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Branching ratios and spectral functions of tau decays: final ALEPH measurements and physics implications

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the ALEPH Collaboration

High Energy Physics - Experiment · Submitted 28 Jun 2005 · 104 references

Pith's verdict: A solid, honestly documented final ALEPH tau paper; the alpha_s headline is credible but the fake-photon correction and the hand-set KKπ axial fraction are the two places to press.

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Citationthe ALEPH Collaboration. "Branching ratios and spectral functions of tau decays: final ALEPH measurements and physics implications." arXiv:hep-ex/0506072 (2005). https://pith.science/paper/W47RYBYH
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The paper

The paper claims

The full ALEPH tau sample yields a consistent set of tau branching ratios and spectral functions, and from them a low-scale strong coupling that runs to the Z mass.

The reading

The paper asks whether the full ALEPH tau sample can be converted into one consistent description of how the tau decays, with enough control over photons and fake photons to trust the result. It measures branching fractions for two leptonic and eleven hadronic topologies, corrects them for kaon, $��eta$ and $��omega$ contributions, and extracts spectral functions for the dominant hadronic modes. Those spectral functions feed a QCD analysis whose output is $��alpha_s(m_��tau^2)=0.340��pm0.005_{��rm exp}��pm0.014_{��rm th}$, evolving to $��alpha_s(M_Z^2)=0.1209��pm0.0018$. The payoff is a low-energy determination of the strong coupling that agrees with the Z-width value, so the running of QCD is tested across a wide energy range; the same data also sharpen tests of lepton universality, isospin in $a_1$ decays, and the separation of vector and axial-vector contributions.

What carries the argument

The machinery is the set of hadronic spectral functions $v_1(s)$, $a_1(s)$, and $a_0(s)$—normalized invariant-mass distributions of vector and axial-vector tau final states divided by the tau-decay kinematic factor—together with a corrected efficiency matrix that maps observed decay classes to true final states. The spectral functions carry the hadronic information into the QCD analysis, while the efficiency matrix, corrected for particle identification, photon efficiency, conversions, nuclear interactions, tracking, and fake photons, carries the detector response into every branching ratio.

Extended reading notes

Core claim

The central claim is that the full LEP-1 ALEPH data set, after data-driven corrections for photon identification and fake-photon rates, gives a complete and mutually consistent set of tau branching ratios covering 22 non-strange and 11 strange hadronic modes, together with spectral functions for the dominant hadronic channels. From those spectral functions the authors extract $��alpha_s(m_��tau^2)=0.340��pm0.005_{��rm exp}��pm0.014_{��rm th}$ and run it to $��alpha_s(M_Z^2)=0.1209��pm0.0018$. They present the agreement with the direct Z-width determination as the most accurate test to date of asymptotic freedom in QCD.

Load-bearing premise

The load-bearing premise is that the excess fake photons in data can be modelled as a random removal of a fixed fraction of simulated fake photons in each decay class, so that the corrected efficiency matrix maps observed classes to true tau final states.

Editorial extensions

If this is right

  • If the result is correct, $��alpha_s(m_��tau^2)$ provides a precise low-energy anchor for the strong coupling, and its evolution to $M_Z$ is a quantitative confirmation of the QCD running predicted by asymptotic freedom.
  • The complete exclusive branching ratios and spectral functions supply improved inputs for hadronic vacuum-polarization calculations, including the muon anomalous magnetic moment, though the paper itself flags a $2.9��sigma$ tau-versus-$e^+e^-$ discrepancy in the $��pi��pi^0$ channel.
  • The measured ratio $B_{3��pi}/B_{��pi2��pi^0}=0.979��pm0.018$ supports the expected isospin relation in $a_1$ decays, with the small breaking coming from charged-versus-neutral pion masses.
  • The separated vector and axial-vector rates, $R_{��tau,V}=1.787��pm0.011��pm0.007$ and $R_{��tau,A}=1.695��pm0.011��pm0.007$, constrain the size of nonperturbative contributions in the non-strange hadronic tau width.

