Title: Connection of the virtual<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:mi>p</mml:mi></mml:mrow></mml:math>cross section of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>e</mml:mi><mml:mi>p</mml:mi></mml:math>deep inelastic scattering to real<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi…
Abstract: We show that it is possible to fit all of the HERA deep inelastic scattering data on ${F}_{2}^{\ensuremath{\gamma}p}$ at small values of Bjorken $x$, including the data at very low ${Q}^{2}$, using a new model for ${F}_{2}^{\ensuremath{\gamma}p}$ which both includes an asymptotic (high-energy) part that satisfies a saturated Froissart bound behavior, with a vector-dominance-like mass factor in the parametrization, and extends smoothly to ${Q}^{2}=0$. We require that the corresponding part of the virtual ${\ensuremath{\gamma}}^{*}p$ cross section match the known asymptotic part of the real $\ensuremath{\gamma}p$ 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 $\ensuremath{\alpha}+\ensuremath{\beta}\mathrm{ln}s+\ensuremath{\gamma}{\mathrm{ln}}^{2}s$. Using this model for the asymptotic part of ${F}_{2}^{\ensuremath{\gamma}p}$ plus a known valence contribution, we fit the asymptotic high--energy part of the HERA data with $x\ensuremath{\le}0.1$ and $W\ensuremath{\ge}25\text{ }\text{ }\mathrm{GeV}$; 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 $\ensuremath{\rho}$-meson mass, and is compatible with vector dominance. We use this fit to obtain accurate results for the high-energy $ep$ and isoscalar $\ensuremath{\nu}N$ total cross sections. Both cross sections obey an analytic expression of the type $a+b\mathrm{ln}E+c{\mathrm{ln}}^{2}E+d{\mathrm{ln}}^{3}E$ at large energies $E$ of the incident particle, reflecting the fact that the underlying strong interaction parts of the ${\ensuremath{\gamma}}^{*}p$, ${Z}^{*}N$ and ${W}^{*}N$ cross sections satisfy the saturated Froissart bound. Since approximately 50% of the $\ensuremath{\nu}N$ 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 strong interactions at incredibly high energies.