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Establishing an explicit connection between the long distance physics ofconfinement and the dynamical interactions of quarks and gluons at shortdistances has been a long-sought goal of quantum chromodynamics. Usingholographic QCD, we derive a direct analytic relation between the scale$\kappa$ which determines the masses of hadrons and the scale $\Lambda_{s}$which controls the predictions of perturbative QCD at very short distances. Theresulting prediction $\Lambda_{s}=0.341\pm0.032$ GeV in the $\overline{MS}$scheme agrees well with the experimental average $0.339\pm0.016$ GeV. We alsoderive a relation between $\Lambda_{s}$ and the QCD string tension $\sigma$.This connection between the fundamental hadronic scale underlying the physicsof quark confinement and the perturbative QCD scale controlling hard collisionscan be carried out in any renormalization scheme.

Connecting the Hadron Mass Scale to the Fundamental Mass Scale of Quantum Chromodynamics