The unintegrated gluon distribution from the GBW and BGK models

Abstract

The gluon distribution is obtained from the Golec-Biernat-W$\ddot{\mathrm{u}}$sthoff (GBW) and Bartels, Golec-Biernat and Kowalski (BGK) models at low $x$. We derive analytical results for the unintegrated color dipole gluon distribution function at small transverse momentum, which provides useful information to constrain the $k_t$-shape of the unintegrated gluon distribution in comparison with the unintegrated gluon distribution (UGD) models. The longitudinal proton structure function $F_L(x,Q^2)$ from the $k_t$ factorization scheme, using the unintegrated gluon density is computed. We compare the predictions for the on-shell and twist-2 corrections with the HERA data and the CJ15 parametrization method for $F_L$. We show that this method is very well described the experimental data within the on-shell and twist-2 framework. Effects of parameters on $F_L$, where charm contribution is taken into account, are investigated. These results are in good agreement with the data at fixed $W$.

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