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Estimates are made of the ultra-high energy neutrino cross sections based on an extrapolation to very small Bjorken x of the logarithmic Froissart dependence in x shown previously to provide an excellent fit to the measured proton structure function F_2^p(x,Q^2) over a broad range of the virtuality Q^2. Expressions are obtained for both the neutral current and the charged current cross sections. Comparison with an extrapolation based on perturbative QCD shows good agreement for energies where both fit data, but our rates are as much as a factor of 10 smaller for neutrino energies above 10^9 GeV, with important implications for experiments searching for extra-galactic neutrinos.
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We reconsider the Standard Model interactions of ultra-high energy neutrinos with matter. The next to leading order QCD corrections are presented for charged-current and neutral-current processes. Contrary to popular expectations, these corrections are found to be quite substantial, especially for very large (anti-) neutrino energies. Hence, they need to be taken into account in any search for new physics effects in high-energy neutrino interactions. In our extrapolation of the parton densities to kinematical regions as yet unexplored directly in terrestrial accelerators, we are guided by double asymptotic scaling in the large Q^2 and small Bjorken x region and to models of saturation in the low Q^2 and low x regime. The sizes of the consequent uncertainties are commented upon. We also briefly discuss some variables which are insensitive to higher order QCD corrections and are hence suitable in any search for new physics.
Neutrino Physics is now entering precision era and neutrino-nucleon cross sections are an im- portant ingredient in all neutrino oscillation experiments. Specially, precise knowledge of neutrino- nucleon cross sections in Ultra High Energy (UHE) regime (TeV-PeV) is becoming more important now, as several experiments worldwide are going to observe processes involving such UHE neutrinos. In this work, we present new results on neutrino-nucleon cross-sections in this UHE regime, using QCD.
Studies on neutrino-nucleon ($ u N$) cross sections at different energy scales have regained interest due to increasing importance of precision measurements, as they are needed as an ingredient in all neutrino experiments. In this paper we have calculated both charged current (CC) and neutral current (NC) $ u$N scattering cross sections at Ultra High Energy (UHE) regime in the neutrino energy ($E_{ u}$) region i.e. $10^{9} GeV le E_{ u} le 10^{12}$ GeV using QCD inspired double asymptotic limit fit of electron-proton structure function $F_{2}^{ep}$ to low $mathit{x}$ HERA data. The form $F_{2}^{ep} sim x^{-lambda(Q^{2})}$ used in our analysis, can be conjectured like a dynamic pomeron (DP)-type behaviour. We also find an analytic form of the total cross sections, $sigma_{CC}^{ u N}$ and $sigma_{NC}^{ u N}$ which appear to be of hard-pomeron exchange types. A comparative analysis of our results with those available in literature is also done. An improved understanding of $ u N$ interactions at UHE are essentially important for future oscillation experiments. Future measurements will support/confront our predictions. textbf{Keywords}: Neutrino cross section, Ultra High Energy, QCD, Double Asymptotic limit, dynamic pomeron, hard-pomeron.
The amplitude A(s,t) for ultra-high energy scattering can be found in the leading eikonal approximation by considering propagation in an Aichelburg-Sexl gravitational shockwave background. Loop corrections in the QFT describing the scattered particles are encoded for energies below the Planck scale in an effective action which in general exhibits causality violation and Shapiro time advances. In this paper, we use Penrose limit techniques to calculate the full energy dependence of the scattering phase shift Theta_scat(hat_s},, where the single variable hat_s = Gs/m^2 b^(d-2) contains both the CM energy s and impact parameter b, for a range of scalar QFTs in d dimensions with different renormalizability properties. We evaluate the high-energy limit of Theta_scat(hat_s) and show in detail how causality is related to the existence of a well-defined UV completion. Similarities with graviton scattering and the corresponding resolution of causality violation in the effective action by string theory are briefly discussed.
In Part I (in this journal) we argued that the structure function $F_2^{gamma p}(x,Q^2)$ in deep inelastic $ep$ scattering, regarded as a cross section for virtual $gamma^*p$ scattering, has a saturated Froissart-bounded form behaving as $ln^2 (1/x)$ at small $x$. This form provides an excellent fit to the low $x$ HERA data, including the very low $Q^2$ regions, and can be extrapolated reliably to small $x$ using the natural variable $ln(1/x)$. We used our fit to derive quark distributions for values of $x$ down to $x=10^{-14}$. We use those distributions here to evaluate ultra-high energy (UHE) cross sections for neutrino scattering on an isoscalar nucleon, $N=(n+p)/2$, up to laboratory neutrino energies $E_ u sim 10^{16}$-$10^{17}$ GeV where there are now limits on neutrino fluxes. We estimate that these cross sections are accurate to $sim$2% at the highest energies considered, with the major uncertainty coming from the errors in the parameters that were needed to fit $F_2^{gamma p}(x,Q^2)$. We compare our results to recently published neutrino cross sections derived from NLO parton distribution functions, which become much larger at high energies because of the use of power-law extrapolations of quark distributions to small $x$. We argue that our calculation of the UHE $ u N$ cross sections is the best one can make based the existing experimental deep inelastic scattering data. Further, we show that the strong interaction Froissart bound of $ln^2 (1/x)$ on $F_2^{gamma p}$ translates to an exact bound of $ln^3E_ u$ for leading-order-weak $ u N$ scattering. The energy dependence of $ u N$ total cross section measurements consequently has important implications for hadronic interactions at enormous cms (center-of-mass) energies not otherwise accessible.
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