Determination of quark-gluon-quark interference within the proton

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 ($2-3\sigma$). 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.