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QCD is well understood at short distances where perturbative calculations arefeasible. Establishing an explicit analytic connection between theshort-distance regime and the large-distance physics of quark confinement hasbeen 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 themasses of hadrons. We show here how new theoretical insights into the behaviorof QCD at large distances leads to such a relation. The resulting predictionfor $\Lambda_{s}$ in the $\overline{MS}$ scheme agrees well with experimentalmeasurements. Conversely, the relation can be used to predict the masses ofhadrons composed of light quarks with the measured value of $\Lambda_{s}$ asthe sole parameter. We also use "light-front holography" to determine theanalytic form of $\alpha_s(Q^2)$ at small $Q^2$.

The Relation between the Perturbative QCD Scale $\Lambda_s$ and Hadronic Masses from Light-Front Holography