Tau energy loss and ultrahigh energy skimming tau neutrinos

Abstract

We consider propagation of high-energy earth-skimming taus produced in interactions of astrophysical tau neutrinos. For astrophysical tau neutrinos, we take generic power-law flux, E −2 and the cosmogenic flux initiated by the protons. We calculate tau energy loss in several approaches, such as dipole models and the phenomenological approach in which parametrization of the F 2 is used. We evaluate the tau neutrino charged-current cross section using the same approaches for consistency. We find that uncertainty in the neutrino cross section and in the tau energy loss partially compensate giving very small theoretical uncertainty in the emerging tau flux for distances ranging from 2 to 100 km and for the energy range between 10 6 and 10 11 GeV, focusing on energies above 10 8 GeV. When we consider uncertainties in the neutrino cross section, inelasticity in neutrino interactions and the tau energy loss, which are not correlated, i.e. they are not all calculated in the same approach, theoretical uncertainty ranges from about 30% and 60% at 10 8 GeV to about factors of 3.3 and 3.8 at 10 11 GeV for the E −2 flux and the cosmogenic flux, respectively, for the distance of 10 km rock. The spread in predictions significantly increases for much larger distances, e.g., ∼1; 000 km. Most of the uncertainty comes from the treatment of photonuclear interactions of the tau in transit through large distances. We also consider Monte Carlo calculation of the tau propagation and we find that the result for the emerging tau flux is in agreement with the result obtained using analytic approach. Our results are relevant to several experiments that are looking for skimming astrophysical taus, such as the Pierre Auger Observatory, HAWC and Ashra. We evaluate the aperture for the Auger and discuss briefly application to the other two experiments.

Comprehensive approach to tau-lepton production by high-energy tau neutrinos propagating through the Earth

“…The work of [44] included the full dependence on the y-distribution and concluded that the results can be reproduced accurately using only the average y as a function of energy. Between the models considered in [44], changes in y range from -3% to 7% at 10 15 eV and -15% to 23% at 10 20 eV. The resulting fluxes in that reference show consistent results with different models within 25%.…”

“…They give us an order of magnitude estimate of the uncertainties involved within the Standard Model. We note that alternative calculations based on the dipole model [44] [50]. The upper and lower curves represent the upper and lower limits of the uncertainties due to the parton distribution function.…”

“…III). However, we also include the effects of a layer of ice or water as well as regeneration, which were not included in [44]. While these effects may not be relevant to estimating the sensitivity of the Pierre Auger Observatory (as done in [44]), they may be relevant to interpreting τ -lepton air-showers observed at altitude, as mentioned in [26].…”

“…Several publications have studied the propagation and detectability of τ leptons exiting the Earth into the atmosphere in different energy and angular ranges, using Monte Carlo simulations and/or semianalytical techniques and with a focus on the observability in underwater/ice and/or ground-level arrays of particle and/or fluorescence detectors [32][33][34][35][36][37][38][39][40][41][42][43][44].…”

“…A recent study [44] produced simulations with detailed models of neutrino interaction crosssections and τ -lepton energy loss models with consistent account of inelasticity. The simulations presented here also allow for variations of the cross-section and energy loss model, although in not as detailed a manner (see Sec.…”