We derive the evolution equations for a system of neutrinos interacting among themselves and with a matter background, based upon the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. This theoretical framework gives an (unclosed) set of first-order coupled integro-differential equations governing the evolution of the reduced density matrices. By employing the hierarchy, we first rederive the mean-field evolution equations for the neutrino one-body density matrix associated with a system of neutrinos and antineutrinos interacting with matter and with an anisotropic neutrino background. Then, we derive extended evolution equations to determine neutrino flavor conversion beyond the commonly used mean-field approximation. To this aim we include neutrino-antineutrino pairing correlations to the two-body density matrix. The inclusion of these new contributions leads to an extended evolution equation for the normal neutrino density and to an equation for the abnormal one involving the pairing mean-field. We discuss the possible impact of neutrino-antineutrino correlations on neutrino flavor conversion in the astrophysical and cosmological environments, and possibly upon the supernova dynamics. Our results can be easily generalized to an arbitrary number of neutrino families.

We present TeV gamma-ray observations of the Crab Nebula, the standard reference source in ground-based gamma-ray astronomy, using data from the High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory. In this analysis we use two independent energy estimation methods that utilize extensive air shower variables such as the core position, shower angle, and shower lateral energy distribution. In contrast, the previously published HAWC energy spectrum roughly estimated the shower energy with only the number of photomultipliers triggered. This new methodology yields a much-improved energy resolution over the previous analysis and extends HAWC’s ability to accurately measure gamma-ray energies well beyond 100 TeV. The energy spectrum of the Crab Nebula is well fit to a log-parabola shape with emission up to at least 100 TeV. For the first estimator, a ground parameter that utilizes fits to the lateral distribution function to measure the charge density 40 m from the shower axis, the best-fit values are (TeV cm2 s)−1, , and . For the second estimator, a neural network that uses the charge distribution in annuli around the core and other variables, these values are (TeV cm2 s)−1, , and β = 0.06 ± 0.01 ± 0.02. The first set of uncertainties is statistical; the second set is systematic. Both methods yield compatible results. These measurements are the highest-energy observation of a gamma-ray source to date.

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We present a new catalog of TeV gamma-ray sources using 1523 days of data from the High-Altitude Water Cherenkov (HAWC) Observatory. The catalog represents the most sensitive survey of the northern gamma-ray sky at energies above several TeV, with three times the exposure compared to the previous HAWC catalog, 2HWC. We report 65 sources detected at ≥5σ significance, along with the positions and spectral fits for each source. The catalog contains eight sources that have no counterpart in the 2HWC catalog, but are within 1° of previously detected TeV emitters, and 20 sources that are more than 1° away from any previously detected TeV source. Of these 20 new sources, 14 have a potential counterpart in the fourth Fermi Large Area Telescope catalog of gamma-ray sources. We also explore potential associations of 3HWC sources with pulsars in the Australia Telescope National Facility (ATNF) pulsar catalog and supernova remnants in the Galactic supernova remnant catalog.

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