neutrino oscillation experiments. The first step, however, is to understand the pion production reactions at the free nucleon level. We present an exhaustive study of the charged-current and neutral-current neutrino and antineutrino pion production off nucleons, paying special attention to the angular distributions of the outgoing pion. We show, using general arguments, that parity violation and time-reversal odd correlations in the weak differential cross sections are generated from the interference between different contributions to the hadronic current that are not relatively real. Next, we present a detailed comparison of three state-of-the-art, microscopic models for electroweak pion production off nucleons, and we also confront their predictions with polarized electron data, as a test of the vector content of these models. We also illustrate the importance of carrying out a comprehensive test at the level of outgoing pion angular distributions, going beyond comparisons done for partially integrated cross sections, where model differences cancel to a certain extent. Finally, we observe that all charged and neutral current distributions show sizable anisotropies, and identify channels for which parity-violating effects are clearly visible. Based on the above results, we conclude that the use of isotropic distributions for the pions in the center of mass of the final pion-nucleon system, as assumed by some of the Monte Carlo event generators, needs to be improved by incorporating the findings of microscopic calculations.

Abstract: We characterize preserved extreme points of the unit ball of Lipschitz-free spaces F (X) in terms of simple geometric conditions on the underlying metric space (X, d). Namely, the preserved extreme points are the elementary molecules corresponding to pairs of points p, q in X such that the triangle inequality d (p, q) <= d (p, r) + d (q, r) is uniformly strict for r away from p, q. For compact X, this condition reduces to the triangle inequality being strict. As a consequence, we give an affirmative answer to a conjecture of N. Weaver that compact spaces are concave if and only if they have no triple of metrically aligned points, and we show that all extreme points are preserved for several classes of compact metric spaces X, including Holder and countable compacta.

Abstract: The ordering of the neutrino masses is a crucial input for a deep understanding of flavor physics, and its determination may provide the key to establish the relationship among the lepton masses and mixings and their analogous properties in the quark sector. The extraction of the neutrino mass ordering is a data-driven field expected to evolve very rapidly in the next decade. In this review, we both analyse the present status and describe the physics of subsequent prospects. Firstly, the different current available tools to measure the neutrino mass ordering are described. Namely, reactor, long-baseline (accelerator and atmospheric) neutrino beams, laboratory searches for beta and neutrinoless double beta decays and observations of the cosmic background radiation and the large scale structure of the universe are carefully reviewed. Secondly, the results from an up-to-date comprehensive global fit are reported: the Bayesian analysis to the 2018 publicly available oscillation and cosmological data sets provides strong evidence for the normal neutrino mass ordering vs. the inverted scenario, with a significance of 3.5 standard deviations. This preference for the normal neutrino mass ordering is mostly due to neutrino oscillation measurements. Finally, we shall also emphasize the future perspectives for unveiling the neutrinomass ordering. In this regard, apart from describing the expectations from the aforementioned probes, we also focus on those arising from alternative and novel methods, as 21 cm cosmology, core-collapse supernova neutrinos and the direct detection of relic neutrinos.

Abstract: A measurement of Z -> tau(+)tau(-) production cross-section is presented using data, corresponding to an integrated luminosity of 2 fb(-1), from pp collisions at root s = 8 TeV collected by the LHCb experiment. The tau(+)tau(-)candidates are reconstructed in final states with the first tau lepton decaying leptonically, and the second decaying either leptonically or to one or three charged hadrons. The production cross-section is measured for Z bosons with invariant mass between 60 and 120 GeV/c(2), which decay to tau leptons with transverse momenta greater than 20 GeV/c and pseudorapidities between 2.0 and 4.5. The cross-section is determined to be sigma(pp -> Z -> tau+tau-)= 95.8 +/- 2.1 +/- 4.6 +/- 0.2 +/- 1.1 pb, where the first uncertainty is statistical, the second is systematic, the third is due to the LHC beam energy uncertainty, and the fourth to the integrated luminosity uncertainty. This result is compatible with NNLO Standard model predictions. The ratio of the cross-sections for Z -> tau(+)tau(- )to Z -> mu(+)mu(-) (Z -> e(+)e(-)), determined to be 1.01 +/- 0.05 (1.02 +/- 0.06), is consistent with the lepton-universality hypothesis in Z decays.

Abstract: A search is performed for a spin-0 boson, phi, produced in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV, using prompt phi -> mu(+)mu(-) decays and a data sample corresponding to an integrated luminosity of approximately 3.0 fb(-1) collected with the LHCb detector. No evidence is found for a signal in the mass range from 5.5 to 15 GeV. Upper limits are placed on the product of the production cross-section and the branching fraction into the dimuon final state. The limits are comparable to the best existing over most of the mass region considered and are the first to be set near the Upsilon resonances.