Reading between the lines

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

  • A useful independent check would be to repeat the fake-photon correction with a multiplicity distribution measured from a different calorimeter observable or control sample, because the branching ratios and spectral normalizations all pass through that correction.
  • If the tau-versus-$e^+e^-$ $��pi��pi^0$ discrepancy persists, the same spectral functions can help decide whether the problem lies in the $e^+e^-$ radiative corrections, in isospin-breaking corrections, or in one of the two data sets.
  • A future larger tau sample would shrink the experimental error on $��alpha_s(m_��tau^2)$, but the quoted theoretical error would then dominate, so the limiting issue would become the treatment of nonperturbative terms rather than statistics.
Original abstract

The full LEP-1 data set collected with the ALEPH detector at the $Z$ pole during 1991-1995 is analysed in order to measure the $\tau$ decay branching fractions. Extensive systematic studies are performed, in order to match the large statistics of the data sample corresponding to over 300 000 measured and identified $\tau$ decays. Branching fractions are obtained for the two leptonic channels and eleven hadronic channels defined by their respective numbers of charged particles and $\pi^0$'s. Using previously published ALEPH results on final states with charged and neutral kaons, corrections are applied to the hadronic channels to derive branching ratios for exclusive final states without kaons. Thus the analyses of the full LEP-1 ALEPH data are combined to yield a complete description of $\tau$ decays, encompassing 22 non-strange and 11 strange hadronic modes. Some physics implications of the results are given, in particular related to universality in the leptonic charged weak current, isospin invariance in $a_1$ decays, and the separation of vector and axial-vector components of the total hadronic rate. Finally, spectral functions are determined for the dominant hadronic modes and updates are given for several analyses. These include: tests of isospin invariance between the weak charged and electromagnetic hadronic currents, fits of the $\rho$ resonance lineshape, and a QCD analysis of the nonstrange hadronic decays using spectral moments, yielding the value $\alpha_s(m^2_\tau) = 0.340 \pm 0.005_{\rm exp} \pm 0.014_{\rm th}$. The evolution to the $Z$ mass scale yields $\alpha_s(M_Z^2) = 0.1209 \pm 0.0018$. This value agrees well with the direct determination from the $Z$ width and provides the most accurate test to date of asymptotic freedom in the QCD gauge theory.

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, 8,001 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The full LEP-1 data set collected with the ALEPH detector at the $Z$ pole during 1991-1995 is analysed in order to measure the $\tau$ decay branching fractions. Extensive systematic studies are performed, in order to match the large statistics of the data sample corresponding to over 300 000 measured and identified $\tau$ decays. Branching fractions are obtained for the two leptonic channels and eleven hadronic channels defined by their respective numbers of charged particles and $\pi^0$'s. Using previously published ALEPH results on final states with charged and neutral kaons, corrections are applied to the hadronic channels to derive branching ratios for exclusive final states without kaons. Thus the analyses of the full LEP-1 ALEPH data are combined to yield a complete description of $\tau$ decays, encompassing 22 non-strange and 11 strange hadronic modes. Some physics implications of the results are given, in particular related to universality in the leptonic charged weak current, isospin invariance in $a_1$ decays, and the separation of vector and axial-vector components of the total hadronic rate. Finally, spectral functions are determined for the dominant hadronic modes and updates are given for several analyses. These include: tests of isospin invariance between the weak charged and electromagnetic hadronic currents, fits of the $\rho$ resonance lineshape, and a QCD analysis of the nonstrange hadronic decays using spectral moments, yielding the value $\alpha_s(m^2_\tau) = 0.340 \pm 0.005_{\rm exp} \pm 0.014_{\rm th}$. The evolution to the $Z$ mass scale yields $\alpha_s(M_Z^2) = 0.1209 \pm 0.0018$. This value agrees well with the direct determination from the $Z$ width and provides the most accurate test to date of asymptotic freedom in the QCD gauge theory.

