POSSIBLE PROBLEMS WITH THE DETERMINATION OF ALPHA(S) USING THE SEMILEPTONIC TAU-DECAY DATA

It is shown that there are considerable uncertainties in the determina tion of the QCD running coupling constant alpha(s), using the finite e nergy sum rule and the operator product expansion in the analysis of t he semileptonic tau decay. The usual claim of a good agreement with th e value of alpha(s) determined from the data from CERN LEP could be ac cidental due to the special value of the physical tau mass. A new sum rule is derived to test strong assumptions made in the analysis of tau decay.