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arxiv: 2603.29803 · v2 · submitted 2026-03-31 · ✦ hep-ph · hep-ex

Recognition: 2 theorem links

· Lean Theorem

Perturbative QCD fitting of KEDR and BESIII e^+e^- data for R(s) and α_s determination

A.L.Kataev (INR RAS , BLTP JINR) , K.Yu.Todyshev (Budker INP RAS , Novosibirsk State University)
Authors on Pith no claims yet

Pith reviewed 2026-05-13 23:16 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords R-ratioperturbative QCDalpha_sKEDRBESIIIe+e- annihilationstrong coupling
0
0 comments X

The pith

Fits of KEDR and BESIII R(s) data to perturbative QCD show α_s(M_Z) increasing with truncation order up to 0.1312

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper fits experimental data on the R-ratio from KEDR and BESIII collaborations below the charm threshold to QCD perturbative expressions at NLO, NNLO, and N3LO. The extracted values of the strong coupling constant at the Z boson mass scale are 0.1179, 0.1221, and 0.1312 respectively, demonstrating a clear dependence on the order of the approximation. A reader would care because the strong coupling is a key parameter in the Standard Model, and its precise value affects predictions for particle interactions at high energies. The work highlights the importance of higher-order terms and analytical continuation in describing low-energy annihilation processes.

Core claim

The next-to-leading order, next-to-next-to-leading order and next-to-next-to-next-to-leading order fits of the combined KEDR data and BESIII data, truncated at the mass scale of J/Ψ meson, give the following results α_s(M_Z)= 0.1179^{+0.0051}_{-0.0069}, α_s(M_Z)=0.1221^{+0.0063}_{-0.0080} and α_s(M_Z)=0.1312^{+0.0027}_{-0.0067}.

What carries the argument

Fixed-order perturbative expansions of the R-ratio in QCD, with effects from analytical continuation from Euclidean to Minkowski space

If this is right

  • The value of α_s(M_Z) extracted from low-energy data increases as higher orders in perturbation theory are included
  • The order dependence indicates that truncation effects are significant at energies below the charm threshold
  • Analytical continuation effects must be carefully accounted for in fits to timelike data

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If higher orders continue this trend, the true α_s might be even larger, affecting global averages
  • These fits could be extended to include more data sets or combined with lattice QCD results for cross-validation
  • Improved precision in R(s) measurements at future colliders could reduce the uncertainties shown here

Load-bearing premise

Fixed-order perturbative QCD expressions, after analytical continuation, accurately describe the measured R(s) data below charm threshold with negligible non-perturbative contributions

What would settle it

Observation of R(s) values that fall outside the predicted bands from the N3LO fit, after including all experimental and theoretical uncertainties, would indicate the breakdown of the fixed-order approach

Figures

Figures reproduced from arXiv: 2603.29803 by A.L.Kataev (INR RAS, BLTP JINR), K.Yu.Todyshev (Budker INP RAS, Novosibirsk State University).

Figure 1
Figure 1. Figure 1: The result of the joint fit of the KEDR and truncated BESIII experimental data. [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: R(s) curves obtained in different orders of perturbative QCD with Λ [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
read the original abstract

The experimental data collected by KEDR and BESIII collaborations at the energies below charm quark thresholds are compared with the QCD expressions for the $e^+e^-$ annihilation R-ratio truncated at different orders of perturbation theory. The fits demonstrate the dependence of the extracted $\alpha_s(M_Z)$ values from orders of the truncation of the corresponding approximations. The next-to-leading order, next-to-next-to-leading order and next-to-next-to-next-to-leading order fits of the combined KEDR data and BESIII data , truncated at the mass scale of $J/\Psi$ meson, give the following results $\alpha_s(M_Z)= 0.1179^{+0.0051}_{-0.0069}$,$\alpha_s(M_Z)=0.1221^{+0.0063}_{-0.0080}$ and $\alpha_s(M_Z)=0.1312^{+0.0027}_{-0.0067}$. The subjects related to the applications of the fixed orders of perturbation theory expansions and careful treatment of the analytical continuation effects are commented.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript compares KEDR and BESIII e+e- data for the R(s) ratio below charm threshold with fixed-order perturbative QCD expressions truncated at the J/ψ mass. Fits at NLO, NNLO and NNNLO are performed to extract α_s(M_Z), yielding 0.1179^{+0.0051}_{-0.0069}, 0.1221^{+0.0063}_{-0.0080} and 0.1312^{+0.0027}_{-0.0067} respectively, with discussion of analytical continuation effects and the observed order dependence.

