Nucleon structure functions at small $x$ via the Pomeron exchange in AdS space with a soft infrared wall

Abstract

We present analyses on nucleon structure functions at the 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 AdS geometry is smoothly cut off at IR. Combining the improved Pomeron-nucleon coupling and the wave function of the 5D U(1) vector field with the BPST Pomeron exchange kernel, then we obtain the structure functions. Here we focus on the nonperturbative kinematical region, where $10^{-6} \leq x \leq 10^{-2}$ and $0.1 \leq Q^2 \leq 10$ [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 of $x$ and $Q^2$.