Tuesday, February 26, 2013

1302.6127 (Martin M. Block et al.)

Implications of a Froissart bound saturation of $γ^*$-$p$ deep
inelastic scattering. Part II. Ultra-high energy neutrino interactions
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Martin M. Block, Loyal Durand, Phuoc Ha, Douglas W. McKay
We extend the results showed in Part I of our paper, and use them to evaluate ultra-high energy (UHE) cross sections for neutrino scattering on an isoscalar nucleon, $N=(n+p)/2$, up to neutrino energies $E_\nu \sim 10^{16}$-$10^{17}$ GeV where there are now limits on neutrino fluxes. The contribution of $F_2^{\nu(\bar{\nu})}$ is strongly dominant in the $\nu$--$N$ cross sections, but we also include the contributions from the remaining structure functions $xF_3^{\nu(\bar{\nu})}(x,Q^2)$ and $F_L^{\nu(\bar{\nu})}(x,Q^2)$, evaluated from $F_2^{\gamma p}$ with NLO corrections. We estimate that our calculated charged current and neutral current neutrino cross sections are accurate to $\sim$2% at the highest energies considered ($E_\nu=10^{17}$ GeV), with the major uncertainty coming from the errors in the parameters that were needed to fit $F_2^{\gamma p}(x,Q^2)$ as measured at HERA. We compare our results to recently published neutrino cross sections derived from NLO parton distribution functions, which are very much larger than our cross sections at high energies because of the use of power-law extrapolations of quark distributions to small $x$. We conclude that our calculation of the UHE $\nu$--$N$ cross sections is the best one can make, given the existing experimental deep inelastic scattering data. Further, the strong interaction Froissart bound of $\ln^2 (1/x)$ translates into a weak cross section bound of $\ln^3E_\nu$ for $\nu -N$ scattering, where $E_\nu$ is the laboratory neutrino energy. Thus, the energy dependence of $\nu-N$ total cross section measurements have important implications for understanding hadronic interactions at enormous cms (center-of-mass) hadron-nucleon energies not otherwise accessible.
View original: http://arxiv.org/abs/1302.6127

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