Abstract
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, where m_p is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the xsimeq 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.
Highlights
Amongst all the hadrons that appear in Nature’s catalogue of bound states, pions would seem to be the simplest
In any realisable experiment, there will always be a neighbourhood x 1 whereupon the longitudinal cross-section exceeds the transverse and access to uπ (x; ζ ) is obscured. These remarks are important because existing attempts to extract the large-x behaviour of the pion valence-quark distribution function (DF) [33–36] are dominated by the data reported in Ref. [32, E615]
Comparison with the continuum prediction from Refs. [69–71], Eq (24), whose dilated profile owes to EHM, demonstrates that, within mutual uncertainties, the set of evolved curves abuts the class of DFs linked to a quark+antiquark interaction with the 1/k2 ultravi
Summary
Amongst all the hadrons that appear in Nature’s catalogue of bound states, pions would seem to be the simplest. Even with Higgs couplings restored, u, d quarks remain light; and so do pions [1], possessing masses, mπ± ≈ mπ0 , far less than that of the proton, m p. Gluons, which appear as massless gauge-boson degrees-of-freedom in the QCD Lagrangian, acquire a momentum dependent mass function, mg(k2), whose value on k2 0 is characterised by a renormalisation group invariant mass m0 ≈ m p/2 [3–10]. This is a primary sign of the dynamical violation of scale invariance in QCD [11], whose origin is strong gluon self-interactions, and the
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