Study of HERA data at low $\mathcal{Q}^2$ and low $\mathcal{x}$

In the HERAPDF2.0 PDF analysis it was noted that the fit $\chi^2$ worsens significantly at low $\mathcal{Q}^2$ or both NLO and NNLO fits. The turn over of the reduced cross section at low-x and low $\mathcal{Q}^2$ due to the contribution of the longitudinal cross section $F_L$ is also not very well described. In this paper the prediction for $F_L$ is highlighted and the corresponding extraction of $F_2$ from the data isfurther investigated, showing discrepancies with description of HERAPDF2.0 at low x and $\mathcal{Q}^2$. The effect of adding a simple higher twist term of the form $F_L \ast A/\mathcal{Q}^2$ to the description of $F_L$ is investigated. This results in a significantly better description of the reduced cross-sections, $F_2$ and $F_L$ at low x, $\mathcal{Q}^2$ and a significantly lower $\chi^2$ for the NNLO fit as compared to the NLO fit. This is not the case if the higher twist term is added to $F_2