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Instead of starting from a theoretically motivated form of the color dipole cross section in the dipole picture of deep inelastic scattering, we start with a parametrization of the deep inelastic structure function for electromagnetic scattering with protons, and then extract the color dipole cross section. Using the parametrizations of $F_2(xi=x {rm or} W^2,Q^2)$ by Donnachie-Landshoff and Block et al., we find the dipole cross section from an approximate form of the presumed dipole cross section convoluted with the perturbative photon wave function for virtual photon splitting into a color dipole with massless quarks. The color dipole cross section determined this way reproduces the original structure function within about 10% for $0.1$ GeV$^2leq Q^2leq 10$ GeV$^2$. We discuss the large and small form of the dipole cross section and compare with other parameterizations.
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The observation of double parton collisions by CDF has provided the first direct information on the structure of the proton in transverse space. The actual quantity which has been measured is the `effective cross section $sigma_{eff}$, which is related to the transverse size of the region where hard interactions are localized. The actual value which has been measured is sizably smaller than naively expected and it is an indication of important correlation effects in the many-body parton distribution of the proton. We discuss the problem pointing out a possible source of correlations in the proton structure, which could have a significant effect on the value of $sigma_{eff}$.
The total $gamma^*gamma^*$ cross-section is derived in the Leading Order QCD dipole picture of BFKL dynamics, and compared with the one from 2-gluon exchange. The Double Leading Logarithm approximation of the DGLAP cross-section is found to be small in the phase space studied. Cross sections are calculated for realistic data samples at the $e^+e^-$ collider LEP and a future high energy linear collider. Next to Leading order corrections to the BFKL evolution have been determined phenomenologically, and are found to give very large corrections to the BFKL cross-section, leading to a reduced sensitivity for observing BFKL.
The description of the inelastic proton -- nucleus cross section at very high energies is still an open question. The current theoretical uncertainty has direct impact on the predictions of the cosmic ray and neutrino physics observables. In this paper we consider different models for the treatment of $sigma_{inel}^{pA}$, compare its predictions at ultrahigh cosmic ray energies and estimate the prompt neutrino flux at the neutrino energies that have been probed by the IceCube Observatory. We demonstrate that depending of the model used to describe $sigma_{inel}^{pA}$, the predictions for the prompt neutrino flux can differ by a factor of order of three. Such result demonstrate the importance of a precise measurement of the inelastic proton -- nucleus cross section at high energies.
The TOTEM collaboration has measured the proton-proton total cross section at $sqrt{s}=13$ TeV with a luminosity-independent method. Using dedicated $beta^{*}=90$ m beam optics, the Roman Pots were inserted very close to the beam. The inelastic scattering rate has been measured by the T1 and T2 telescopes during the same LHC fill. After applying the optical theorem the total proton-proton cross section is $sigma_{rm tot}=(110.6 pm 3.4$) mb, well in agreement with the extrapolation from lower energies. This method also allows one to derive the luminosity-independent elastic and inelastic cross sections: $sigma_{rm el} = (31.0 pm 1.7)$ mb and $sigma_{rm inel} = (79.5 pm 1.8)$ mb.
We suggest a simple physical picture for the diffractive parton distributions that appear in diffractive deeply inelastic scattering. In this picture, partons impinging on the proton can have any transverse separation, but only when the separation is small can they penetrate the proton without breaking it up. By comparing the predictions from this picture with the diffractive data from HERA, we determine rough values for the small separations that dominate the diffraction process.
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