Long-range forces between macroscopic objects are mediated by light particles that interact with the electrons or nucleons, and include spin-dependent static components as well as spin-and velocity-dependent components. We parametrize the long-range potential between two fermions assuming rota-

During 2004, four divisions of the American Physical Society commissioned a study of neutrino physics to take stock of where the field is at the moment and where it is going in the near and far future. Several working groups looked at various aspects of this vast field. The summary was published as a main report entitled "The Neutrino Matrix" accompanied by short 50 page versions of the report of each working group. Theoretical research in this field has been quite extensive and touches many areas and the short 50 page report [1] provided only a brief summary and overview of few of the important points. The theory discussion group felt that it may be of value to the community to publish the entire study as a white paper and the result is the current article. After a brief overview of the present knowledge of neutrino masses and mixing and some popular ways to probe the new physics implied by recent data, the white paper summarizes what can be learned about physics beyond the Standard Model from the various proposed neutrino experiments. It also comments on the impact of the experiments on our understanding of the origin of the matter-antimatter asymmetry of the Universe and the basic nature of neutrino interactions as well as the existence of possible additional neutrinos. Extensive references to original literature are provided.2

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The ProtoDUNE-SP detector is a single-phase liquid argon time projection chamber with an active volume of 7.2× 6.1× 7.0 m3. It is installed at the CERN Neutrino Platform in a specially-constructed beam that delivers charged pions, kaons, protons, muons and electrons with momenta in the range 0.3 GeV/c to 7 GeV/c. Beam line instrumentation provides accurate momentum measurements and particle identification. The ProtoDUNE-SP detector is a prototype for the first far detector module of the Deep Underground Neutrino Experiment, and it incorporates full-size components as designed for that module. This paper describes the beam line, the time projection chamber, the photon detectors, the cosmic-ray tagger, the signal processing and particle reconstruction. It presents the first results on ProtoDUNE-SP's performance, including noise and gain measurements, dE/dx calibration for muons, protons, pions and electrons, drift electron lifetime measurements, and photon detector noise, signal sensitivity and time resolution measurements. The measured values meet or exceed the specifications for the DUNE far detector, in several cases by large margins. ProtoDUNE-SP's successful operation starting in 2018 and its production of large samples of high-quality data demonstrate the effectiveness of the single-phase far detector design.

We show that a sterile neutrino with a mass in the 1-20 keV range and a small mixing with the electron neutrino can simultaneously explain the origin of the pulsar motions and the dark matter in the Universe. An asymmetric neutrino emission from a hot nascent neutron star can be the explanation of the observed pulsar velocities. In addition to the pulsar kick mechanism based on resonant neutrino transitions, we point out a new possibility: an asymmetric off-resonant emission of sterile neutrinos. The two cases correspond to different values of the masses and mixing angles. In both cases we identify the ranges of parameters consistent with the pulsar kick, as well as cosmological constraints.