All-Orders Evolution of Parton Distributions: Principle, Practice, and Predictions

Parton distribution functions (DFs) are defining expressions of hadron structure. Exploiting the role of effective charges in quantum chromodynamics, an algebraic scheme is described which, given any hadron's valence parton DFs at the hadron scale, delivers predictions for all its DFs -- unpolarised and polarised -- at any higher scale. The scheme delivers results that are largely independent of both the value of the hadron scale and the pointwise form of the charge; and, inter alia, enables derivation of a model-independent identity that relates the strength of the proton's gluon helicity DF, $\Delta G_p^\zeta$, to that of the analogous singlet polarised quark DF and valence quark momentum fraction. Using available data fits and theory predictions, the identity yields $\Delta G_p(\zeta_{\rm C}=\surd 3{\rm GeV})=1.48(10)$. It furthermore entails that the measurable quark helicity contribution to the proton spin is $\tilde a_{0p}^{\zeta_{\rm C}}=0.32(3)$, thereby reconciling contemporary experiment and theory.