Proton helicity structure function $g_1^p$ from a holographic Pomeron

We present a detailed analysis of the polarized and the unpolarized deep-inelastic scattering structure functions of the proton, $g_1^p$ and $F_2^p$ respectively, in the context of a holographic dual description based on type-IIB superstring theory. We compare this description with experimental data and quantum chromodynamics estimates computed at leading, next-to-leading and next-to-next-to-leading order in perturbation. We confront the predictions of a holographic dual model and those of perturbative QCD for $g_1^p$ at the kinematics that will be probed by the forthcoming electron-ion collider. We find that the extrapolation of $g_1^p$ to very small values the Bjorken variable computed with a holographic Pomeron model based on actual data at higher-momentum fractions is always positive and differs significantly with standard projections based on perturbative QCD.

Figure 1

The proton $F_2^p$ structure function using a single BPST Pomeron exchange against data from H1-ZEUS, BCDMS, NMC, E665, and SLAC Collaborations within the ranges $0.1{\mathrm{GeV}}^2<Q^2\le 400{\mathrm{GeV}}^2$ and $2.43\times {10}^{-6}\le x<0.01$. The number of data points depicted has been limited for a better visualization. Error bands are included in both figures. Due to the logarithmic vertical scale in the right-hand side plot, though the error bands are present, they are very narrow and cannot be distinguished from their central values.

Figure 2

The ratios between the LO, NLO, and NNLO DGLAP-based estimates for $F_2^p$ and the BPST-Pomeron parametrization.

Figure 3

$g_1$ structure function using a single holographic-$A$ Pomeron exchange to fit experimental data within the range $0.0036\le x\le 0.009$ at $Q^2=10{\mathrm{GeV}}^2$ against the one obtained in DSSV14 DGLAP NLO analysis.