Connection of the virtualγ*pcross section ofepdeep inelastic scattering to realγpscattering, and the implications forνNandeptotal cross sections

Abstract

We show that it is possible to fit all of the HERA DIS (deep inelastic scattering) data on $F_2^{\gamma p}$ at small values of Bjorken $x$, including the data at {\em very low} $Q^2$, using a new model for $F_2^{\gamma p}$ which both includes an asymptotic (high energy) part that satisfies a saturated Froissart bound behavior, with a vector-dominance like mass factor in the parameterization, and extends smoothly to $Q^2=0$. We require that the corresponding part of the virtual $\gamma^* p$ cross section match the known asymptotic part of the real $\gamma p$ cross section at $Q^2=0$, a cross section which is determined by strong interactions and asymptotically satisfies a saturated Froissart bound of the form $\alpha +\beta\ln s+\gamma\ln^2s$. Using this model for the asymptotic part of $F_2^{\gamma p}$ plus a known valence contribution, we fit the asymptotic high energy part of the HERA data with $x\le 0.1$ and $W\ge 25$ GeV; the fit is excellent. We find that the mass parameter in the fit lies in the region of the light vector mesons, somewhat above the $\rho$ meson mass, and is compatible with vector dominance. We use this fit to obtain accurate results for the high energy $ep$ and isoscalar $\nu N$ total cross sections. Both cross sections obey an analytic expression of the type $a +b \ln E +c \ln^2 E +d \ln^3 E$ at large energies $E$ of the incident particle, reflecting the fact that the underlying strong interaction parts of the $\gamma^*p$, $Z^*N$ and $W^*N$ cross sections satisfy the saturated Froissart bound. Since approximately 50% of the $\nu N$ center of mass (cms) energy is found in $W$---the cms energy of the strongly interacting intermediate vector boson-nucleon system---a study of ultra-high-energy neutrino-nucleon cross sections would allow us, for the first time, to explore {\em strong interactions at incredibly high energies}.