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 The full LEP-1 data set collected with the ALEPH detector at the $Z$ pole during 1991-1995 is analysed in order to measure the $\tau$ decay branching fractions. method 0.63 0.93 0.03 asserted 0.99
s1 Extensive systematic studies are performed, in order to match the large statistics of the data sample corresponding to over 300 000 measured and identified $\tau$ decays. method 0.96 0.93 0.02 asserted 1.00
s2 Branching fractions are obtained for the two leptonic channels and eleven hadronic channels defined by their respective numbers of charged particles and $\pi^0$'s. result 0.92 0.94 0.06 asserted 1.00
s3 Using previously published ALEPH results on final states with charged and neutral kaons, corrections are applied to the hadronic channels to derive branching ratios for exclusive final states without kaons. method 0.96 0.82 0.03 asserted 1.00
s4 Thus the analyses of the full LEP-1 ALEPH data are combined to yield a complete description of $\tau$ decays, encompassing 22 non-strange and 11 strange hadronic modes. contribution 0.50 0.91 0.15 asserted 1.00
s5 Some physics implications of the results are given, in particular related to universality in the leptonic charged weak current, isospin invariance in $a_1$ decays, and the separation of vector and axial-vector components of the total hadronic rate. interpretation 0.99 0.81 0.12 asserted 0.79
s6 Finally, spectral functions are determined for the dominant hadronic modes and updates are given for several analyses. contribution 0.53 0.94 0.07 asserted 1.00
s7 These include: tests of isospin invariance between the weak charged and electromagnetic hadronic currents, fits of the $\rho$ resonance lineshape, and a QCD analysis of the nonstrange hadronic decays using spectral moments, yielding the value $\alpha_s(m^2_\tau) = 0.340 \pm 0.005_{\rm exp} \pm 0.014_{\rm th}$. result 0.59 0.91 0.14 asserted 0.99
s8 The evolution to the $Z$ mass scale yields $\alpha_s(M_Z^2) = 0.1209 \pm 0.0018$. result 1.00 0.91 0.16 asserted 1.00
s9 This value agrees well with the direct determination from the $Z$ width and provides the most accurate test to date of asymptotic freedom in the QCD gauge theory. interpretation 0.99 0.83 0.36 asserted 0.99

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from analysis of existing data 0.76.

