Study of HERA data at Low Q^2 and Low x
  In the HERAPDF2.0 PDF analysis it was noted that the fit $\chi^2$ worsens significantly at low $Q^2$ for both NLO and NNLO fits. The turn over of the reduced cross section at low-$x$ and low $Q^2$ 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 is further investigated, showing discrepancies with description of HERAPDF2.0 at low $x$ and $Q^2$. The effect of adding a simple higher twist term of the form ~$F_L*A/Q^2$ 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 $x$, $Q^2$ 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 $F_2$ 
A. M Cooper-Sarkar, I. Abt, B. Foster, M. Wing, V. Myronenko, K.   Wichmann
hep-ph hep-ex