  We consider the assumption that a tachyonic gluon mass imitates
short-distance nonperturbative physics of QCD. The phenomenological
implications include modifications of the QCD sum rules for correlators of
currents with various quantum numbers. The new 1/Q^2 terms allow to resolve in
a natural way old puzzles in the pion and scalar-gluonium channels. They lead
to a slight reduction of the values of the running light quark masses from the
(pseudo)scalar sum rules and of alpha_s(M_\tau) from tau decay data. Further
tests can be provided by precision measurements of the correlators on the
lattice and by the e^+e^- --> hadrons data.
