Determination of quark-gluon-quark interference within the proton

TL;DR

This work delivers the first direct extraction of twist-three parton distribution functions, which encode quark–gluon–quark interference inside the proton. By performing a global fit to diverse observables (g_2, the d_2 moment, and SIDIS asymmetries A_{UT}^{\sin(\phi_h-\phi_s)} and A_{LT}^{\cos(\phi_h-\phi_s)}) with the complete LO twist-three QCD evolution, the authors reconstruct a 17-parameter minimal ansatz for the twist-three sector and its gluon components. The results reveal nonzero, flavor-dependent twist-three distributions at the 2–3$\sigma$ level, providing quantitative evidence for parton interference beyond the naïve parton densities and highlighting the proton’s intrinsically quantum nature. This approach also yields rich, ancillary information on related TMDs such as the Sivers function and worm-gear–T distributions, demonstrating the power of a unified twist-three global analysis to constrain partonic correlations and guide future precision studies.

Abstract

Quarks and gluon, as quantum particles, are subjects to various effects that go beyond the naive parton picture and are not captured by ordinary parton densities. In this work, we investigate the twist-three parton distribution functions, which encode quantum interference between quark-gluon-quark states, and for the first time, determine them directly from experimental data. The analysis combines observables described by collinear and transverse-momentum-dependent factorization theorems within a unified global fit, incorporating a complete leading-order QCD evolution at the twist-three level. The extracted distributions reveal a clear flavor-dependent patterns and distinct from zero at a statistically significant level ($2-3σ$). These findings provide the first quantitative evidence for quark-gluon-quark correlations within the proton, revealing its genuinely quantum nature and opening a new direction for precision studies of partonic correlations.

Figures (3)

• Figure 1: The domain of twist-three PDFs. Each sector corresponds to an interference between particular partonic configurations, shown in diagrams (with wavy lines being gluons, and straight lines being quarks). Different physical observables are sensitive to various sub-regions of the hexagon shown in colors and explained in the text.
• Figure 2: Twist-three PDF for $u$ quark at 4GeV determined in this work. The uncertanties of the extraction (68%CI) can be understood from the panels showing the sections of function by planes $x_2=0$ (red line) and $x_3=x_1$ (blue line).
• Figure 3: The mean value of twist-three PDFs for $u$, $d$ and $s$ quarks at 4GeV. The uncertainty bands are demonstrated in smaller gray plots as the ratio of the size of the uncertainty band to the mean value measured in $\sigma$'s. I.e. the white regions imply that the zero value is covered by the uncertainty band, while darker regions do not contain the zero value within uncertainty bands.