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Neutrinos in the cosmic ray flux with energies near 1 EeV and above are detectable with the Surface Detector array of the Pierre Auger Observatory. We report here on searches through Auger data from 1 January 2004 until 20 June 2013. No neutrino cand idates were found, yielding a limit to the diffuse flux of ultra-high energy neutrinos that challenges the Waxman-Bahcall bound predictions. Neutrino identification is attempted using the broad time-structure of the signals expected in the SD stations, and is efficiently done for neutrinos of all flavors interacting in the atmosphere at large zenith angles, as well as for Earth-skimming neutrino interactions in the case of tau neutrinos. In this paper the searches for downward-going neutrinos in the zenith angle bins $60^circ-75^circ$ and $75^circ-90^circ$ as well as for upward-going neutrinos, are combined to give a single limit. The $90%$ C.L. single-flavor limit to the diffuse flux of ultra-high energy neutrinos with an $E^{-2}$ spectrum in the energy range $1.0 times 10^{17}$ eV - $2.5 times 10^{19}$ eV is $E_ u^2 dN_ u/dE_ u < 6.4 times 10^{-9}~ {rm GeV~ cm^{-2}~ s^{-1}~ sr^{-1}}$.
We argue that the increase of the ratio baryon/meson due to the presence of strong colour fields and percolation in ultra-high energy hadronic collisions, helps to explain some of the global features of ultra-high energy cosmic ray cascades at E>10^1 8 eV and, in particular the observed excess in the number of muons with respect to current models of hadronic interactions. A reasonable agreement with the small value and slope of the average depth of shower maximum Xmax vs shower energy -- as seen in data collected at the Pierre Auger Observatory -- can be obtained with a fast increase of the p-Air production cross-section compatible with the Froissart bound.
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