A detailed study on the prospects for a $\mathrm{t\overline{t}}$ threshold scan in $\mathrm{e^+e^-}$ collisions

TL;DR

This work analyzes the prospects of a $t\overline{t}$ threshold scan at FCC-ee to precisely determine the top-quark mass $m_t$, width $\Gamma_t$, and Yukawa coupling $y_t$. It combines state-of-the-art NR-QCD predictions up to $\mathrm{N^3LO}$ with a realistic, detector-level assessment of the $WbWb$ cross section near threshold, including parametric and systematic uncertainties and correlations. The study forecasts an experimental precision of $m_t$ and $\Gamma_t$ of about $6.8$ MeV and $11.5$ MeV (in the PS scheme) with a theory uncertainty of roughly $35$ MeV and $25$ MeV at $\mathrm{N^3LO}$, and shows that a high-luminosity run at $\sqrt{s}=365$ GeV$ could determine $y_t$ to about $2\%$ (contingent on theory reaching $\sim 0.1\%$). The results highlight the importance of reducing theoretical uncertainties to match experimental precision and demonstrate FCC-ee’s potential to test SM predictions via the $m_W$–$m_t$ relationship and to constrain top-quark BSM couplings and SMEFT effects.

Abstract

A scan of the beam energy across the top quark pair ($\mathrm{t\overline{t}}$) production threshold is part of the program of future Higgs, top, and electroweak factory projects. In this paper, we provide projections for the achievable precision in the top quark mass ($m_\mathrm{t}$), width ($Γ_\mathrm{t}$), and Yukawa coupling ($y_\mathrm{t}$) at the electron-positron ($\mathrm{e^+e^-}$) stage of the Future Circular Collider (FCC-ee). The study includes a detailed assessment of parametric and systematic uncertainties, as well as a rigorous estimate of the effect of point-to-point correlations. We project that $m_\mathrm{t}$ and $Γ_\mathrm{t}$ can be determined with an experimental precision of about 6.8 and 11.5 MeV, respectively, when $m_\mathrm{t}$ is defined in the potential-subtracted (PS) scheme. The impact of theoretical uncertainties due to missing higher orders is found to be of about 35 (25) MeV on $m_\mathrm{t}$ ($Γ_\mathrm{t}$) at N$^3$LO in non-relativistic QCD. Therefore, improvements in the theoretical accuracy, which is an active area of development, are key to match the achievable experimental precision at a future $\mathrm{e^+e^-}$ collider. Finally, we explore the prospects for a measurement of $y_\mathrm{t}$ at FCC-ee via a dedicated run above the $\mathrm{t\overline{t}}$ production threshold.

Figures (13)

• Figure 1: Left: total parametric uncertainty in the SM prediction of $m_\mathrm{W}$ as a function of the input uncertainty in $m_\mathrm{t}$, for two different assumptions on $\alpha_\mathrm{EM}$ (solid and dashed curves). The solid diagonal line represents the contribution from $m_\mathrm{t}$ alone. The horizontal line represents the expected experimental precision in $m_\mathrm{W}$ at FCC-ee, while the vertical line indicates the expected precision in $m_\mathrm{t}$ after HL-LHC. Uncertainties in $\alpha_\mathrm{S}\xspace(m_\mathrm{Z}\xspace^2)$ ($10^{-4}$), $\alpha_\mathrm{EM}$ ($3\cdot 10^{-5}$ baseline, $10^{-5}$ improved Riembau:2025ppc), $m_\mathrm{Z}$ (1$\,\mathrm{keV}$), and $m_\mathrm{H}$ (3$\,\mathrm{MeV}$) according to recent projections for FCC-ee are assumed. Right: Comparison of indirect determination of $m_\mathrm{t}$ and $m_\mathrm{W}$ from the fit to EWPO (elliptical contours) and the projected precision from direct measurements (bands). We show in grey the projections for the HL-LHC, while in blue we show the FCC-ee ones. These results include the projected future intrinsic theory uncertainties in EWPO. The FCC-ee results in a scenario where theory calculations are improved so that these uncertainties become subdominant is shown in the (small) yellow ellipse. More details can be found in Appendix \ref{['app:EW_fit']}.
• Figure 2: Final-state distributions used in the fit of the WbWb production cross section at 345$\,\mathrm{GeV}$. Events with zero, one, and two or more b-tagged jets are shown in the upper, middle, and lower rows, respectively, for the semi-hadronic (left) and hadronic (right) final states. An integrated luminosity of 41$\,\mathrm{fb^{-1}}$ is assumed, which corresponds to the total luminosity of 410$\,\mathrm{fb^{-1}}$ for the $\mathrm{t\overline{t}}$ threshold scan equally split between 10 scan points.
• Figure 3: Left: effect of the initial state radiation (ISR) and of the FCC-ee beam energy spectrum (BES) on the $\mathrm{t\overline{t}}$ production threshold prediction at $\mathrm{N^3LO}$. Right: prediction for the $\mathrm{t\overline{t}}$ threshold scan at different orders in perturbation theory. In both cases, we assume $m_\mathrm{t}^\mathrm{PS}\xspace = 171.5\,\mathrm{GeV}\xspace$ and $\Gamma_\mathrm{t}\xspace = 1.33\,\mathrm{GeV}\xspace$.
• Figure 4: Left: dependence of the $\mathrm{WbWb}$ production cross section on $m_\mathrm{t}$, $\Gamma_\mathrm{t}$, $y_\mathrm{t}$, and $\alpha_\mathrm{S}$. The plot shows the ratio of the cross section calculated after varying each parameter to the one obtained using the reference values. The solid lines represent positive variations, while the dashed ones show the corresponding negative variations. Right: Fitted lineshape (solid line) as a function of the centre-of-mass energy, normalised to the reference cross section (horizontal dashed line). The fitted lineshape is derived by applying the parameters obtained in the 10-point fit to the full lineshape calculated with $\texttt{QQbar\_Threshold}$, taking correlations into account. The fit is performed to pseudo-data (markers) generated according to the pseudo-data cross section (curved dashed line) obtained with different parameters with respect to the reference cross section. The uncertainty in the pseudo-data (vertical bars) represents the experimental uncertainty in the $\mathrm{WbWb}$ cross section. The solid band corresponds to the post-fit uncertainty in the fitted cross section, all profiled uncertainties included.
• Figure 5: Left: two-dimensional confidence intervals in $m_\mathrm{t}$ and $\Gamma_\mathrm{t}$, corresponding to 68% (inner ellipse) and 95% (outer ellipse) confidence level (C.L.). Right: shift in fitted $m_\mathrm{t}$ and $\Gamma_\mathrm{t}$ as a function of the choice of the renormalisation scale in the $\mathrm{N^3LO}$ calculation, with respect to a reference value (starting point) of 170$\,\mathrm{GeV}$.