Comparison of muon and neutrino times from decays of mesons in the atmosphere

We propose a test to compare the speed of muons and muon neutrinos produced in the same bundles in the atmosphere. By comparing the arrival times of primary muons and muons induced by neutrinos, experiments such as Super-Kamiokande, IceCube and ANTARES could verify recent hints on the possibility that neutrinos have a velocity larger than the speed of light. For smaller detectors such as MINOS and OPERA, where it may be challenging to recognize downgoing muons induced by neutrinos inside the active volume, another measurement may be possible thanks to the ns-time resolution. The arrival times of muons in a bundle produced by one cosmic ray interaction in the atmosphere should return a value compatible with the time resolution, while if neutrinos have larger velocity than muons some of the muons may arrive slightly earlier in a bundle of particles than others.