  QCD is well understood at short distances where perturbative calculations are
feasible. Establishing an explicit analytic connection between the
short-distance regime and the large-distance physics of quark confinement has
been a long-sought goal. A major challenge is to relate the scale $\Lambda_{s}$
underlying the evolution of the QCD coupling in the perturbative regime to the
masses of hadrons. We show here how new theoretical insights into the behavior
of QCD at large distances leads to such a relation. The resulting prediction
for $\Lambda_{s}$ in the $\overline{MS}$ scheme agrees well with experimental
measurements. Conversely, the relation can be used to predict the masses of
hadrons composed of light quarks with the measured value of $\Lambda_{s}$ as
the sole parameter. We also use "light-front holography" to determine the
analytic form of $\alpha_s(Q^2)$ at small $Q^2$.
