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.