The hadronic decays of the τ lepton can be used to determine the effective charge α τ (m 2 τ ′ ) for a hypothetical τ -lepton with mass in the range 0 < m τ ′ < m τ . This definition provides a fundamental definition of the QCD coupling at low mass scales. We study the behavior of α τ at low mass scales directly from first principles and without any renormalization-scheme dependence by looking at the experimental data from the OPAL Collaboration. The results are consistent with the freezing of the physical coupling at mass scales s = m 2 τ ′ of order 1 GeV 2 with a magnitude α τ ∼ 0.9 ± 0.1.

In the framework of conventional Regge theory we present a common description of total photon-proton cross-section and proton structure functions in the region $0 \leq Q^2 \leq 5 \ {\rm GeV}^2$. Using it as an initial condition in the perturbative QCD evolution equation, we describe structure functions at any $Q^2$ and $x$ - including the small $x$ region explored at HERA.Comment: 10 pages + 7 figures available on request, Plain TeX, Preprint LPTHE Orsay 94-3