Nucleon structure functions at small<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math>via the Pomeron exchange in AdS space with a soft infrared wall

Abstract

We present analyses on nucleon structure functions at small Bjorken $x$ in the framework of holographic QCD. In this study, we improve the description of the target nucleon in the current setup of the holographic model by introducing a soft-wall AdS/QCD model, in which the anti--de Sitter geometry is smoothly cut off at the infrared boundary. Combining the improved Pomeron-nucleon coupling and the wave function of the five-dimensional U(1) vector field with the Brower-Polchinski-Strassler-Tan Pomeron exchange kernel, we obtain the structure functions. Here we focus on the nonperturbative kinematical region, where ${10}^{\ensuremath{-}6}\ensuremath{\le}x\ensuremath{\le}{10}^{\ensuremath{-}2}$ and ${Q}^{2}\ensuremath{\le}$ a few (${\mathrm{GeV}}^{2}$), and show that our calculations for ${F}_{2}^{p}$ and ${F}_{L}^{p}$ are consistent with experimental data of the deep inelastic scattering at HERA. Furthermore, we find that the resulting longitudinal-to-transverse ratio of the structure functions, ${F}_{L}^{p}/{F}_{T}^{p}$, depends on both $x$ and ${Q}^{2}$.