The ANTARES detector is at present the most sensitive neutrino telescope in the northern hemisphere. The highlysignificant cosmic neutrino excess observed by the Antarctic IceCube detector can be studied with ANTARES,exploiting its complementing field of view, exposure, and lower energy threshold. Searches for an all-flavor diffuseneutrino signal, covering nine years of ANTARES data taking, are presented in this Letter. Upward-going eventsare used to reduce the atmospheric muon background. This work includes for the first time in ANTARES bothtrack-like (mainly nm) and shower-like (mainly ne) events in this kind of analysis. Track-like events allow for anincrease of the effective volume of the detector thanks to the long path traveled by muons in rock and/or sea water.Shower-like events are well reconstructed only when the neutrino interaction vertex is close to, or inside, theinstrumented volume. A mild excess of high-energy events over the expected background is observed in nine yearsof ANTARES data in both samples. The best fit for a single power-law cosmic neutrino spectrum, in terms of perflavorflux at 100 TeV, is φ01f100 TeV (1.7±1.0) × 10-18GeV-1 cm-2 s-1 sr-1 with spectral index γ=2.4-0.4+0.5. The null cosmic flux assumption is rejected with a significance of 1.6δ.
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