  The results of a search with the DELPHI Barrel RICH for anomalous Cherenkov
rings having radii greater than those produced by ultrarelativistic particles
were reported in our previous paper [1]. The search was based on the data
collected by the DELPHI Collaboration at CERN during the LEP1 and LEP2 periods.
A detailed study of background sources capable of producing apparently
anomalous rings has been done; it indicated that the background hypothesis has
a low probability ($10^{-3}$ or less). An additional strong argument against
the background hypothesis was provided by the observation of a high degree of
correlation between anomalous ring radii in the liquid and gaseous radiators in
the selected events.The results obtained are interpreted in this paper in terms
of observation of faster-than-light particles (tachyons). In the framework of
this interpretation two peaks in the tachyon mass parameter distribution are
observed, at $(0.29 \pm 0.01)$~GeV/c$^2$ and $(4.6 \pm 0.2)$~GeV/c$^2$.
  This work has been performed by the authors following the rules for external
access to the DELPHI archived data, as established in
http://delphiwww.cern.ch/delsec/finalrules/FINALrules011203.pdf
  The opinions, findings and conclusions expressed in this material are those
of the authors alone and do not reflect in any way the views of the DELPHI
Collaboration.
