Concerning pion parton distributions

Analyses of the pion valence-quark distribution function (DF), , which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict , $$\beta (\zeta \gtrsim m_p)>2$$ β ( ζ ≳ m p ) > 2 , where $$m_p$$ m p is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the $$x\simeq 1$$ x ≃ 1 behaviour of , the empirical status remains uncertain because some methods used to fit existing data return a result for that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz . there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated.