  Various approaches aim to describe the recent analysis by the OPERA
experiment, which indicates that neutrinos travel faster than the speed of
light. We demonstrate that any such theoretical or experimental explanation
must not destroy the complicated (nonlinear) structure of the proton waveform
recovered in the neutrino signal. As one example, consider that only a fraction
of the neutrinos travel faster than the speed of light, such as sterile
neutrinos. We fit the OPERA data including this fraction as a free variable,
assuming that the OPERA result is correct. In our analysis, the best-fit values
are 50% of the neutrinos being superluminal and (v-c)/c = 4.5 10^{-5}, where
the neutrino velocity increases as the fraction of superluminal neutrinos
decreases. The minimal fraction of superluminal neutrinos is found to be 17% (3
sigma), which is constrained by the non-linearity of the proton waveform. This
minimal fraction challenges the hypothesis that only sterile neutrinos travel
faster than the speed of light. In addition, we demonstrate that an
experimental effect introducing a smearing between the proton waveform and
neutrino signal, as expected for some systematical errors, is also limited by
the shape of the waveform. Finally, we illustrate that even stronger
constraints may be obtained from the recent analysis with a short-bunch beam,
in spite of the low statistics.
