On the x-Independence of the $${{R}^{Q}} = F_{L}^{Q}{\text{/}}F_{2}^{Q}$$ Ratio at Low x

Abstract

We give predictions for the ratio $${{R}^{Q}}(x,{{Q}^{2}}) = F_{L}^{Q}(x,{{Q}^{2}}){\text{/}}F_{2}^{Q}(x,{{Q}^{2}})$$ at small values of Bjorken variable x in the first three orders of perturbation theory. We show an approximate x-independence of $${{R}^{Q}}(x,{{Q}^{2}})$$ at low x and non-large $${{Q}^{2}}$$ values ($${{Q}^{2}} \leqslant 8{-} 10m_{Q}^{2}$$), irrespectively on the gluon density in a proton used in the calculations. This observation could be useful in subsequent phenomenological studies of the heavy flavor production at future lepton–hadron and hadron–hadron colliders.