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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. Determination of the remaining Bhabha contribution in the fi
Figure 2. Determination of the remaining e +e − → µ +µ − contribution in the final µ-µ sample for 1994-1995 data using the kinematically calculated energy of a hypothetical photon emitted along one of the e ± momenta: (a) data, (b) τ τ simulation, and (c) e +e − → µ +µ − simulation. The solid line represents a fit of the data with the relative normalization of the τ τ and µ-pair contributions left free. 12
Figure 3. Determination of the remaining γ ∗γ ∗ → µ +µ − contribution in the final µ-µ sample for 1994-1995 data: acoplanarity angle distributions for (a) data, (b) τ τ simulation, and (c) e +e − → (e +e −)µ +µ − simulation. The solid line represents a fit of the data with the relative normalization of the τ τ and γγ-induced µ-pair contributions left free. 13
Figure 4. Hadron identification efficiency and misidentification probab
Figure 5. Lepton identification efficiencies obtained from the
Figure 6. Energy spectra of reconstructed photons in simulated
Figure 7. Genuine-to-fake photon ratio as a function of photon en
Figure 8. Reference distributions for fake photons (histogram) a
Figure 9. Correlations between R1 and R2, and between R1 and R3, for photons with energy below 3 GeV. (1) R3 is used instead of R2. This change was made because of the large correlation between R2 and R1 for genuine photons, whereas the likelihood method ignores correlations between the discriminating variables. Also, R3 contributes some additional discriminating power against fake photons (see
Figure 10. Comparison of the reference distributions for genuine p
Figure 11. Comparison of the reference distributions in the barrel
Figure 12. Comparison of the reference distributions in the barrel
Figure 13. Comparison of R1, R3 and T distributions in data (points) and simulation (histogram) for photons with energy between 3.0 and 6.0 GeV, in ECAL barrel and endcap parts. 5.2.4 Total set of reference distributions Fine granularity is introduced when needed in the reference distributions. Due to the observed strong energy dependence of some distributions, more energy bins are considered: for genuine photons 7 bins (0.3-0.5, 0.5-1.0, 1.0-1.5, 1.5-2.0, 2.0-2.5, 2.5-4.0, above 4 GeV) and for fake photons 4 bins (0.3-0.5, 0.5-1.0, 1.0-2.0, above 2 GeV). Different distributions are set up…
Figure 14. Comparison of the data probability distributions of a clust
Figure 15. Reconstructed π 0 mass (upper plot) and resolution (lower plot) after photon energy and resolution calibration. Good agreement between data and simulation is observed. ECAL information as for a neutral cluster. This method is reliable only above 2 GeV because the electron track curvature in the magnetic field causes the shower to be ill￾pointing to the interaction region. The results are then extrapolated to lower energies. The bias introduced by the extrapolation is studied with the simulation comparing the true and the extrapolated energies, and the same correction is applied to…
Figure 16. Comparison of the distributions of the conversion point r
Figure 17. Comparison of the π 0 mass distributions of unresolved π 0 ’s between data (points) and simulation (histogram) in different energy ranges. 30
Figure 18. Energy spectra of observed photons in data (error ba
Figure 19. Fit to the photon probability distribution in observed
Figure 20. Relative photon efficiency in data and Monte Carlo for 1991
Figure 21. Comparison of dc distributions for high energy photons (Eγ > 3 GeV ) in data (points) and in Monte Carlo (histogram) for 1991-1993 and 1994-1995 data sets. The distributions are normalized to each other for dc > 8 cm. of efficiency depends on the simulation of hadronic interactions in ECAL, which can be checked against data by comparing the actual dc distributions
Figure 22. Ratio of converted photon energy spectra in data and M
Figure 23. Comparison of hadron misidentification in multihadronic fina
Figure 24. Measured dE/dx as a function of momentum for all (good and bad) tracks in the selected τ sample: the proton band from nuclear interactions is clearly observed, and predicted by the simulation. 48
Figure 25. Comparison of photon identification probability distributio
Figure 26. Comparison of Dij distributions in data (points) and simulation (dark histogram) for 1991-1993 and 1994-1995 data sets. The light histograms show the distribution before fake photon correction. 51
Figure 27. Comparison of measured energy spectra of bremsstra
Figure 28. Comparison of the angle between produced radiative pho
Figure 29. Comparison of the numbers of selected τ decays with secondary interactions for each channel (see
Figure 30. Comparison of the distributions of the maximum
Figure 31. Comparison of electron momentum spectra in data (point
Figure 32. Comparison of muon momentum spectra in data (points) a
Figure 33. Comparison of charged hadron momentum spectra in dat
Figure 34. Comparison of photon energy spectra for all
Figure 35. Comparison of photon energy spectra for all
Figure 36. Comparison of π 0 energy spectra for all τ events in data (points) and simulation (histogram) after all the corrections for 1991-1993 data set. The dotted line shows the simulated distribution before correction and the shaded histogram is the contribution of non-τ background. 65
Figure 37. Comparison of π 0 energy spectra for all τ events in data (points) and simulation (histogram) after all the corrections for 1994-1995 data set. The dotted line shows the simulated distribution before correction and the shaded histogram is the contribution of non-τ background. 66
Figure 38. Comparison of mass spectra (assuming all charged part
Figure 39. Comparison of hadronic mass spectra in data (points) an
Figure 40. Comparison of ALEPH measurement with published precise
Figure 41. Comparison of ALEPH measurement with published precise
Figure 42. Comparison of ALEPH measurement with published precise
Figure 43. Comparison of ALEPH measurement with published precise
Figure 44. Comparison of ALEPH measurement with published precise
Figure 45. Comparison of ALEPH measurement with published precise
Figure 46. Comparison of ALEPH measurement with published precise
Figure 47. Comparison of ALEPH measurement with published precise
Figure 48. Comparison of ALEPH measurement with published precise
Figure 49. Comparison of ALEPH measurement with published precise
Figure 50. Comparison of ALEPH measurement with published precise
Figure 51. The measured value for Be compared to predictions from other measurements assuming leptonic universality. The vertical band gives the average of all determinations. Universality of the τ and µ charged-current couplings holds at the 0.29% level with about equal contributions from the present determination of Be and Bπ, and the world-averaged value for the τ lifetime. The consistency of the present branching ratio measurements with leptonic universality is displayed in