Significance. If the assumption that non-perturbative contributions remain negligible holds, the results demonstrate the pronounced sensitivity of low-scale α_s extractions to perturbative truncation order, underscoring slow convergence when α_s ≳ 0.25 and the potential value of such studies for assessing the reliability of R(s)-based determinations.

major comments (2)
  1. [Fitting procedure] Fitting procedure (results section): the central α_s values are obtained by direct fits of fixed-order pQCD expressions to data without inclusion or quantitative bound on power corrections (gluon condensate or higher-twist terms); at the fitted scales below ~3 GeV this assumption is load-bearing, as residual resonance tails or non-perturbative contributions could systematically shift the central values upward with increasing order.
  2. [Discussion of analytical continuation] Analytical continuation (discussion section): while effects are commented upon, no explicit verification (e.g., comparison of the continued expressions to independent calculations or dispersion-relation checks) is provided; this is required to support the claim that the truncated series accurately describes the time-like data.
minor comments (2)
  1. [Abstract] Abstract: the three α_s results are quoted with asymmetric uncertainties but without stating the fit statistic or how the errors were propagated from the data; a one-sentence clarification would aid readability.
  2. [Data and fits] Data handling: the precise selection of KEDR and BESIII points entering the combined fit, any energy cuts beyond the J/ψ truncation, and treatment of systematic correlations are not fully detailed, limiting reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond point by point to the major comments below, indicating where revisions have been made.

read point-by-point responses

  1. Referee: Fitting procedure (results section): the central α_s values are obtained by direct fits of fixed-order pQCD expressions to data without inclusion or quantitative bound on power corrections (gluon condensate or higher-twist terms); at the fitted scales below ~3 GeV this assumption is load-bearing, as residual resonance tails or non-perturbative contributions could systematically shift the central values upward with increasing order.

    Authors: We agree that the assumption of negligible power corrections is central to the analysis at these scales. Our primary objective is to quantify the truncation-order dependence of the perturbative series under the standard assumption that higher-twist terms remain small below the charm threshold. In the revised manuscript we have added a dedicated paragraph in the results section that cites literature estimates for the size of gluon-condensate and higher-twist contributions and discusses how they could shift the extracted α_s values, particularly at higher orders. We have not performed a full re-fit including these terms, as that lies outside the scope of the present work. revision: partial

  2. Referee: Analytical continuation (discussion section): while effects are commented upon, no explicit verification (e.g., comparison of the continued expressions to independent calculations or dispersion-relation checks) is provided; this is required to support the claim that the truncated series accurately describes the time-like data.

    Authors: The time-like expressions employed are obtained from the standard analytic continuation of the space-like Adler function via the dispersion relation, following the procedure established in the cited literature. We have expanded the discussion section to include a direct numerical comparison of our continued R(s) expressions against independent results from the literature and a brief consistency check against the dispersion integral. These additions provide the explicit verification requested. revision: yes

Circularity Check

0 steps flagged

No significant circularity in fitting procedure

full rationale

The paper performs explicit least-squares fits of fixed-order perturbative QCD expressions (NLO/NNLO/NNNLO) for R(s), after analytic continuation, directly to the combined KEDR+BESIII data truncated at m_J/ψ. The reported α_s(M_Z) central values and uncertainties are the direct numerical outputs of these fits; no quantity is presented as a first-principles prediction that reduces by construction to the fitted inputs. No self-citation chain, uniqueness theorem, or ansatz smuggling is used to justify the central results. The observed upward drift with perturbative order is a straightforward numerical consequence of the different truncation levels applied to the same data set and is not claimed to be an independent derivation. The analysis is therefore self-contained empirical extraction under the stated assumption of negligible non-perturbative contributions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of truncated perturbative QCD to R(s) data and the validity of the fitting procedure; no new entities are introduced.

free parameters (1)
  • α_s(M_Z)
    The strong coupling is the parameter fitted to match the perturbative expressions to the experimental R(s) data at each truncation order.
axioms (1)
  • domain assumption Fixed-order perturbative QCD expressions describe R(s) below charm threshold after analytical continuation
    Invoked when comparing theory truncations to KEDR and BESIII data.

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