I haven’t spent any time keeping up on particle physics since high school (a long time ago) so maybe it is a stupid question, but how exactly do you accelerate a neutrally charged particle?
In this experiment the neutrinos were not accelerated by the experimental equipment. There was acceleration of something else, however: the neutrino beam is produced by accelerating a beam of protons to an extremely high speed (400 GeV/c - this is actually their mean momentum value) - the acceleration of the protons is accomplished by controlling precisely configured magnetic fields in a device called a synchrotron (the CERN Super proton synchrotron). The accelerated protons are then allowed to collide with a specially prepared “neutrino production target” made up mostly of graphite. There the protons decay into a number of other types of particles, the important ones of which are called pions and kaons. There is a natural pion/kaon decay process into muons and their associated neutrinos that then takes place along a long, evacuated tunnel. A variety of decay products are “stopped” using various materials, and what finally results is a highly pure beam of neutrinos, that continue to propagate forward. (There are actually three types of neutrinos that we know about, and this beam is almost purely (~97%) made up of so-called muon neutrinos.)