Summary
We compare the rapidity, $y$, and the beam energy, $\sqrt{s}$, behaviors of the cross section of the data for $D$ meson production in the forward direction that were measured by the LHCb Collaboration. We describe the observed cross sections using NLO perturbative QCD, and choose the optimal factorization scale for the LO contribution which provides the resummation of the large double logarithms. We emphasize the inconsistency observed in the $y$ and $\sqrt{s}$ behaviors of the $D$ meson cross sections. The $y$ behavior indicates a very flat $x$ dependence of the gluon PDF in the unexplored low $x$ region around $x\ensuremath{\sim}1{0}^{\ensuremath{-}5}$. However, to describe the $\sqrt{s}$ dependence of the data we need a steeper gluon PDF with decreasing $x$. Moreover, an even steeper be
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