Figure 52. The differences between the measured values for
Figure 53. The axial-vector fraction fA of the hadrons in the τ → ντKKπ decay mode from three independent determinations: ALEPH [9] using CVC and e +e − data, CLEO [63] with a partial-wave analysis of a1 → π −2π 0 decays, and CLEO [65] with a direct partial￾wave analysis of the τ → ντK+K−π − decays. The shaded band corresponds to the conservative range used in this analysis. 14.5.3 Total V and A contributions in the non-strange sector The total nonstrange vector and axial-vector contributions obtained in this analysis are: BV = (31.82 ± 0.18 ± 0.12) % , (37) Rτ,V = 1.787 ± 0.011 ± 0.007 , (3
Figure 54. The spectral function for the ππ0 hadronic mode. Figures 57 and 58 show the unfolded 2π −π + ντ and π −2π 0 ντ spectral functions which are the dominant contributions to the axial-vector spectral function. Both spectra are dominated by the a1 resonance and indeed the two distributions have consistent shape, while their normalization was already observed to agree, as expected from isospin invariance with a small correction from the slightly different charged and neutral pion masses. The comparison is seen in
Figure 55. The spectral function for the 3ππ0 hadronic mode. While the original spectral function is determined in 0.025 GeV2 bins, it is rebinned here to 0.1 GeV2 for easier reading. 0 0.1 0.2 0.3 0.4 0.5 0.6 0 1 2 3 Mass2 (GeV/c2 ) 2 v1 τ −→π− 3π 0 ντ ALEPH 91-95
Figure 56. The spectral function for the π3π 0 hadronic mode. While the original spectral function is determined in 0.025 GeV2 bins, it is rebinned here to 0.1 GeV2 for easier reading. 99
Figure 57. The spectral function for the 3π hadronic mode. 0 0.1 0.2 0.3 0.4 0.5 0.6 0 1 2 3 Mass2 (GeV/c2 ) 2 a1 τ −→π− 2π 0 ντ ALEPH 91-95
Figure 58. The spectral function for the π2π 0 hadronic mode. 100
Figure 59. Comparison of the corrected mass spectra for the 3
Figure 60. Comparison of the background-subtracted mass-squ
Figure 61. Relative comparison of the π +π − spectral functions extracted from τ data from different experiments, expressed as a ratio to the average τ spectral function. The lower figure emphasizes the ρ region. For CLEO only statistical errors are shown. 103
Figure 62. The total vector spectral function. The shaded area
Figure 63. The total axial-vector spectral function. The shaded
Figure 64. The inclusive vector plus axial-vector (
Figure 65. The vector minus axial-vector (v1 −a1) spectral function. In the parton model as well as in perturbative QCD vector and axial-vector contributions are degenerate. resonances, the spectral function qualitatively averages out to the quark contribution from perturbative [72]. This observation is the physical basis for the quantitative QCD analysis performed in Section 17. In the case of the (v1 − a1) spectral function, uncertainties on the V/A separation are reinforced due to their anticorrelation. In addition, anticorrelations in the branching ratios between τ final states with…
Figure 66. Comparison of the π +π − spectral functions from e +e − and isospin-breaking corrected τ data from ALEPH, CLEO, and OPAL expressed as e +e − cross sections. The band indicates the combined e +e − and τ result within 1σ errors. It is given for illustration purpose only. The complete references for the e +e − data are given in Refs. [57, 61] and [81]. 112
Figure 67. Relative comparison of the π +π − spectral functions from e +e − and isospin￾breaking corrected τ data from ALEPH, CLEO, and OPAL expressed as a ratio to the τ spectral function. The band shows the uncertainty on the latter function. The complete references for the e +e − data are given in Refs. [57, 61] and [82]. 113
Figure 68. Comparison of the 2π +2π − spectral functions from e +e − and isospin-breaking corrected τ data, expressed as e +e − cross sections. The complete references for the e +e − data are given in Refs. [57, 61]. 114
Figure 69. Comparison of the π +π −2π 0 spectral functions from e +e − and isospin-breaking corrected τ data, expressed as e +e − cross sections. The complete references for the e +e − data are given in Refs. [57, 61]. 115
Figure 70. The measured branching ratios for τ → ντπ −π 0 compared to the prediction from the e +e − → π +π − spectral function applying the isospin-breaking correction factors discussed in Section 16.1. The measured branching ratios are from ALEPH, CLEO [37] and OPAL [36]. The OPAL result was obtained from their hπ0 branching ratio, reduced by the small Kπ0 contribution measured by ALEPH [9] and CLEO [83]. presented [84]; while the new data contradict earlier results from the same experiments, they are in good agreement with the ALEPH spectral functions. 16.3 Fits to the ππ0 spectral fu
Figure 71. Fit of the ALEPH π −π 0 form factor squared using the Gounaris-Sakurai parametrization. Γρ− − Γρ 0 = (0.2 ± 1.0) MeV (63) The mass splitting is somewhat larger than the theoretical prediction (< 0.7 MeV) [75], but only at the 2σ level. The expected width splitting, from known isospin breaking, but not taking into account any ρ mass splitting, is (0.7 ± 0.3) MeV [24, 57]. However, if the mass difference is taken as an experimental fact, then a larger width difference would be expected. From the chiral model of the ρ resonance [86, 24], one expects Γρ 0 = Γρ−
Figure 72. Results for αs(m2 τ ) from the fits of Rτ,V,A,V +A and the moments Dkl V,A,V +A using the FOPTCIand FOPT perturbative expansions. The measurements are correlated due to the theoretical errors (see
Figure 73. The ratio Rτ,V +A versus the square “τ mass” s0. The curves are plotted as error bands to emphasize their strong point-to-point correlations in s0. Also shown is the theoretical prediction using FOPTCI and the results for Rτ,V +A and the nonperturbative terms from
Figure 74. The running of αs(s0) obtained from the fit of the theoretical prediction to Rτ,V +A(s0). The shaded band shows the data including experimental errors. The curve gives the four-loop RGE evolution for three flavours. by the small mass difference between the two bins and the slightly different weight function. They are reinforced by the original experimental and theoretical correlations. Below 1 GeV2 the error of the theoretical prediction of Rτ,V +A(s0) starts to blow up due to the increasing uncertainty from the unknown K4 perturbative term; errors of the nonperturbative…
Figure 75. The evolution of the measured αs(m2 τ ) to higher scales µ using the 4-loop RGE and the 3-loop matching conditions applied at the heavy quark-pair thresholds (hence the discontinuities at 2 mc and 2 mb). The evolution of the ALEPH αs(m2 τ ) determination is in agreement with the direct value obtained from the Z width through the global electroweak fit [105]. it uses a global analysis of all modes, classified according to charged particle identification, and charged particle and π 0 multiplicity up to 4 π 0 s in the final state. Major improvements are introduced with respect to t

