Studying low-$x$ structure function models with astrophysical tau neutrinos: double bang, lollipop and sugardaddy topologies

Despite not have been yet identified by the IceCube detector, events generated from $\nu_{\tau}$ deep inelastic neutrino scattering in ice with varied topologies, such as double cascades (often called \textit{double bangs}), \textit{lollipops} and \textit{sugardaddies}, constitute a potential laboratory for low-x parton studies. Here we investigate these events, analyzing the effect of next-to-next-to-leading order (NNLO) Parton Distribution Function (PDFs) in the total neutrino--nucleon cross section, as compared with the color dipole formalism, where saturation effects play a major role. Energy deposit profiles in the `bangs' are also analysed in terms of virtual $W$-boson and tauon energy distributions and are found to be crucial in establishing a clear signal for gluon distribution determination at very small $x$. By taking the average (all flavor) neutrino flux ($\Phi_{\nu}\sim E_{\nu}^{-2.3}$) into differential cross sections as a function of $\tau$ and $W$ energies, we find significant deviations from pure DGLAP parton interactions for neutrino energies already at a few PeV. With these findings one aims at providing not only possible observables to be measured in large volume neutrino detectors in the near future, but also theoretical ways of unraveling QCD dynamics using unintegrated neutrino-nucleon cross sections in the ultrahigh-energy frontier.