Recognition: 2 theorem links
· Lean TheoremMeasurement of the top-quark mass using decays with a J/psi meson at sqrt{s}=13 TeV with the ATLAS detector
Pith reviewed 2026-05-17 04:34 UTC · model grok-4.3
The pith
The top-quark mass is measured to be 172.17 GeV with a total uncertainty of 1.56 GeV using the invariant mass of a lepton and J/ψ from top decays.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The top-quark mass is measured to be m_top = 172.17 ± 0.80 (stat) ± 0.81 (syst) ± 1.07 (recoil) GeV, with a total uncertainty of 1.56 GeV, by performing an unbinned maximum-likelihood fit to the m(ℓ μ⁺μ⁻) distribution in top-quark decays that produce an isolated lepton and a J/ψ meson reconstructed in its μ⁺μ⁻ mode.
What carries the argument
The invariant mass m(ℓ μ⁺μ⁻) of the isolated lepton from the W boson decay and the non-isolated muon pair from the J/ψ decay of a b-hadron, which is sensitive to the top-quark mass through the decay kinematics.
If this is right
- The measurement supplies an independent top-quark mass value obtained from a decay channel that uses the J/ψ signature.
- The largest single uncertainty component of 1.07 GeV is traced directly to the choice of gluon-recoil modeling in the parton shower.
- The method can be repeated with larger integrated luminosities to reduce the statistical and certain systematic contributions.
- The result demonstrates that the m(ℓ μ⁺μ⁻) observable can be used for precision extraction of the top-quark mass.
Where Pith is reading between the lines
- If future simulations reduce the recoil modeling uncertainty, the overall precision of this J/ψ-based method could improve relative to conventional approaches.
- Agreement of this mass value with results from other reconstruction techniques would provide a cross-check on parton-shower modeling assumptions.
- The same kinematic sensitivity could be tested in other heavy-flavor meson decays within top-quark events to expand the set of observables.
Load-bearing premise
The analysis assumes that variations in the dipole parton shower gluon-recoil scheme adequately capture the dominant modeling uncertainty in top-quark decays.
What would settle it
A shift larger than 1.07 GeV in the extracted top-quark mass when an alternative gluon-recoil scheme is used in the parton shower simulation would indicate that the recoil uncertainty is underestimated.
read the original abstract
The top-quark mass is measured using top-quark decays producing an isolated lepton and $J/\psi$ meson reconstructed in its $\mu^+\mu^-$ decay mode. The data sample was recorded with the ATLAS detector in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13$ TeV during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb$^{-1}$. The measurement is based on the invariant mass $m(\ell \mu^+\mu^-)$ of the system made of the isolated lepton $\ell$ from the $W$ boson decay and the non-isolated $\mu^+\mu^-$ pair from a $J/\psi$ decay of a $b$-hadron, exploiting its sensitivity to the top-quark mass. An unbinned maximum-likelihood fit to the $m(\ell \mu^+\mu^-)$ distribution is performed to extract the top-quark mass. The top-quark mass is measured to be $m_{top} = 172.17 \pm 0.80 (stat) \pm 0.81 (syst) \pm 1.07 (recoil)$ GeV, with a total uncertainty of 1.56 GeV. The third uncertainty arises from changing the dipole parton shower gluon-recoil scheme used in top-quark decays.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports a measurement of the top-quark mass in 140 fb^{-1} of ATLAS proton-proton collision data at √s = 13 TeV. The analysis reconstructs the invariant mass m(ℓ μ⁺μ⁻) of an isolated lepton from W-boson decay and a μ⁺μ⁻ pair from J/ψ decay of a b-hadron in top-quark decays. An unbinned maximum-likelihood fit to this distribution extracts m_top = 172.17 ± 0.80 (stat) ± 0.81 (syst) ± 1.07 (recoil) GeV, with the recoil component obtained by varying the dipole parton-shower gluon-recoil scheme.
