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

TL;DR

This paper investigates the geometrical scaling of top structure functions at the LHeC, revealing that the top reduced cross section exhibits scaling behavior and that the top longitudinal structure function significantly impacts the cross section around certain energy scales.

Contribution

It introduces the analysis of geometrical scaling in top structure functions at small x, highlighting its effect on the top reduced cross section at the LHeC.

Findings

Top reduced cross section shows geometrical scaling over a wide range of photon virtualities.

The top longitudinal structure function significantly influences the cross section near Q^2 ≈ 4m_t^2.

Geometrical scaling can serve as a probe of the top content of the proton.

Abstract

We consider the ratio of the top structure functions $R^{t}(\tau_{t})$ 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 $Q^{2}{\approx}~ 4m_{t}^{2}$.