A limit on top quark pair production at future electron-proton colliders

Abstract

The ratio of the structure functions for deep inelastic scattering in top pair production at future electron-proton colliders is analyzed at a fixed $\sqrt{s}$ and $Q^2$ relative to the minimum value of $x$ given by $Q^2/s$ using collinear factorization. This compact formula for the ratio $F_{L2}(Q^2/s,Q^2,m_{t})$ is useful for extracting a bound on the top structure function. The reduced cross-section for top production at this limit is determined, establishing a bound value for $t\overline{t}$ production at the LHeC and FCC-eh center-of-mass energies based on renormalization scales. The modification of the Bjorken scaling is applied to this bound of the reduced top cross-section at the renormalization scale $μ^2=Q^2+4m_{t}^{2}$, which improves the scaling quantity at $Q^2{<}4m_{t}^{2}$. The dipole cross-section for top pair production is examined across a wide range of dipole sizes, denoted as $r$. It is expected that there will be limited behavior in observing top saturation in future electron-proton colliders according to the bound behavior. The probability of the Higgs boson in $γ^{*}g$ interactions is compared to the $gg$ process at the order of $\mathcal{O}(α^{\mathrm{em}}/α_{s})$.

Figures (8)

• Figure 1: The function $g(\mu^2,s, m_{t})$ is compared versus $\mu^2=Q^2$ at the LO (left panel) and NLO (right panel) approximations for the LHeC (black circles) and FCC-eh (red squares) colliders with $\sqrt{s}=1.3$ and $3.5~\mathrm{TeV}$ respectively.
• Figure 2: Saturation scale at $x_{\mathrm{min}}$ is shown at $\mu^2=Q^2$ and $\mu^2=Q^2+4m_{t}^{2}$ for the LHeC and FCC-eh COM energies. LHeC: $\mu^2=Q^2$ (solid black curve) and $\mu^2=Q^2+4m_{t}^{2}$ (dashed-dot blue curve); FCC-eh: $\mu^2=Q^2$ (dashed red curve) and $\mu^2=Q^2+4m_{t}^{2}$ (short-dashed green curve).
• Figure 3: UGD obtained at $x_{\mathrm{min}}$ is shown at $\mu^2=Q^2$ ($Q^2=10~\mathrm{GeV}^2$ (solid black curve) and $Q^2=10000~\mathrm{GeV}^2$ (dashed-dot blue curve)) and $\mu^2=Q^2+4m_{t}^{2}$ ($Q^2=10~\mathrm{GeV}^2$ (dot green curve) and $Q^2=10000~\mathrm{GeV}^2$ (dashed red curve)) for the LHeC (left panel) and FCC-eh (right panel) COM energies as a function of $k^2_{t}$.
• Figure 4: The extracted ratio $\sigma_{\mathrm{dip}}(\mu_{r}^2/s,r)/\sigma_{0}$ as a function of $r$ at $x_{\mathrm{min}}$ is shown at $\mu^2=\mu_{r}^2$ and $\mu^2=\mu_{r}^2+4m_{t}^{2}$ for the LHeC and FCC-eh COM energies. LHeC: $\mu^2=\mu_{r}^2$ (dashed-dot red curve) and $\mu^2=\mu_{r}^2+4m_{t}^{2}$ (dot green curve); FCC-eh: $\mu^2=\mu_{r}^2$ (dashed blue curve) and $\mu^2=\mu_{r}^2+4m_{t}^{2}$ (solid black curve).
• Figure 5: The ratio $F_{L2}^{t}{\equiv}\frac{F_{L}^{t}}{F_{2}^{t}}(\mu^2,s,m_{t})$ as a function of $Q^2$ at $x_{\mathrm{min}}$ is shown at $\mu^2=Q^2$ (left panel) and $\mu^2=Q^2+4m_{t}^{2}$ (right panel) for the LHeC (black circles) and FCC-eh (red squares) COM energies with $\sqrt{s}=1.3$ and $3.5~\mathrm{TeV}$ respectively.