All-Orders Evolution of Parton Distributions: Principle, Practice, and Predictions
Pei-Lin Yin1, Yin-Zhen Xu2,3, Zhu-Fang Cui4,5, Craig D. Roberts4,5*, and José Rodríguez-Quintero2
1College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China 2Dpto. Ciencias Integradas, Centro de Estudios Avanzados en Fis., Mat. y Comp., Fac. Ciencias Experimentales, Universidad de Huelva, Huelva 21071, Spain 3Dpto. Sistemas Físicos, Químicos y Naturales, Univ. Pablo de Olavide, E-41013 Sevilla, Spain 4School of Physics, Nanjing University, Nanjing 210093, China 5Institute for Nonperturbative Physics, Nanjing University, Nanjing 210093, China
Abstract：Parton distribution functions (PDFs) are defining expressions of hadron structure. Exploiting the role of effective charges in quantum chromodynamics, an algebraic scheme is described which, given any hadron's valence parton PDFs at the hadron scale, delivers predictions for all its PDFs (unpolarized and polarized) at any higher scale. The scheme delivers results that are largely independent of both the value of the hadron scale and the pointwise form of the charge; and, inter alia, enables derivation of a model-independent identity that relates the strength of the proton's gluon helicity PDF, $\Delta G_p^\zeta$, to that of the analogous singlet polarized quark PDF and valence quark momentum fraction. Using available data fits and theory predictions, the identity yields $\Delta G_p(\zeta_{_{\scriptstyle \rm C}}=\sqrt{3}\,{\rm GeV})=1.48(10)$. It furthermore entails that the measurable quark helicity contribution to the proton spin is $\tilde a_{0p}^{\zeta_{_{\scriptstyle \rm C}}}=0.32(3)$, thereby reconciling contemporary experiment and theory.
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2023, Vol. 40 
