https://doi.org/10.1140/epja/s10050-021-00658-7
Regular Article - Theoretical Physics
Concerning pion parton distributions
1
School of Physics, Nanjing University, 210093, Nanjing, Jiangsu, China
2
Institute for Nonperturbative Physics, Nanjing University, 210093, Nanjing, Jiangsu, China
3
Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328, Dresden, Germany
4
Department of Integrated Sciences and Center for Advanced Studies in Physics, Mathematics and Computation, University of Huelva, 21071, Huelva, Spain
5
Departamento de Física Teórica y del Cosmos, Universidad de Granada, 18071, Granada, Spain
6
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510, CDMX, Mexico
7
European Centre for Theoretical Studies in Nuclear Physics and Related Areas, Villa Tambosi, Strada delle Tabarelle 286, 38123, Villazzano, TN, Italy
8
School of Physics, Nankai University, 300071, Tianjin, China
9
Department of Theoretical Physics and IFIC, University of Valencia and CSIC, 46100, Valencia, Spain
10
RWTH Aachen University, III. Physikalisches Institut B, 52074, Aachen, Germany
Received:
21
December
2021
Accepted:
22
December
2021
Published online:
24
January
2022
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 
, 
, where 
is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the 
behaviour of uπ, the empirical status remains uncertain because some methods used to fit existing data return a result for uπ 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.
© The Author(s) 2022
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