ULTRAHIGH ENERGY NEUTRINOS, SMALL X AND UNITARITY. Page: 1 of 5
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Ultrahigh energy neutrinos, small x and unitarity
Mary Hall Reno*
Department of Physics and Astronomy, University of Iowa, Iowa City, IA 52242 USA
Department of Physics, University of Arizona, Tucson, AZ 85721 USA
C. N. Yang Institute for Theoretical Physics, SUNY Stony Brook, Stony Brook, NY 11794 USA
Institut fir Theoretische Physik, Universit&t Regensburg, D-93040 Regensburg, Germany
Physics Department and RIKEN-BNL Research Center,
(Ni Brookhaven National Laboratory, Upton, NY 11973 USA
0 The ultrahigh energy cross section for neutrino interactions with nucleons is reviewed, and uni-
tarity constraints are discussed. We argue that existing QCD extrapolations are self-consistent, and
do not imply a breakdown of the perturbative expansion in the weak coupling.
'n Ultrahigh energy neutrinos are predicted from a number of sources. One source is from cosmic ray interactions
(KI with the microwave background radiation , producing charged pions which decay into neutrinos. Another
O possible source is decaying cosmic strings or extremely massive relics , which ultimately contribute to a cosmic
r"" neutrino flux. Detection of ultrahigh energy neutrinos may shed light on the observation of air shower events
with energies in excess of 1011 GeV, reveal aspects of grand unification or yield some insight into the sources of
the highest energy cosmic rays.
,- A number of detectors are able or will be able to detect neutrino induced showers. For example, the Auger
+ experiment should be able to detect neutrino induced horizontal air showers initiated by neutrinos with energies
above 10" GeV. The proposed OWL/EUSO satellite experiments should be able to detect upward air showers
I.) produced by v.T - r just below the Earth's surface. The event rates predictions depend on the ultrahigh energy
- neutrino cross section, extrapolated beyond the measured regime, as well as on the predicted neutrino fluxes.
Recent discussions by Dicus, Kretzer, Repko, and Schmidt  about the implications of perturbative unitarity
have refocused attention on the ultrahigh energy extrapolation of the neutrino-nucleon cross section. In the next
section we review the cross section evaluation including the extrapolation of the parton distribution function
to small parton momentum fraction x. We examine to what extent the cross section may be sensitive to the
presence of saturation effects in the evolution of the parton distributions. In the following section, we outline the
unitarity argument and comment on what can and cannot be learned by relating the neutrino-nucleon forward
scattering amplitude to the total neutrino-nucleon cross section.
II. NEUTRINO-NUCLEON CROSS SECTION
The expression for the neutrino-nucleon charged current cross section, for v,(k)N(p) - l(k')X(p'), is
__ _JI. -
dxdQ2 - a -2+ Ai - [9(',I) +(1 - y) 9(x, Q)] ,(1)
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Hall Reno, M.; Sarcevic, I. N.; Sterman, G.; Stratmann, M. & Vogelsang, W. ULTRAHIGH ENERGY NEUTRINOS, SMALL X AND UNITARITY., article, June 30, 2001; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc742880/m1/1/: accessed January 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.