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arxiv: 2605.06996 · v1 · submitted 2026-05-07 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Renormalon-based resummation for B(D) Mesons

Cesar Ayala , Gorazd Cvetic
Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:27 UTC · model grok-4.3

classification ✦ hep-ph
keywords renormalon resummationquark pole massesMS-bar massesheavy quarksB and D mesonschromomagnetic Wilson coefficientQCD running couplingtimelike resummation
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The pith

Renormalon resummation determines pole masses of bottom and charm quarks from known MS-bar masses using a holomorphic coupling.

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

The paper applies a renormalon-based resummation technique to the perturbative series that relates the pole masses of heavy quarks to their MS-bar masses. It takes as input the known MS-bar mass values, the first few expansion coefficients, and the known structure of infrared renormalon singularities. A timelike version of the QCD coupling, derived from a holomorphic spacelike coupling, is used to avoid Landau poles and to resum the series in both spacelike and timelike regimes. The infrared regulator parameter of the coupling is varied over a plausible range to estimate the residual ambiguity. The same framework is used to reevaluate the chromomagnetic Wilson coefficient and to extract several hadronic parameters relevant to B and D mesons.

Core claim

By applying renormalon-based resummation to the ratio m_q over MS-bar m_q, incorporating the known perturbative coefficients and renormalon singularities, and employing the timelike QCD running coupling obtained from a holomorphic spacelike coupling, the pole masses of the b and c quarks are evaluated while the principal infrared regulator parameter is varied over an expected range; the same approach also yields a reevaluated chromomagnetic Wilson coefficient and several corresponding hadronic parameters.

What carries the argument

The renormalon-based resummation method for spacelike and timelike QCD observables, implemented via a timelike coupling constructed from a holomorphic spacelike QCD coupling that includes an adjustable principal infrared regulator parameter.

If this is right

  • Pole masses of the b and c quarks are obtained with the infrared renormalon ambiguity under better control.
  • The chromomagnetic Wilson coefficient of the heavy quark is reevaluated within the same resummed framework.
  • Several hadronic parameters for B and D mesons are extracted directly from the resummed quantities.
  • These results supply improved numerical inputs for precision calculations of heavy-meson decays and lifetimes.

Where Pith is reading between the lines

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

  • The extracted pole masses could be inserted into existing phenomenological analyses of semileptonic B and D decays to test consistency with experimental data.
  • The holomorphic-coupling construction offers a systematic route for resumming other QCD observables that suffer from similar infrared renormalon ambiguities.
  • Direct confrontation with lattice determinations of the same pole masses would provide a clean external test of the regulator-variation procedure.
  • The method suggests that consistent treatment of spacelike and timelike sectors via holomorphic couplings may reduce scheme dependence in a wider class of perturbative QCD calculations.

Load-bearing premise

The principal IR regulator parameter of the holomorphic coupling can be varied in an expected range that adequately captures all relevant ambiguities without introducing uncontrolled errors in the timelike resummation.

What would settle it

A comparison of the computed pole masses and hadronic parameters with independent nonperturbative determinations, such as those from lattice QCD, would falsify the central claim if the values differ by more than the estimated uncertainty band obtained from varying the regulator parameter.

Figures

Figures reproduced from arXiv: 2605.06996 by Cesar Ayala, Gorazd Cvetic.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

We apply a previously developed method of renormalon-based resummation of spacelike and timelike QCD observables, to evaluate of the values of the pole masses $m_q$ of $q=b$ and $c$ quarks, using as input the knowledge of the values of the corresponding ${\overline{\rm MS}}$ masses ${\overline m}_q \equiv {\overline m}_q({\overline m}_q^2)$. The evaluation also uses the knowledge of the first few coefficients of the perturbation expansion of $m_q$ (i.e., of $m_q/{\overline m}_q$), as well as the known renormalon structure of that expansion. In the evaluation, we use the timelike QCD running coupling based on a specific holomorphic spacelike QCD coupling, in order to avoid additional ambiguities due to the Landau poles of the usual perturbative coupling. The principal IR regulator parameter of the coupling is varied in an expected range. We also reevaluate the chromomagnetic Wilson coefficient of heavy quark ${\hat C}(m_q^2)$, and extract values of several corresponding hadronic parameters.

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 applies a renormalon-based resummation technique, previously developed by the authors, to determine the pole masses m_b and m_c of bottom and charm quarks from their known MS-bar masses m_bar_q, incorporating the first few perturbative coefficients of the ratio m_q/m_bar_q and the known renormalon structure of the series. It employs a timelike QCD coupling obtained by analytic continuation from a specific holomorphic spacelike coupling (to avoid Landau poles), with the principal IR regulator parameter varied over an expected range; the work also reevaluates the chromomagnetic Wilson coefficient Ĉ(m_q²) and extracts associated hadronic parameters for B and D mesons.

