Concerning pion parton distributions

Abstract

Analyses of the pion valence-quark distribution function (DF), "Equation missing", which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict "Equation missing", $$\beta (\zeta \gtrsim m_p)>2$$ 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 "Equation missing", the empirical status remains uncertain because some methods used to fit existing data return a result for "Equation missing" 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.

Proton and pion distribution functions in counterpoint

“…further, that all glue and sea DFs vanish identically at ζ H . At this point, given hadron scale valence DFs for the proton and pion, then predictions for all DFs at any scale ζ > ζ H follow immediately from the following proposition [31,32]:…”

“…Working with QCD, some predictions are available. For instance, considering DFs measured in processes that do not involve beam or target polarisation, then at some hadron scale, ζ H < m p , the valence-quark DFs in the proton and pion behave as follows [29][30][31][32]:…”

“…With increasing scale, ζ > ζ H , all these exponents increase logarithmically in a manner prescribed by the DGLAP equations [33][34][35][36]. However, feeding controversy and leading some to challenge the veracity of QCD [31,32,37], these constraints are typically ignored in fits to the world's deep inelastic scattering data [38][39][40][41][42]. Furthermore, proton and pion data have not been considered simultaneously, largely because pion data are scarce [17, Table 9.5].…”

“…Against this backdrop, we exploit recent progress made using continuum Schwinger function methods (CSMs) [31,32,[43][44][45][46] in developing a unified set of predictions for all proton and pion DFs. Crucially, their common origin enables meaningful comparisons to be made between them.…”

“…Hadron scale and DF evolution. Using CSMs, the hadron scale, ζ H , is naturally identified with the resolving scale at which dressed valence degrees-of-freedom carry all measurable properties of the hadron, including its light-front momentum [31,32,[43][44][45][46], and ζ H is the same for both the proton and the pion. Defining the n th moment of a given DF as (H = p, π)…”