Concerning pion parton distributions

Abstract

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", $$\beta (\zeta \gtrsim m_p)&gt;2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>(</mml:mo> <mml:mi>ζ</mml:mi> <mml:mo>≳</mml:mo> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo>)</mml:mo> <mml:mo>&gt;</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , where $$m_p$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:math> is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the $$x\simeq 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> 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.