First study of polarized proton-proton scattering with small-x helicity evolution

We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-x helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton ($pp$) scattering at parton momentum fractions $x < 0.1$. We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing $x < 0.1$. Employing the polarized small-x pure-glue calculation of pp→ gX for the jet production cross section, we modify the large-Nc&Nf KPS-CTT evolution equations by setting Nf = 0 to replicate the large-Nc (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the $pp$ data have a considerable impact on the helicity PDFs at small x, reducing their uncertainties and leading to a total quark and gluon helicity in the proton for $x < 0.1$ of -0.04 ± 0.23. Combining our analysis with the a recent JAM helicity PDF analysis of the world polarized data, which includes $x > 0.1$, we find a total quark and gluon helicity contribution for x > 10⁻⁷ of between 0.02 and 0.51.