Geometrical scaling behavior of the top structure functions ratio at the LHeC

We consider the ratio of the top structure functions $R^{t}(τ_{t})$ in top pair production as a probe of the top content of the proton at the LHeC project. We study the top structure functions with the geometrical scaling of gluon distribution at small $x$ and show that top reduced cross section exhibits geometrical scaling in a large range of photon vitualities. This analysis shows that top longitudinal structure function has sizeable impact on the top reduced cross section at $Q^{2}{\approx}~ 4m_{t}^{2}$.

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