- CEPC: A Versatile Machine
- Higgs factory @~240 GeV, Diboson factory @~160 GeV, Z factory @~90 GeV.
- @~360 GeV it acts as a playground for Top quark precision measurements.
- Top quark mass measurements at LHC
- The "pole" mass is measured using top reconstruction at hadron colliders.
- Heavily relies on the performance of missing transverse energy (MET) and JER & JES.
- ATLAS+CMS combined measurements reached uncertainties of 330 MeV.
- HL-LHC projection anticipates a precision of 200 MeV.
- Fundamentally limited by systematic uncertainties (e.g., $\Lambda_{\text{QCD}}$ ambiguity).
F. Bedeschi
ATLAS-CONF-2023-066, CMS-PAS-TOP-22-001 for Run1
New results such as CMS Eur. Phys. J. C 83 (2023) 963 with 370 MeV using Run2
New results such as CMS Eur. Phys. J. C 83 (2023) 963 with 370 MeV using Run2
- 1. Baseline cross-section:
Calculated at N$^3$LO precision usingQQbar_threshold (v2.2.0). - 2. Nominal Reference Setting:
$$ \begin{aligned} m_t^{\text{PS}} &= 171.5 \text{ GeV}, & \alpha_s(m_Z) &= 0.1184 \\[1ex] \Gamma_t &= 1.33 \text{ GeV}, & y_t &= 1.0 \end{aligned} $$
- 3. Initial-State Radiation (ISR):
ISR photons carry away beam energy, reducing the effective cross-section. (Included at Leading Logarithmic precision). - 4. Luminosity Spectrum (LS) at CEPC:
Integrated via a Gaussian function reflecting CEPC expected beam energy spread: $$ \sigma_{\text{LS}} \approx 0.51 \text{ GeV} \times (\sqrt{s} / 360 \text{ GeV})^2 $$
Fig 1. The $t\bar{t}$ cross-section at N$^3$LO with ISR and LS effects.
- 1. Fisher Information Definition:
- Objective: Quantify sensitivity to physical parameters $\theta \in \{\mt, \wt, \alphas, \yt\}$.
- Statistical Model: Observed count $n$ follows a Gaussian $G(n \mid n_0, \sqrt{n_0})$.
- Expected Yield: $n_0 = \mathcal{L}\sigma_0$ ($\mathcal{L}$: luminosity, $\sigma_0$: theoretical cross-section).
$$ I(\sqrt{s}) = \int \left( \frac{\partial \log G(n \mid n_0, \sqrt{n_0})}{\partial\theta} \right)^{2} \times G(n \mid n_0, \sqrt{n_0}) \, dn $$ - 2. Sensitivity Peaks → Scan
Points (Fig 2):
- The threshold region maximizes sensitivity to $\mt$.
- The cross-section peak is most sensitive to $\wt$ (broadens the resonance), $\alphas$ and $\yt$ (govern overall rate).
- To capture all information peaks → 5-point scan:
\(\displaystyle \sqrt{s} = \{342.0,\ \underbrace{342.5}_{\mt},\ 343.0,\ \underbrace{343.5}_{\alphas,\, \yt},\ \underbrace{344.0}_{\wt}\} \text{ GeV} \) - 3. Luminosity
Scenarios:
- BASE: 56 $\text{fb}^{-1}$ / point (Total 280 $\text{fb}^{-1}$, 1 yr × 2 IPs)
- EXT: 84 $\text{fb}^{-1}$ / point (Total 420 $\text{fb}^{-1}$, 50% upgrade)
Fig 2. Normalized Fisher information for the four parameters.
- Target Signal Topologies:
- Full-hadronic: $t\bar{t} \to bq\bar{q}'\bar{b}q''\bar{q}'''$ (BR = 44.2%)
- Semi-leptonic: $t\bar{t} \to bq\bar{q}'\bar{b}l\nu$, $l \in \{e, \mu\}$ (BR = 29.9%)
- Excluding $W \to \tau\nu$ channels, as the multiple neutrinos from $\tau$ decays severely degrade the kinematic fit resolution.