Significance. If the central result holds, the measurement supplies an independent top-mass determination whose dominant sensitivity arises from the b-hadron decay chain rather than from the top-quark decay kinematics alone. The explicit separation of statistical, systematic, and recoil uncertainties, together with the use of a standard unbinned fit, strengthens the result. The total uncertainty of 1.56 GeV is competitive for this channel and could provide a useful cross-check once modeling uncertainties are fully quantified.
major comments (1)
- [Systematic uncertainties and modeling section] The recoil uncertainty of 1.07 GeV is the largest quoted component and is obtained solely by toggling the dipole parton-shower gluon-recoil scheme. This single variation may not envelope correlated modeling effects in b-hadron fragmentation, J/ψ polarization, or non-perturbative hadronization parameters that also shift the m(ℓ μ⁺μ⁻) distribution. A more complete set of variations (or a dedicated envelope) is required to substantiate that the total uncertainty is not underestimated.
minor comments (2)
- [Abstract] The abstract states the integrated luminosity and centre-of-mass energy but could explicitly note the Run-2 data-taking period for immediate context.
- [Results section] Notation for the three uncertainty components (stat, syst, recoil) is clear in the abstract but should be repeated verbatim in the first results paragraph to avoid any ambiguity.
Simulated Author's Rebuttal
We thank the referee for the careful review of our manuscript and the constructive comment on the treatment of modeling uncertainties. We address the major comment in detail below and indicate the planned revisions.
read point-by-point responses
-
Referee: [Systematic uncertainties and modeling section] The recoil uncertainty of 1.07 GeV is the largest quoted component and is obtained solely by toggling the dipole parton-shower gluon-recoil scheme. This single variation may not envelope correlated modeling effects in b-hadron fragmentation, J/ψ polarization, or non-perturbative hadronization parameters that also shift the m(ℓ μ⁺μ⁻) distribution. A more complete set of variations (or a dedicated envelope) is required to substantiate that the total uncertainty is not underestimated.
Authors: We thank the referee for highlighting this aspect of the uncertainty evaluation. The variation of the dipole parton-shower gluon-recoil scheme is specifically chosen as it directly modifies the momentum balance in the top-quark decay, thereby shifting the kinematics of the b-hadron and the resulting m(ℓ μ⁺μ⁻) distribution. Effects from b-hadron fragmentation, J/ψ polarization, and non-perturbative hadronization are addressed through dedicated systematic variations of the corresponding parameters in the Monte Carlo simulation; their contributions are incorporated into the 0.81 GeV systematic uncertainty. The recoil uncertainty is quoted separately to isolate the impact of this particular parton-shower modeling choice. We have verified internally that the chosen variation provides a conservative envelope for the dominant correlated shifts relevant to this observable. To address the referee's concern and improve clarity, we will expand the discussion in the systematic uncertainties section of the revised manuscript with additional justification for the envelope and explicit statements on how the variations are combined. revision: partial
Circularity Check
Direct extraction from data fit with external modeling variations
full rationale
The top-quark mass is extracted via an unbinned maximum-likelihood fit directly to the observed m(ℓ μ⁺μ⁻) distribution in 140 fb⁻¹ of collision data. The central value and statistical uncertainty arise from this fit to real events rather than from any internal equation or prior measurement. The dominant recoil uncertainty is obtained by varying an external parton-shower scheme choice in simulation; this is an external modeling variation, not a redefinition or self-referential fit that forces the result by construction. No self-citation, ansatz, or uniqueness theorem is invoked to justify the central claim, and the analysis chain remains independent of the fitted output itself.
Axiom & Free-Parameter Ledger
axioms (2)
- domain assumption Top quark decays via t → Wb with subsequent b-hadron formation and J/ψ → μ⁺μ⁻ decay occur as described by the Standard Model.
- domain assumption The dipole parton shower gluon-recoil scheme provides a reasonable model for final-state radiation in top decays.
Lean theorems connected to this paper
-
IndisputableMonolith/Foundation/RealityFromDistinction.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
An unbinned maximum-likelihood fit to the m(ℓ μ⁺μ⁻) distribution is performed to extract the top-quark mass. The top-quark mass is measured to be m_top = 172.17 ± 0.80 (stat) ± 0.81 (syst) ± 1.07 (recoil) GeV
-
IndisputableMonolith/Cost/FunctionalEquation.leanwashburn_uniqueness_aczel unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
The third uncertainty arises from changing the dipole parton shower gluon-recoil scheme used in top-quark decays.
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
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discussion (0)
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