Impact-parameter dependent color glass condensate dipole model and new combined HERA data

The impact-parameter dependent color glass condensate (b-CGC) dipole model is based on the Balitsky-Kovchegov nonlinear evolution equation and improves the Iancu-Itakura-Munier dipole model by incorporating the impact-parameter dependence of the saturation scale. Here we confront the model to the recently released high precision combined Hadron Electron Ring Accelerator (HERA) data and obtain its parameters. The b-CGC results are then compared to data at small $x$ for the structure function, the longitudinal structure function, the charm structure function, exclusive vector meson ($J/\ensuremath{\psi}$, $\ensuremath{\phi}$, and $\ensuremath{\rho}$) production and deeply virtual Compton scattering. We also compare our results with the impact-parameter dependent saturation (IP-Sat) model. We show that most features of inclusive deep inelastic scattering and exclusive diffractive data, including the ${Q}^{2}$, $W$, $|t|$, and $x$ dependence, are correctly reproduced in both models. Nevertheless, the b-CGC and the impact-parameter dependent saturation (IP-Sat) models give different predictions beyond the current HERA kinematics, namely for the structure functions at very low $x$ and high virtualities ${Q}^{2}$, and for the exclusive diffractive vector meson and deeply virtual Compton scattering production at high $t$. This can be traced back to the different power-law behavior of the saturation scale in $x$ and to a different impact-parameter $b$ dependence of the saturation scale in these models. Nevertheless, both models give approximately similar saturation scales ${Q}_{S}<1\text{ }\text{ }\mathrm{GeV}$ for the proton in HERA kinematics, and also both models lead to the same conclusion that the typical impact parameter probed in the total ${\ensuremath{\gamma}}^{*}p$ cross section is about $b\ensuremath{\approx}2--3\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$. Our results provide a benchmark for further investigation of QCD at small $x$ in heavy ion collisions at RHIC and the LHC and also at future experiments such as an electron-ion collider and the LHeC.