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REVIEW

High precision fundamental constants at the TeV scale

High Energy Physics - Phenomenology · Submitted 19 May 2014 · 263 references

Pith's verdict: A candid 2014 status report on α_s and m_t whose diagnosis is solid and whose proposed fix is demonstrated on the wrong data.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

  1. T0 AI review An AI read the paper and answered a fixed list of questions.
  2. T1 Audit Automatic checks that the references and files the paper relies on exist and match.
  3. T2 Compute The paper's code or calculations re-run with the same results.
  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

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arXiv ID1405.4781 (version 1)
Pith IDW36LWYBM, Pith's permanent record of this paper and its review
CitationA.H. Hoang, A. Huss, A.S. Papanastasiou, C. Schwinn, E. Shintani, J. Blumlein, J. Erler, J. Fuster, J. Piclum, J.R. Espinosa, K. Rabbertz, L. de la Cruz, M. Dowling, M. Mulders, M. Schulze, N. Zerf, P. Uwer, S. Alekhin, S. Dittmaier, S. Kluth, S. Moch, S. Weinzierl, X. Garcia i Tormo. "High precision fundamental constants at the TeV scale." arXiv:1405.4781 (2014). https://pith.science/paper/W36LWYBM
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Claim paper

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Referee report
The paper

The paper claims

The two most precisely quoted numbers in particle physics do not agree with themselves, and the report argues the quoted errors are too small.

The reading

This is the written record of a two-week workshop on the two Standard Model parameters that most often limit the accuracy of collider predictions: the strong coupling $alpha_s$ and the top-quark mass $m_t$. Its central message is a consistency warning rather than a new measurement. Individual determinations of $alpha_s$ now quote errors of well under one percent, but the values themselves scatter by more than those errors allow, from about 0.113 in deep-inelastic fits to about 0.121 from $tau$ decays, against a 2012 world average of $0.1184 pm 0.0007$. The top-quark mass has a different problem: the number experiments report, $173.34 pm 0.76$ GeV, is a parameter of a Monte Carlo generator, not a Lagrangian mass in any named renormalization scheme, and the translation to a well-defined short-distance mass carries an estimated uncertainty of order 1 GeV. A reader should care because both numbers feed almost every precision prediction at the LHC, and because the top mass enters the question of whether the electroweak vacuum is stable.

What carries the argument

Two pieces of machinery carry the argument. The first is the renormalization-group evolution of $alpha_s$: because a fixed-order extraction freezes the scale near the process, while a resummed extraction already runs the coupling inside the prediction, combining results quoted at $M_Z$ mixes measurements that used different couplings to get there. The report proposes replacing weighted averaging of evolved values with a global fit directly to the running, and demonstrates it on three jet data sets, obtaining $alpha_s(M_Z) = 0.1153 pm 0.0029$ with $chi^2/text{ndof} = 1.27$. The second is the scheme-translation chain for the top mass, running from the Monte Carlo parameter through the MSR mass $m_t^{MSR}(R)$ at a low scale $R$ to the pole mass or to $m_t(m_t)$, with the scale $R$ in the range 3 to 9 GeV spanning the conceptual uncertainty. The report tabulates this conversion at $O(alpha_s^3)$ and shows that the pole mass obtained depends strongly both on the order of perturbation theory and on the scale at which the conversion is performed.

Extended reading notes

Core claim

The report's load-bearing assertion is that the precision frontier on $alpha_s$ and $m_t$ has moved past the point where the quoted uncertainties are honest. For $alpha_s$, the evidence is a table of determinations that cluster into two groups: deep-inelastic and thrust analyses near $0.113$-$0.114$, and $Z$-decay, three-jet-rate, $tau$-decay and some lattice analyses near $0.118$-$0.121$. The report states the situation directly: individual determinations quote rather small errors, yet different determinations are at best marginally compatible within those errors. It identifies candidate sources, including uncalculated NNLO corrections to jet production in PDF fits (estimated at about $0.0015$ in $alpha_s(M_Z)$), heavy-flavour scheme ambiguities of about $0.001$, and power corrections at low $Q^2$. For the top mass, the report corrects a misreading it found circulating in experimental combinations: the statement that the Monte Carlo mass may differ from the pole mass by up to 1 GeV is a mistranslation of a claim about the translation to a low-scale short-distance mass, not the pole mass. It endorses the relation $m_t^{MC} = m_t^{MSR}(3^{+6}_{-2}~text{GeV})$, under which the Tevatron average corresponds to $m_t(m_t) = 163.0 pm 1.3$ GeV in the $overline{text{MS}}$ scheme.

