Martin M. Block, Loyal Durand, Phuoc Ha, Douglas W. McKay
We revisit arguments that the structure function $F_2^{\gamma p}(x, Q^2)$ for deep inelastic $\gamma^*p$ scattering is hadronic in nature, similar to vector dominance for real $\gamma p$ scattering. Thus, like all other known hadronic scattering, including $\gamma p$, the growth of $F_2^{\gamma p}(x,Q^2)$ is limited by the Froissart bound at high hadronic energies, giving a $\ln^2 (1/x)$ bound as Bjorken $x\rightarrow 0$. The same bound holds for the individual quark distributions that contribute to $F_2^{\gamma p}$. In earlier work, we presented a very accurate global fit to the combined HERA data based on a fit function which respects the Froissart bound at small $x$, and is equivalent in its $x$ dependence to the function used successfully to describe all high energy hadronic data. We discuss the extrapolation of the fit to the values of $x$ down to $x=10^{-14}$ encountered in the calculation of neutrino cross sections at energies up to $E_\nu=10^{17}$ GeV, an extrapolation of a factor of $\sim$3 beyond the HERA region in the natural variable $\ln(1/x)$. We show how the results can be used to derive the relevant quark distributions. These distributions do not satisfy the "wee parton" condition, that they all converge toward a common distribution $xq(x,Q^2)$ at small $x$ and large $Q^2$ which is just a multiple of $F_2^{\gamma p}$, but still give results for the dominant neutrino structure function $F_2^{\nu(\bar{\nu})}$ which differ only slightly from those obtained assuming that the wee parton limit holds.
View original:
http://arxiv.org/abs/1302.6119
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