An algorithm for the reconstruction of high-energy neutrino-induced particle showers and its application to the ANTARES neutrino telescope

A novel algorithm to reconstruct neutrino-induced particle showers within the ANTARES neutrino telescope is presented. The method achieves a median angular resolution of $6^{\circ }$ for shower energies below 100 TeV. Applying this algorithm to 6 years of data taken with the ANTARES detector, 8 events with reconstructed shower energies above 10 TeV are observed. This is consistent with the expectation of about 5 events from atmospheric backgrounds, but also compatible with diffuse astrophysical flux measurements by the IceCube collaboration, from which 2 - 4 additional events are expected. A 90% C.L. upper limit on the diffuse astrophysical neutrino flux with a value per neutrino flavour of $E^2\cdot {\mathrm{\Phi }}^{90\mathrm{\%}}=4.9\cdot {10}^{-8}$ GeV $\cdot$ cm${}^{-2}\cdot$ s${}^{-1}\cdot$ sr${}^{-1}$ is set, applicable to the energy range from 23 TeV to 7.8 PeV, assuming an unbroken $E^{-2}$ spectrum and neutrino flavour equipartition at Earth.