Load-bearing premise

The top-mass interpretation rests on identifying the Monte Carlo mass parameter with the MSR short-distance mass at a scale in the range 3 to 9 GeV, a relation the report itself calls an estimate of conceptual uncertainty that is likely not calculable, because analytic control of the generator's shower and hadronization is out of reach.

Editorial extensions

If this is right

  • If the spread in $alpha_s$ reflects unquantified systematics rather than statistics, then the 2012 world average of $0.1184 pm 0.0007$ understates the true uncertainty, and every prediction that inherits that number inherits the understatement.
  • The combined Tevatron and LHC value $m_t = 173.34 pm 0.76$ GeV should be read as a Monte Carlo mass parameter, corresponding to $m_t(m_t) = 163.0 pm 1.3$ GeV in the $overline{text{MS}}$ scheme under the MSR relation.
  • On that reading, the measured top mass lies above the NNLO stability bound $M_t < 171.36 pm 0.46$ GeV, so the electroweak vacuum is metastable rather than absolutely stable up to the Planck scale.
  • A future $e^+e^-$ threshold scan could reach an uncertainty below 100 MeV on a threshold mass, an order of magnitude better than current direct measurements, provided the NNNLO threshold calculation now in progress is brought under control.
  • Measuring the ratio $R(rho_s)$ in $tbar{t}$ plus one jet, where a one percent change in $m_t$ produces a seventeen percent change in the observable near $rho_s approx 0.8$, offers a mass extraction that does not rely on the Monte Carlo mass identification.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The $alpha_s$ and $m_t$ problems are not independent: PDF fits and the $tbar{t}$ total cross section both consume $alpha_s(M_Z)$, so a shift of $0.001$ in the coupling propagates into the extracted pole mass at the few-hundred-MeV level, which is comparable to the translation uncertainty the report is worried about.
  • If the discrepancy is genuinely an observable-dependent effect rather than a statistical fluctuation, then a global fit directly to measured observables with one consistent running should return $chi^2/text{ndof}$ near one; the combined value of 1.27 quoted for the three jet data sets is a hint that the residual spread is not yet modelled rather than that the data are wrong.
  • The report's own recommended remedy, a standing working group that cross-checks competing analyses, is itself testable: if the spread shrinks after such comparisons, range averaging was over-conservative; if it persists, the individual errors were underestimated.
  • Since the low-scale MSR mass and the jet mass of the factorized invariant-mass distribution are conceptually the same object, a hadron-level comparison of a Monte Carlo generator against a resummed NLO+NLL calculation in the peak region would convert the 1 GeV conceptual uncertainty into a measured number.
Original abstract

This report summarizes the proceedings of the 2014 Mainz Institute for Theoretical Physics (MITP) scientific program on "High precision fundamental constants at the TeV scale". The two outstanding parameters in the Standard Model dealt with during the MITP scientific program are the strong coupling constant $\alpha_s$ and the top-quark mass $m_t$. Lacking knowledge on the value of those fundamental constants is often the limiting factor in the accuracy of theoretical predictions. The current status on $\alpha_s$ and $m_t$ has been reviewed and directions for future research have been identified.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,585 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.12 · human participants 0.03 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This report summarizes the proceedings of the 2014 Mainz Institute for Theoretical Physics (MITP) scientific program on "High precision fundamental constants at the TeV scale". The two outstanding parameters in the Standard Model dealt with during the MITP scientific program are the strong coupling constant $\alpha_s$ and the top-quark mass $m_t$. Lacking knowledge on the value of those fundamental constants is often the limiting factor in the accuracy of theoretical predictions. The current status on $\alpha_s$ and $m_t$ has been reviewed and directions for future research have been identified.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This report summarizes the proceedings of the 2014 Mainz Institute for Theoretical Physics (MITP) scientific program on "High precision fundamental constants at the TeV scale". background 0.64 0.21 0.03 asserted 0.97
s1 The two outstanding parameters in the Standard Model dealt with during the MITP scientific program are the strong coupling constant $\alpha_s$ and the top-quark mass $m_t$. background 0.67 0.09 0.09 asserted 1.00
s2 Lacking knowledge on the value of those fundamental constants is often the limiting factor in the accuracy of theoretical predictions. background 0.79 0.06 0.09 asserted 0.86
s3 The current status on $\alpha_s$ and $m_t$ has been reviewed and directions for future research have been identified. contribution 0.79 0.37 0.37 asserted 1.00

