Implications of a Froissart bound saturation ofγ*−pdeep inelastic scattering. II. Ultrahigh energy neutrino interactions

Abstract

In Part I (in this journal) we argued that the structure function F γp 2 (x, Q 2 ) in deep inelastic ep scattering, regarded as a cross section for virtual γ * 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 Eν ∼ 10 16 -10 17 GeV where there are now limits on neutrino fluxes. We estimate that these cross sections are accurate to ∼2% at the highest energies considered, with the major uncertainty coming from the errors in the parameters that were needed to fit F γp 2 (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 νN 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 γp 2 translates to an exact bound of ln 3 Eν for leading-order-weak νN scattering. The energy dependence of νN total cross section measurements consequently has important implications for hadronic interactions at enormous cms (center-of-mass) energies not otherwise accessible.

Neutrino telescopes as QCD microscopes

“…As discussed in Sect. 1, predictions for the UHE neutrino-nucleus cross-sections based on a variety of the different theoretical setups have been provided in the past by a number of groups [8,[19][20][21][22][23][24][25][26][27][28][29][30]. In the following, we provide a comparison of our results (labelled as BGR18) to a number of calculations of the UHE cross-sections present in the literature.…”

“…It is the main goal of this work to present a state-of-the-art calculation, taking into account recent developments in our understanding of perturbative and non-perturbative QCD, for the UHE neutrino-nucleon cross-section relevant for signal detection at neutrino telescopes. While a number of calculations have been provided by different groups in the past, both in the framework of collinear DGLAP factorisation [8,[19][20][21][22][23][24] and beyond it [25][26][27][28][29][30], there are now several significant motivations to revisit this calculation. The improvements made in this work, and their motivation, are detailed below.…”

Cosmic tau neutrino detection via Cherenkov signals from air showers from Earth-emerging taus

“…(BDHM) extrapolation [83][84][85] of F 2 . As discussed below, these two expressions for the electromagnetic structure function will be used for the photonuclear energy loss of the τ -lepton .…”

“…(ALLM) form [81,82], and the Block, Durand, Ha and McKay (BDHM) parameterization [83][84][85]. The ALLM extrapolation of F 2 gives a more strongly energy dependent b nuc τ than the BDHM parameterization, however, in both cases, the growth with energy is only (approximately) logarithmic in tau energy.…”

Demystifying the PeV cascades in IceCube: Less (energy) is more (events)

“…The neutrino-nucleon cross sections σ(E ν ) near 1 PeV are well known [52][53][54][55]. In CC cascade events initiated by ν e +ν e , the neutrino interacts with a nucleon, leading to a hadronic cascade, and produces an electron or positron, leading to an electromagnetic cascade.…”