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The results of a search with the DELPHI Barrel RICH for anomalous Cherenkovrings having radii greater than those produced by ultrarelativistic particleswere reported in our previous paper [1]. The search was based on the datacollected by the DELPHI Collaboration at CERN during the LEP1 and LEP2 periods.A detailed study of background sources capable of producing apparentlyanomalous rings has been done; it indicated that the background hypothesis hasa low probability ($10^{-3}$ or less). An additional strong argument againstthe background hypothesis was provided by the observation of a high degree ofcorrelation between anomalous ring radii in the liquid and gaseous radiators inthe selected events.The results obtained are interpreted in this paper in termsof observation of faster-than-light particles (tachyons). In the framework ofthis interpretation two peaks in the tachyon mass parameter distribution areobserved, 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 externalaccess to the DELPHI archived data, as established inhttp://delphiwww.cern.ch/delsec/finalrules/FINALrules011203.pdf  The opinions, findings and conclusions expressed in this material are thoseof the authors alone and do not reflect in any way the views of the DELPHICollaboration.

Physical interpretation of the anomalous Cherenkov rings observed with the DELPHI detector