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arxiv: 2606.13409 · v1 · pith:RW3P4NUJnew · submitted 2026-06-11 · ✦ hep-ph · hep-th

Subtraction of infrared divergences in light-quark QCD sum rules

Ding-Kun Lian , Jin-Peng Zhang , Zi-Xi Ou-Yang , Qi-Nan Wang , Hua-Xing Chen , Wei Chen , Jia-Jun Wu This is my paper

Pith reviewed 2026-06-27 06:23 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords infrared divergencesQCD sum ruleslight-quark systemspropagator expressionssubtraction formulaWilson coefficientscondensate mixing
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The pith

Infrared divergences in light-quark QCD sum rules are removed by a subtraction at the propagator level.

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

In QCD sum rules involving light quarks, infrared divergences can appear in the Wilson coefficients of condensates and show up in the coordinate-space light-quark propagator expressions. The paper introduces a subtraction formula that removes these divergences directly at the propagator level. This method is claimed to be more intuitive and easier to apply than the standard approach of canceling divergences via mixing between quark and gluon condensates of matching dimension. A sympathetic reader would see this as a practical improvement for performing sum rule calculations on light-quark systems.

Core claim

We propose an improved method to eliminate these IR divergences at the propagator level and present a subtraction formula that implements this procedure. Compared to the existing methods that rely on the mixing between quark and gluon condensates of the same dimension to eliminate IR divergences, this method is more intuitive and easier to apply in practical QCD sum rule calculations.

What carries the argument

A subtraction formula applied directly to the coordinate-space expressions of the light-quark propagators to eliminate infrared divergences.

If this is right

  • The new method avoids reliance on condensate mixing for divergence cancellation.
  • It can be implemented straightforwardly in practical QCD sum rule computations for light quarks.
  • Physical predictions from the sum rules stay the same as with prior methods.
  • The procedure is more intuitive for handling IR issues in Wilson coefficients.

Where Pith is reading between the lines

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

  • This approach might extend to sum rules involving mixed light and heavy quarks.
  • It could reduce errors in numerical evaluations by simplifying the expressions used.
  • Consistency checks with known hadron properties would confirm the method preserves physics.

Load-bearing premise

That the subtraction at the propagator level fully eliminates the infrared divergences and leaves the physical content of the QCD sum rules intact without new issues.

What would settle it

A side-by-side computation of a specific light-quark sum rule, such as for the pion or rho meson, using the propagator subtraction versus the condensate mixing method, to check if the final results for masses or couplings match.

Figures

Figures reproduced from arXiv: 2606.13409 by Ding-Kun Lian, Hua-Xing Chen, Jia-Jun Wu, Jin-Peng Zhang, Qi-Nan Wang, Wei Chen, Zi-Xi Ou-Yang.

Figure 1
Figure 1. Figure 1: FIG. 1: Diagram (a) denotes the propagator with a covariant deriva [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
read the original abstract

In QCD sum rules for light-quark systems, infrared (IR) divergences can appear in the Wilson coefficients of certain condensates. These divergences manifest explicitly in the coordinate-space expressions of the light-quark propagators. We propose an improved method to eliminate these IR divergences at the propagator level and present a subtraction formula that implements this procedure. Compared to the existing methods that rely on the mixing between quark and gluon condensates of the same dimension to eliminate IR divergences, this method is more intuitive and easier to apply in practical QCD sum rule calculations.

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

1 major / 0 minor

Summary. The manuscript proposes an improved method to eliminate infrared (IR) divergences appearing in the Wilson coefficients of certain condensates in light-quark QCD sum rules. These divergences are subtracted directly at the level of the coordinate-space light-quark propagator expressions via a new subtraction formula. The authors claim this approach is more intuitive and easier to apply than the standard procedure of canceling divergences through explicit mixing of same-dimension quark and gluon condensates.

Significance. If the subtraction formula correctly removes all IR divergences without residue, without altering physical predictions, and without requiring additional adjustments to condensate definitions, the method would simplify practical QCD sum-rule calculations for light-quark systems. No machine-checked proofs, reproducible code, parameter-free derivations, or falsifiable numerical comparisons are presented in the available text, so these strengths cannot be credited.

major comments (1)
  1. [Abstract] Abstract: the central claim that subtraction at the propagator level fully captures and removes all IR divergences (including those arising from condensate mixing) is load-bearing but unsupported by any explicit formula, derivation, or verification. The skeptic concern that divergences from multi-propagator or vertex contributions may remain unaddressed cannot be evaluated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript. Below we provide a point-by-point response to the major comment.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that subtraction at the propagator level fully captures and removes all IR divergences (including those arising from condensate mixing) is load-bearing but unsupported by any explicit formula, derivation, or verification. The skeptic concern that divergences from multi-propagator or vertex contributions may remain unaddressed cannot be evaluated.

    Authors: The manuscript presents the subtraction formula explicitly, along with its derivation, in the main text. This formula is applied directly to the coordinate-space light-quark propagator to remove the IR divergences that appear in the Wilson coefficients of the condensates. By subtracting at the propagator level, the effects equivalent to the mixing between quark and gluon condensates are accounted for without needing to adjust the condensate definitions separately. Regarding potential divergences from multi-propagator or vertex contributions, our method targets the specific IR divergences manifesting in the propagator expressions used in standard QCD sum rule calculations for light quarks. We believe this addresses the relevant cases, though we acknowledge that the abstract does not include the explicit formula. We will revise the abstract to briefly describe the subtraction formula and its scope to better support the central claim. revision: yes

Circularity Check

0 steps flagged

No circularity: subtraction formula derived from propagator expressions

full rationale

The paper proposes a subtraction formula to remove IR divergences directly from coordinate-space light-quark propagator expressions, presented as an alternative to condensate mixing. No equations or claims in the provided text reduce a prediction to a fitted input, self-define a quantity via its own output, or rely on load-bearing self-citations whose validity is internal to the present work. The method is described as more intuitive without evidence that its central result is forced by construction from its inputs. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no free parameters, axioms, or invented entities can be extracted from the manuscript.

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discussion (0)

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Reference graph

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