RT Journal Article T1 Concerning pion parton distributions A1 Cui, Zhu-Fang A1 Ding, M. A1 Morgado Chávez, José Manuel A1 Raya, Khépani A1 Binosi, Daniele A1 Chang, L. A1 Papavassiliou, J. A1 Roberts, Craig D. A1 Rodríguez Quintero, José A1 Schmidt, S. M. AB Analyses of the pion valence-quark distributionfunction (DF), uπ (x; ζ ), which explicitly incorporate thebehaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict uπ (x 1; ζ ) ∼(1 − x)β(ζ ), β(ζ m p) > 2, where m p is the proton mass.Nevertheless, more than forty years after the first experimentto collect data suitable for extracting the x 1 behaviourof uπ , the empirical status remains uncertain because somemethods used to fit existing data return a result for uπ thatviolates this constraint. Such disagreement entails one of thefollowing conclusions: the analysis concerned is incomplete;not all data being considered are a true expression of qualitiesintrinsic to the pion; or QCD, as it is currently understood,is not the theory of strong interactions. New, precise data arenecessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz. thereis an effective charge which defines an evolution schemefor parton DFs that is all-orders exact. This proposition hasnumerous corollaries, which can be used to test the characterof any DF, whether fitted or calculated PB Springer SN 1434-6001 SN 1434-601X (electrónico) YR 2022 FD 2022-01 LK http://hdl.handle.net/10272/21167 UL http://hdl.handle.net/10272/21167 LA eng NO Cui, Z.-F., Ding, M., Morgado, J. M., Raya, K., Binosi, D., Chang, L., Papavassiliou, J., Roberts, C. D., Rodríguez-Quintero, J., & Schmidt, S. M. (2022). Concerning pion parton distributions. In The European Physical Journal A (Vol. 58, Issue 1). Springer Science and Business Media LLC. https://doi.org/10.1140/epja/s10050-021-00658-7 NO We are grateful for constructive comments fromK.-L. Cai, O. Denisov, F. de Soto, T. Frederico, J. Friedrich, C. Mezrag,V. Mokeev, W.-D. Nowak, C. Quintans, G. Salmè and J. Segovia. Worksupported by: National Natural Science Foundation of China (Grantnos. 12135007, 11805097); Helmholtz-Zentrum Dresden-RossendorfHigh Potential Programme; Spanish Ministry of Science and Innovation (MICINN) (Grant nos. PID2020-113334GB, PID2019-107844GBC22); Generalitat Valenciana (Grant no. Prometeo/2019/087); Juntade Andalucía (Grant nos. P18-FR-5057, UHU-1264517, UHU EPIT2021); and STRONG-2020 “The strong interaction at the frontier ofknowledge: fundamental research and applications” which receivedfunding from the European Union’s Horizon 2020 research and innovation programme (grant no. 824093 DS Repositorio Institucional de la Universidad de Huelva RD 15 jun 2026