Significance. If the central assumption on the IR regulator variation holds and the resummation controls the ambiguities, the results would furnish improved, theoretically consistent values for heavy-quark pole masses and related hadronic matrix elements, with direct relevance to precision calculations in flavor physics. The approach benefits from using established perturbative coefficients and explicit renormalon input rather than ad-hoc modeling, which is a methodological strength.

major comments (2)
  1. [section on the holomorphic coupling and timelike resummation] The central numerical outputs for m_b, m_c and the hadronic parameters rest on the claim that varying the principal IR regulator parameter of the holomorphic coupling over an 'expected range' fully captures residual renormalon ambiguities in the timelike resummation without introducing uncontrolled errors. The manuscript does not supply an explicit sensitivity analysis or comparison demonstrating that this range bounds all IR sensitivities that the timelike continuation can map into the physical region; this assumption is load-bearing for the quoted values and their uncertainties.
  2. [numerical results and extraction of hadronic parameters] The results section presents extracted values but does not include a tabulated error budget that isolates the contribution of the IR-regulator variation to the final uncertainties on m_q and Ĉ(m_q²). Without such a breakdown, it is difficult to verify that the quoted theoretical errors are realistic and that the resummation has been successfully validated against the known perturbative coefficients.
minor comments (2)
  1. [abstract] The abstract contains a grammatical error ('to evaluate of the values').
  2. [method section] Notation for the holomorphic spacelike coupling and its timelike continuation should be introduced with a brief equation or diagram to clarify the analytic continuation step for readers unfamiliar with the prior work.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and will revise the manuscript accordingly to strengthen the presentation and validation of our results.

read point-by-point responses

  1. Referee: [section on the holomorphic coupling and timelike resummation] The central numerical outputs for m_b, m_c and the hadronic parameters rest on the claim that varying the principal IR regulator parameter of the holomorphic coupling over an 'expected range' fully captures residual renormalon ambiguities in the timelike resummation without introducing uncontrolled errors. The manuscript does not supply an explicit sensitivity analysis or comparison demonstrating that this range bounds all IR sensitivities that the timelike continuation can map into the physical region; this assumption is load-bearing for the quoted values and their uncertainties.

    Authors: The 'expected range' for the principal IR regulator parameter is determined from the construction of the holomorphic spacelike coupling in our prior work, ensuring consistency with the known high-scale perturbative behavior of the QCD coupling while regulating infrared effects. The timelike continuation is performed analytically, and the variation is intended to capture the leading residual renormalon ambiguities mapped into the physical region. We acknowledge that an explicit sensitivity analysis would make this more transparent. In the revised manuscript we will add a dedicated discussion with numerical comparisons, showing the dependence of m_b, m_c and the hadronic parameters on the regulator parameter (within and at the boundaries of the range) together with comparisons to truncated perturbative series, to demonstrate that the chosen range bounds the relevant IR sensitivities. revision: yes

  2. Referee: [numerical results and extraction of hadronic parameters] The results section presents extracted values but does not include a tabulated error budget that isolates the contribution of the IR-regulator variation to the final uncertainties on m_q and Ĉ(m_q²). Without such a breakdown, it is difficult to verify that the quoted theoretical errors are realistic and that the resummation has been successfully validated against the known perturbative coefficients.

    Authors: The quoted uncertainties are driven by the variation of the IR regulator parameter, with the perturbative coefficients of m_q / m_bar_q and the renormalon structure serving as fixed inputs. We agree that an explicit tabulated error budget would improve clarity and allow direct verification of the resummation. In the revised version we will include a table that isolates the contribution from the IR-regulator variation to the uncertainties on m_b, m_c and Ĉ(m_q²), together with a comparison of the resummed results against the known partial sums of the perturbative series to validate convergence and realism of the errors. revision: yes

Circularity Check

1 steps flagged

Pole-mass results depend on holomorphic spacelike coupling and IR-regulator range imported from authors' prior work

specific steps
  1. self citation load bearing [Abstract]
    "We apply a previously developed method of renormalon-based resummation of spacelike and timelike QCD observables, to evaluate of the values of the pole masses m_q of q=b and c quarks, using as input the knowledge of the values of the corresponding MS-bar masses m_bar_q ≡ m_bar_q(m_bar_q²). ... In the evaluation, we use the timelike QCD running coupling based on a specific holomorphic spacelike QCD coupling, in order to avoid additional ambiguities due to the Landau poles of the usual perturbative coupling. The principal IR regulator parameter of the coupling is varied in an expected range."

    The specific holomorphic spacelike coupling and the 'expected range' for its principal IR regulator parameter are taken directly from the authors' prior publications; the extracted pole masses and hadronic parameters are therefore not independent of those earlier definitions and choices.

full rationale

The derivation applies a renormalon-resummation framework and a specific holomorphic coupling (with its principal IR regulator varied in an 'expected range') that are both taken from the authors' earlier publications. While the MS-bar masses and low-order perturbative coefficients are external inputs, the central numerical outputs for m_b, m_c and Ĉ(m_q²) are obtained only after adopting that prior coupling construction and regulator range; this makes the quoted values dependent on the self-cited framework rather than independently derived from first principles or external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim rests on the known renormalon structure of the mass-ratio series, the accuracy of the first few perturbative coefficients, and the suitability of the chosen holomorphic coupling; the IR regulator is treated as a free parameter whose range is assumed to cover the dominant uncertainty.

free parameters (1)
  • principal IR regulator parameter
    Varied over an expected range to estimate uncertainty in the timelike resummation; its specific central value is not fixed by first principles.
axioms (2)
  • domain assumption The renormalon structure of the perturbative expansion of m_q / m_bar_q is known and can be used for resummation
    Invoked as input for the resummation procedure.
  • domain assumption The first few coefficients of the perturbation series for m_q / m_bar_q are accurately known from prior calculations
    Used directly as input data.

pith-pipeline@v0.9.0 · 5486 in / 1454 out tokens · 47280 ms · 2026-05-11T01:27:45.982346+00:00 · methodology

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