Speaker
Description
We apply the valence quark model with corrections coming from gluon emissions to constrain the moderate-energy behavior of the polarized dipole amplitudes responsible for the quark and gluon helicity inside the proton at small Bjorken $x$. Our model radically reduces the number of free parameters associated with the moderate-energy initial conditions to the small-$x$ helicity evolution, ultimately allowing us to determine the quark and gluon helicity inside the proton with much smaller uncertainties, compared to similar analyses employing the conventional Born-inspired initial condition. The remaining free parameters from the valence quark model are constrained via a global analysis to the available polarized small-$x$ deep inelastic scattering data, akin to contemporary works within the Jefferson Lab Angular Momentum (JAM) framework. A good description of the world data is obtained with only 8 free parameters, which are are tightly constrained by the data, allowing us to predict the proton polarized structure function, $g_1^p$, to be negative at small $x$. Furthermore, we obtain the small-$x$ quark and gluon spins to give a contribution,
$$\int_{10^{-5}}^{0.1} dx \left(\frac{1}{2}\Delta\Sigma + \Delta G\right) = 0.63 \pm 0.10\;\;\text{or}\;\;1.35\pm 0.16$$
to the proton spin, depending on the specific running coupling prescription employed.
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