What kind of paper the classifier reports this is: review 0.96 · evidence from literature 0.96.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. 7: Differential thrust distribution normalised to σhad at different CM energies √ s (upper plots) and corre￾sponding relative corrections (lower plots). Jet event-shape observables in e +e − colliders At e +e − colliders the strong coupling constant can be determined upon measuring the 3-jet produc￾tion cross section and related event-shape observables. The QCD corrections, which are known to next-to-next-to-leading-order including dedicated resummations, comprise the major part of radiative corrections, but at this level of accuracy EW corrections are relevant as well. In Refs. [95,…
Figure 2. 1: Left: Dependence of the measured top mass observable on the transverse momentum of the hadronically decaying top [113]. Right: Dependence of the measured top mass observable on the transverse momentum of the tt¯pair [113]. LHC combination and World Average The ATLAS and CMS collaborations provided an updated combination of their most precise top mass measurements available as of September 2013 [101]. This combination relies on a proper understand￾ing of the systematic uncertainties assigned to the measurements by both experiments, and correlations between them. These uncertainties…

Figures reproduced from arXiv:1405.4781 by the authors.

References
How later papers used it

70 later papers cite it

Evidence: substantial. 43 of the citing papers share no author with it, and 7 of those carry a confident label from Pith's citation classifier.

Pith read 15 of the 89 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its data or values 3 of 7 papers with this label
How the literature uses it

70 arXiv papers cite this in 89 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 59 sentences without a confident label

Uses its data or values 7 papers
  • We refer the interested reader to [ref] and [ref] for more details; here we just mention our reference values: * for the strong coupling constant at $m_Z$, $α_s^(5)$: we take the present [ref] world average experimental value of the strong coupling constant at $m_Z$, $α_s^(5,exp)=0.1181$, and its associated $1 σ$ error, $Δα_s^(5,exp)=0.0013$; * for the Higgs mass, $m_H$: we take the combined ATLAS and CMS result (after Run1) at $1 σ$, $m_H^exp=125.09$ GeV and $Δm_H^exp =0.24$ GeV [ref] ; * for the top pole mass, $m_t$: we take the present combined Tevatron and LHC value of the MC top mass, $m_t^MC=(173.34 ±0.76$) GeV [ref] ; the uncertainty in the identification between the pole and MC top mass is currently estimated to be of order $200$ MeV [ref] (or even $1$ GeV for the most conservative groups [ref] ).

    Ruling out Critical Higgs Inflation? · Matching and running · 0.87

  • For the top quark we obtain $m_t(m_h)=(166.8±0.7)$ GeV starting from $m_t(m_t)=(163.4±0.7)$ GeV, which we have derived from the present world average obtained in [ref] using the conversion tables provided in [ref] .

    Exclusive Radiative Higgs Decays as Probes of Light-Quark Yukawa Couplings · Effective Higgs couplings · 0.85

  • For the 1$σ$ level, this is given by [ref] M_t=171.2±2.4GeV.If we assume that all the other parameters of the SM except for $M_t$ are fixed, we can find the scale $Λ_β$ where $β_λ_eff$ becomes zero as a function of $M_t$.

    Multiple Point Principle of the Standard Model with Scalar Singlet Dark Matter and Right Handed Neutrinos · Preliminary - Multiple Point Principle of SM - · 1.00

Compares with it 1 paper
Cites it as support 1 paper
  • Nonetheless, the MC mass definition can be translated to a theoretically well-defined short-distance mass definition at a low scale with an uncertainty currently estimated to be of the order of 1 GeV, see [ref] .

    Precision determination of the top-quark mass · Monte Carlo mass · 0.96

Cites it as background 18 papers
  • While initially only qualitative arguments for the interpretation problem for $m_t^MC$ were available [ref] , recently some quantitative studies appeared, which have shed some light on the numerical aspect of the issue.

    What is the Top Quark Mass? · Numerical Size of the Interpretation Problem · 0.85

  • The different mass definition can be related to each other in perturbation theory, see, e.g., Ref. [ref] and Ref. [ref] for a review of relations between these and other renormalization schemes such as the so-called MSR mass.

    Top-Quark Physics at the LHC · Top-quark mass determination · 0.92

  • Explicitly, the running top-quark mass is determined in the SM with the highest available precision from the experimentally measured pole mass [For a detailed discussion about the distinction between the pole and the measured top-quark mass we refer to [ref] .].

    O(\alpha_s^2) corrections to the running top-Yukawa coupling and the mass of the lightest Higgs boson in the MSSM · Introduction · 0.85

Discussion

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