Ratio of the structure functions and the color dipole model bound

Abstract

We observe that the DGLAP evolution equations at NNLO analysis predicts a ratio of the structure functions in region of small Bjorken variable $x$. The ratio $F_{L}(x,Q^{2})/F_{2}(x,Q^{2})$ is obtained and compared with the prediction of the dipole model and HERA data. In particular we show that this ratio is lower than dipole model bound at high-$Q^{2}$ values and it is higher at low-$Q^{2}$ values . Then the effect of adding a higher twist term to the description of the ratio $F_{L}(x,Q^{2})/F_{2}(x,Q^{2})$ for $Q^{2}< 20~GeV^{2}$ is investigated. Also the bounds are discussed by including charm distribution on $F_{L}/F_{2}$. We discuss, furthermore, how this ratio can be determine the proton structure function with respect to the reduced cross section at high-$y$ values.