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We predict the neutrino-nucleon cross section at ultrahigh energies relevant in connection with the search for high-energy cosmic neutrinos. Our investigation, employing the color-dipole picture, among other things allows us to quantitatively determine which fraction of the ultrahigh-energy neutrinonucleon cross section stems from the saturation versus the color-transparency region. We disagree with various results in the literature that predict a strong suppression of the neutrino-nucleon cross section at neutrino energies above E ∼ = 10 9 GeV . Suppression in the sense of a diminished increase of the neutrino-nucleon cross section with energy only starts to occur at neutrino energies beyond E ∼ = 10 14 GeV .

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As has been shown almost two years ago , generalized vector dominance (GVD) quite successfully quantitatively accounts for the data on deep inelastic electron nucleon scattering. There is, however, one principal feature within this approach, which became more and more unsatisfactory as progressively higher energy data on e+e-+hadrons became available: these showing roughly a 1/s law in the Frascatil 3 1range, and an even slower fall off for c.m. energies /8 beyond about 3.5 GeV has been reported by CEAI 4 1 and more recently by the SLAC-LBL collaboration at SPEARisl. The problem, as discussed in I 1 I, with a 1/s law for e+e-annihilation is that in the usual diagonal form of GVD (i. then for p''(1600) photoproduction one expectswhere the addition.e e ann1h1lat1on result Experimentally one finds I 11 I Denoting the ratio of the first off-diagonal to the diagonal (t = 0) transition amplitude as (3) we thus obtain the isovector photon part of the transverse virtual photon ab- which for large N gives (negJ.ecting order I/~)Then the sum in (4) turns out to be convergent, provided the constant in (5) and (6) is chosen to be 1/2. Thus inserting (2) and (6) 2Generalizing to include the isoscalar parts and evaluating (7) The only free parameter introduced, o, which fixes the magnitude of the off-diagonal transitions, may now be determined fromfue normalization ( Although (II) may easily be evaluated numerically from the tables for 1/J (z), it is advantageous to give a much simp lac formula for oT' which for A = 2 approximates (II) extremely well, the error being at most 2% (around (13). (14) -6 -It is amusing to note that the simple pole formula (14) which is equivalent to(ll); had p~evi~u~~y'fgf be~n ~how~::tO'to de~c~ib~ extremely weilthe.•. Agreement of (II) and (14) •· are substantially unchanged.From our Ansatz (5), we note that diffraction dissociation, as exemplified by a single, effective off-diagonal term parametrized with CN, increases with N, becoming a constant fraction of the elastic reaction. This feature seems a necessary one for convergence and scaling. We have checked that a constant, N independent CN gives a logarithmically divergent non-scaling expression except for the singular point CN = 1/2, for which case the result is convergent, but also non-scaling with a leading term proportional to (1/q 4 ) ln (q 2 tm 2 ).

We elaborate on a recently suggested effective Lagrangian for charged-current and neutral-current electroweak interactions which in comparison with the standard electroweak theory contains three free parameters ∆x, ∆y, ε which quantify different sources for violations of SU(2) symmetry. Within the standard SU(2) I ×U(1) Y electroweak theory, we present both exact and very much refined approximate analytical one-loop expressions for these parameters in terms of the canonical input, G µ , M Z , α(M 2 Z ), the top-quark mass, m t , and the Higgs-boson mass, M H . We reemphase the importance of discriminating between the empirically well-known purely fermionic (vacuum polarization) contributions to ∆x, ∆y, ε and the empirically unknown bosonic ones with respect to present and future electroweak precision tests. The parameters ∆x and ε are hardly affected by standard bosonic corrections, while the full one-loop results for ∆y differ appreciably from the ones obtained by taking into account fermion loops only. A detailed comparison with the experimental data on M W ± /M Z ,s 2 W , Γ l shows that these data start to become accurate enough to be sensitive to standard (bosonic) contributions to ∆y beyond fermion loops.

We provide a formulation of generalised vector dominance (GVD) for low-x deep-inelastic scattering that explicitly incorporates the γ * → q q transition and a QCD-inspired ansatz for the (q q)p forward-scattering amplitude. The destructive interference originally introduced in off-diagonal GVD is recovered in the present formulation and traced back to the generic structure of two-gluon-exchange as incorporated into the notion of colour transparency. Asymptotically, the transverse photoabsorption cross section behaves as (ln Q 2 )/Q 2 , implying a logarithmic violation of scaling for F 2 , while the longitudinal-to-transverse ratio decreases as 1/ ln Q 2 .

We show that the experimental data for the total virtual-photon proton cross section, σ γ * p (W 2 , Q 2 ), for x bj ∼ < 0.1 lie on a universal curve, when plotted against η = (Q 2 + m 2 0 )/Λ 2 (W 2 ), where Λ 2 (W 2 ) = C 1 (W 2 + W 2 0 ) C 2 is determined by the parameters C 1 , C 2 and W 2 0 . The observed scaling law follows from the generalizedvector-dominance/colour-dipole picture (GVD/CDP) of low-x deep inelastic scattering.