Study of HERA $ep$ Data at Low $Q^2$ and Low $x_{Bj}$ and the Need for Higher-Twist Corrections to Standard pQCD Evolution

A detailed comparison of HERA data at low Bjorken-$x$ and low four-momentum-transfer squared, $Q^2$, with predictions based on $\ln{Q^2}$ evolution (DGLAP) in perturbative Quantum Chromo Dynamics suggests inadequacies of this framework. The standard DGLAP evolution was augmented by including an additional higher-twist term in the description of the longitudinal structure function, $F_{\rm L}$. This additional term, $F_{\rm L}~A_{\rm L}^{\rm HT}/Q^2$, improves the description of the reduced cross sections significantly. The resulting predictions for $F_{\rm L}$ suggest that further corrections are required for $Q^2$ less than about 2 GeV$^2$