Does Nature know about perturbation theory? A study of HERA data at low $\mathrm{Q^2}$

A phenomenological study of the final combined HERA data on inclusive deep inelastic scattering (DIS) has been performed. The data are presented and investigated for a kinematic range extending from values of the four-momentum transfer, Q$^2$, above 104 GeV$^2$ down to the lowest values observable at HERA of Q$^2$ = 0.045 GeV$^2$ and Bjorken x, x Bj = 6 x 10−7. The data are well described by fits based on perturbative quantum chromodynamics (QCD) using collinear factorisation and evolution of the parton densities encompassed in the DGLAP formalism from the highest Q$^2$ down to Q$^2$ of a few GeV$^2$. The standard DGLAP evolution was augmented by including an additional higher-twist term in the description of the longitudinal structure function, FL. This additional term, FLAHTL/Q$^2$, improves the description of the reduced cross sections significantly. The resulting predictions for FL suggest that further corrections are required for Q$^2$ less than about 2 GeV$^2$. The Regge formalism can describe the data up to Q$^2$ ~ 0.65 GeV$^2$. The complete data set can be described by a new fit using the ALLM parameterisation. The region between the Regge and the perturbative QCD regimes is of particular interest