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The Ratio $R=F_L/F_T$ in DIS as a Probe of the Charm Content of the Proton

We analyze the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ in heavy-quark leptoproduction as a probe of the charm content of the proton. To estimate the charm-initiated contributions, we use the ACOT($χ$) variable-flavor-number scheme. Our analysis shows that charm densities of the recent CTEQ sets of parton distributions have sizeable impact on the Callan-Gross ratio in a wide region of $x$ and $Q^2$. In particular, the ACOT($χ$) predictions for the quantity $R(x,Q^2)$ are about half as large as the corresponding expectations of the photon-gluon fusion mechanism for $x\sim 10^{-2}-10^{-1}$ and $Q^2\gg m^2$. This is because the structure functions $F_T (x,Q^2)$ and $F_L (x,Q^2)$ have different dependences on the mass logarithms of the type $α_{s}\ln(Q^{2}/m^{2})$. On the other hand, our recent studies indicate that, contrary to the production cross sections, the Callan-Gross ratio is sufficiently stable under radiative corrections to the photon-gluon fusion component for $x\gtrsim 10^{-4}$. We conclude that the quantity $R(x,Q^2)$ in heavy-quark leptoproduction is perturbatively stable but sensitive to resummation of the mass logarithms. For this reason, in contrast to the structure functions, the ratio $R(x,Q^2)=F_L/F_T$ could be good probe of the charm density in the proton.