- MC Generation Chain:
- Signal XS Calculation: N$^3$LO precision using
QQbar_threshold 2.2.0. - Event Generation (Sig & Bkg):
MG5_aMC@NLO 3.6.3with ISR effects enabled. - Shower & Hadronization:
PYTHIA 8.3. - Note: The $q\bar{q}$ background represents $q = u, d, s, c$.
- Signal XS Calculation: N$^3$LO precision using
Tab 1. Cross-sections of signal and background processes.
- Pre-selection Requirements:
- Semi-leptonic: 1 isolated lepton ($E > 12$ GeV, $\text{IPS} < 3.3$) + 4 jets ($\geq 2$ b-tags).
- Full-hadronic: Lepton veto + 6 jets ($\geq 2$ b-tags).
- Event shape variables cuts:
- Jet clustering bounds ($y_{ij}$) and global shapes ($S, T$) strongly suppress backgrounds with fewer or softer jets (e.g. $b\bar{b}$, $q\bar{q}$, multi-bosons).
- After these 8 criteria, total remaining backgrounds (excluding single-top) are heavily reduced to $\mathbf{\lesssim 1\text{ fb}}$ in both channels.
| Variable / Cut | Semi-leptonic | Full-hadronic |
|---|---|---|
| $\log y_{34}$ | $> -3.0$ | $> -2.0$ |
| $\log y_{45}$ | $> -4.3$ | $> -2.5$ |
| $\log y_{56}$ | - | $> -3.0$ |
| Total PFOs ($N_{\text{PFO}}$) | $\geq 40$ | $\geq 50$ |
| Charged PFOs ($N_{\text{PFO}}^{\text{charged}}$) | $\geq 14$ | $\geq 28$ |
| Max momentum [GeV] | $< 86$ | $< 65$ |
| Visible energy $E_{\text{vis}}$ [GeV] | $[212, 318]$ | $[262, 359]$ |
| Sphericity ($S$) | $> 0.34$ | $> 0.42$ |
| Thrust ($T$) | $< 0.87$ | $< 0.82$ |
Tab 2. Optimized multi-dimensional selection criteria for the semi-leptonic and
full-hadronic channels.
- Two-dimensional Likelihood Scans:
- Full systematic uncertainties except theoretical $t\bar{t}$ XS are profiled.
- BASE scenario: 56 fb$^{-1}$/pt (total 280 fb$^{-1}$).
- Precision (BASE):
$\Delta m_t$: stat. = ±5.6 MeV, total
= ±7.5 MeV
$\Delta\Gamma_t$: stat. = ±18.0 MeV, total = ±19.4 MeV
$\delta\alpha_S = 0.00143$, $\;\delta y_t = 0.197$
$\Delta\Gamma_t$: stat. = ±18.0 MeV, total = ±19.4 MeV
$\delta\alpha_S = 0.00143$, $\;\delta y_t = 0.197$
Fig 3. 2D likelihood scan over $m_t$ and
$\Gamma_t$, BASE scenario
(56 fb$^{-1}$/pt).
- Two-dimensional Likelihood Scans:
- Full systematic uncertainties except theoretical $t\bar{t}$ XS are profiled.
- EXT scenario: 84 fb$^{-1}$/pt (420 fb$^{-1}$ total), 50% lumi upgrade.
- Precision (EXT):
$\Delta m_t$: stat. = ±4.6 MeV, total
= ±6.7 MeV
$\Delta\Gamma_t$: stat. = ±14.6 MeV, total = ±16.2 MeV
$\delta\alpha_S = 0.00116$, $\;\delta y_t = 0.160$
$\Delta\Gamma_t$: stat. = ±14.6 MeV, total = ±16.2 MeV
$\delta\alpha_S = 0.00116$, $\;\delta y_t = 0.160$
Fig 4. 2D likelihood scan over $m_t$ and
$\Gamma_t$, EXT scenario
(84 fb$^{-1}$/pt).
- To distinguish between semi-leptonic (sl) and fully hadronic (hh) events, the number of isolated leptons in the event is a key discriminant.
- Leptons with E > 12 GeV and IPS < 3.3 are selected as isolated leptons.
