Aspirations set much higher to energies above 1015 ev

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Unformatted text preview: A) (Achterberg et al., 2007), IceCube (de los Heros, 2011), Radio Ice Cerenkov Experiment (RICE) (Kravchenko et al., 2003), Fast On-orbit Recording of Transient Events (FORTE) (Lehtinen et al., 2004), ANITA (Barwick et al., 2006)], the Earth’s atmosphere [Pierre Auger (Abraham et al., 2008), HiRes (Abbasi et al., 2004)], and the lunar regolith [Goldstone Lunar Ultra-High Energy experiment (GLUE) (Gorham et al., 2004)]. Even more future programs are in the planning stages. As such, the knowledge of neutrino cross section in this high-energy region is becoming ever increasing in importance. Once first detection is firmly established, the emphasis is likely to shift toward obtaining more detailed information about the observed astrophysical objects, and thus the neutrino fluxes will need to be examined in much greater detail. The neutrino cross sections in this energy range12 are essentially extensions of the high-energy parton model discussed in Sec. VI. However, at these energies, the propagation term from the interaction vertex is no longer dominated by the W-Z boson mass. As a result, the cross section no longer grows linearly with neutrino energy. The propagator term in fact suppresses the cross sections for energies above 10 TeV. Likewise, the ð1 À yÞ2 suppression that typically allows distinction between neutrino and antineutrino interactions is much less pronounced, making the two cross sections (N and N ) nearly identical. " For a rough estimate of the neutrino cross section at these high energies (1016 E 1021 eV), the following power Typically, the high-energy region is demarcated by E ! 106 GeV. 12 1336 Joseph A. Formaggio and G. P. Zeller: From eV to EeV: Neutrino cross sections . . . law dependence provides a reasonable approximation (Gandhi et al., 1996):   E CC ¼ 5:53 Â 10À36 cm2 ; (90) N 1 GeV NC ¼ 2:31 Â 10À36 cm2 N  E 1 GeV  ; (91) where ’ 0:363. There is one peculiar oddity that is worth highlighting for neutrino cross sections at such high energies. Neutrino- electron scattering is usually subdominant to any neutrinonucleus interaction because of its small target mass. There is one notable exception, however when the neutrino undergoes a resonant enhancement from the formation of an intermediate W boson in e eÀ interactions. This resonance formation " 2 takes place at Eres ¼ MW =2me ¼ 6:3 PeV and is by far more prominent than any N interaction up to 1021 eV (see Fig. 29). The mechanism was first suggested by Glashow in 1960 as a means to directly detect the W boson (Glashow, 1960). The cross section was later generalized by Berezinsky and Gazizov (1977) to other possible channels: 2   dðe eÀ ! e eÀ Þ 2G2 me E " " g2 gL 1 F R ¼ þ 1 þ 2m E y=M2 þ 1 À 2m E =M2 þ iÀ =M ; 2 dy  ð1 þ 2me E y=MZ Þ2 e e W W Z W where gL;R are the left- and right-handed fermion couplings, MW is the W -boson mass, and ÀW is the W -decay width ($ 2:08 GeV). This resonance occurs...
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