Figures reproduced from arXiv:hep-ex/0506072 by the authors.

References
How later papers used it

86 later papers cite it

Evidence: substantial. 86 of the citing papers share no author with it, and 50 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 147 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 6 of 44 papers with this label
How the literature uses it

77 arXiv papers cite this in 129 sentences

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Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper
  • Together with the other determination at the $Z$ boson mass pole, they constitutes the most accurate test of the asymptotic freedom in QCD.

    Tau Decays and $\alpha_s$ · 0.90

Papers citing it · 54 sentences without a confident label

Uses its method or tool 3 papers
  • Fits performed in our analysis are based on FESRs of the following form [ref]

    $\alpha_s$ from the updated ALEPH data for hadronic $\tau$ decays · Analysis framework · 0.92

  • Using a physically motivated model for the DV and through a procedure detailed in Ref. [ref] , we have studied the possible high-energy behavior of the LR spectral function, once the most recent experimental data [ref] and the known theoretical constraints have been imposed.

    Duality violation in QCD Sum Rules with the LR correlator · Conclusions and comparisons · 0.90

  • Following Refs. [ref] , we compute the five spectral moments at the tau mass as a function of the parameters $λ_2k$ with $k=0,2,3,4$, using Eq. ([ref]), and making the replacement $C_2k→λ_2k C_2k$ in Eqs. ([ref]).

    Unraveling duality violations in hadronic tau decays · The moments method applied to the model · 0.86

Uses its data or values 37 papers
Compares with it 7 papers
Cites it as background 10 papers
  • The standard framework to describe hadronic $τ$ decays is to organize the QCD description in an operator product expansion (OPE) where, apart from the perturbative contribution and quark-mass corrections, the QCD condensates intervene [ref] .

    $\alpha_s$ from the updated ALEPH data for hadronic $\tau$ decays · Introduction · 0.92

  • A detailed study of the $V-A$ correlation function was given in Refs. [ref] , using the published ALEPH $τ$ data [ref] .

    ChPT parameters from tau-decay data · Introduction · 0.90

  • Ever since the seminal work of Ref. [ref] , it has been recognized that hadronic tau decays provide an excellent experimental setting for extracting precise values of Standard Model parameters such as the strong coupling constant $α_s$ [ref] , the strange quark mass $m_s$ [ref] , and the CKM matrix element $|V_us|$ [ref] .

    Unraveling duality violations in hadronic tau decays · Introduction · 0.93

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