- The distributions shown below are based on $W^+$ decays as a representative example; $W^-$ decays exhibit identical kinematic trends as expected from charge symmetry.
e$^+$ Energy
e$^+$ IPS
$\mu^+$ Energy
$\mu^+$ IPS
- In the $e^+e^- k_T$ algorithm, the distance measure is defined as $d_{ij}=2\min(E_i^2,E_j^2)(1-\cos\theta_{ij})$, and the dimensionless clustering cost is $y_{ij} = d_{ij} / s$.
- Strong Discriminating Power: Signal events ($t\bar{t}$) contain more Born-level partons and hard gluon emissions, incurring significantly higher clustering costs (e.g. $y_{34}$) when clustering to fewer jets. This allows for an effective separation of signal from multi-boson and $q\bar{q}$ backgrounds.
$\log y_{34}$ distribution in the sl
channel
$\log y_{34}$ distribution in the hh
channel
- Sphericity ($S$): Calculated from the sphericity tensor $S^{\alpha\beta} = \left(\sum_i p_i^\alpha p_i^\beta / |\mathbf{p}_i|\right) / \left(\sum_i |\mathbf{p}_i|\right)$ with eigenvalues $\lambda_1 \geq \lambda_2 \geq \lambda_3$. Defined as $S = \frac{3}{2}(\lambda_2+\lambda_3) \to 1$ for sphere-like events ($t\bar{t}$), distinguishing them from pencil-like topologies (dijet, diboson, $\to 0$).
- Thrust ($T$): Defined as $T = \max_{|\mathbf{n}|=1} [\sum_i |\mathbf{p}_i \cdot \mathbf{n}| / \sum_i |\mathbf{p}_i|]$, it ranges from $0.5$ (isotropic events) to $1$ (back-to-back topologies).
- (Both distributions shown below take the sl channel as a representative example.)
Sphericity ($S$)
Thrust ($T$)
- Energy scale factor $s_f$ in kinematic fit:
- The kinematic fit introduces an energy scale factor $s_f$ for each jet to absorb detector resolution effects.
- Taking the fully hadronic (hh) channel as an example, the fitted $s_f$ distribution peaks sharply at $s_f \approx 1$, confirming that the detector energy response is well-calibrated.
- A narrow spread around unity indicates that the kinematic constraints are functioning as designed, with minimal bias introduced by the fit.
Energy scale factor $s_f$ distribution
for fully hadronic $t\bar{t}$ events.
- Comparison with FCC-ee latest result (arXiv:2503.18713):
- At comparable luminosity (EXT), the CEPC projected $m_t$ precision is highly consistent with FCC-ee.
- The $\Gamma_t$ precision is worse than FCC-ee, mainly from
theory:
- CEPC: $^{+0.0}_{-79.9}$ MeV vs. FCC-ee: ~$-$25 MeV.
- $\Gamma_t$ is extracted from the width of the threshold peak — scale variation's downward shift compresses the peak shape, impacting $\Gamma_t$ far more than $m_t$.
- This work takes a conservative full envelope (×0.5/×2), while FCC-ee applies a more refined scale decomposition → smaller envelope.
- Both studies are dominated by the same N$^3$LO theoretical XS uncertainty bottleneck.
| Source | $\Delta m_t$ [MeV] | $\Delta\Gamma_t$ [MeV] | ||
|---|---|---|---|---|
| BASE | EXT | BASE | EXT | |
| Statistics ★ | ±5.6 | ±4.6 | ±18.0 | ±14.6 |
| $\alpha_S$ | ±2.4 | ±3.1 | ||
| $y_t$ | ±4.2 | ±5.9 | ||
| Lumi / BE / LS / $b$-tag | sub-dom. | sub-dom. | ||
| Total ★ | ±7.5 | ±6.7 | ±19.4 | ±16.2 |
| Theory ★ | ${}^{+1.3}_{-32.9}$ | ${}^{+0.0}_{-79.9}$ | ||
Tab. 3. CEPC uncertainty budget. ★ =
comparison rows.
FCC-ee projected
precision (2503.18713)