Connection of the virtual $γ^*p$ cross section of $ep$ deep inelastic scattering to real $γp$ scattering, and the implications for $νN$ and $ep$ total cross sections

Martin M. Block; Loyal Durand; Phuoc Ha

doi:10.1103/PhysRevD.89.094027

paper

Connection of the virtual $γ^{*} p$ cross section of $e p$ deep inelastic scattering to real $γ p$ scattering, and the implications for $ν N$ and $e p$ total cross sections

arXiv:1404.4530 · doi:10.1103/PhysRevD.89.094027

Abstract

We show that it is possible to fit all of the HERA DIS (deep inelastic scattering) data on $F_{2}^{γ p}$ at small values of Bjorken $x$ , including the data at {\em very low} $Q^{2}$ , using a new model for $F_{2}^{γ p}$ 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 $γ^{*} p$ cross section match the known asymptotic part of the real $γ p$ 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 $α + β ln s + γ ln^{2} s$ . Using this model for the asymptotic part of $F_{2}^{γ p}$ plus a known valence contribution, we fit the asymptotic high energy part of the HERA data with $x \leq 0.1$ and $W \geq 25$ 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 $ρ$ meson mass, and is compatible with vector dominance. We use this fit to obtain accurate results for the high energy $e p$ and isoscalar $ν N$ 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 $γ^{*} p$ , $Z^{*} N$ and $W^{*} N$ cross sections satisfy the saturated Froissart bound. Since approximately 50% of the $ν N$ 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}.

arXiv comment17 pages, 9 figures. This version was accepted for publication in Phys. Rev. D

Connection of the virtual $γ^{*} p$ cross section of $e p$ deep inelastic scattering to real $γ p$ scattering, and the implications for $ν N$ and $e p$ total cross sections

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Connection of the virtual γ∗p cross section of ep deep inelastic scattering to real γp scattering, and the implications for νN and ep total cross sections

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Cited by in corpus (56)

Connection of the virtual $γ^{*} p$ cross section of $e p$ deep inelastic scattering to real $γ p$ scattering, and the implications for $ν N$ and $e p$ total cross sections