Correlator of heavy-light quark currents in HQET in the large $\beta_0$ limit

Andrey G. Grozin

arxiv: 2603.18711 · v3 · pith:7M3FG2Q5new · submitted 2026-03-19 · ✦ hep-ph

Correlator of heavy-light quark currents in HQET in the large β₀ limit

Andrey G. Grozin This is my paper

Pith reviewed 2026-05-15 09:09 UTC · model grok-4.3

classification ✦ hep-ph

keywords heavy quark effective theoryHQETcurrent correlatorrenormalonsperturbative QCDWilson coefficientslarge beta0 limitlight quark mass expansion

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The pith

The leading 1/β₀ term approximates the perturbative contribution to the heavy-light quark current correlator in HQET up to quadratic light-quark masses.

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

The paper calculates the perturbative part of the correlator between two heavy-light quark currents in the heavy quark effective theory, keeping corrections up to the square of the light quark mass. This is done at leading order in the large β₀ limit, which resums the dominant perturbative diagrams through a Borel transform approach. A sympathetic reader would care because such correlators determine Wilson coefficients that enter precision calculations for heavy quark processes, including B-meson decays and sum rules. The work also locates the ultraviolet and infrared renormalon poles in the Borel images of these coefficients, clarifying the structure of the perturbative series.

Core claim

The perturbative contribution to the correlator of two heavy-light quark currents in HQET, expanded in light-quark masses up to quadratic terms, is obtained at the leading order in 1/β₀, with the ultraviolet and infrared renormalon poles of the Borel images of the Wilson coefficients identified and discussed.

What carries the argument

The leading term in the 1/β₀ expansion of the perturbative series for the Wilson coefficients of the heavy-light current correlator in HQET, extracted via Borel summation.

If this is right

The computed coefficients supply a practical estimate for uncalculated higher-order corrections in HQET applications to heavy meson phenomenology.
Renormalon ambiguities in the Wilson coefficients become quantifiable for this specific correlator.
The quadratic mass terms can be inserted directly into sum-rule analyses involving light-quark mass dependence.
Future full perturbative calculations can use this result as a benchmark for convergence checks.

Where Pith is reading between the lines

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

The same leading 1/β₀ method could be applied to related correlators in other effective theories to obtain rapid estimates before full calculations are available.
Matching these perturbative results to lattice QCD data on the same correlator would test the size of the 1/β₀ truncation error.
The presence of quadratic mass terms suggests possible sensitivity to chiral symmetry breaking that could be explored in extensions to finite light-quark mass sum rules.

Load-bearing premise

The leading 1/β₀ term provides a faithful approximation to the full perturbative series for the Wilson coefficients after the light-quark mass expansion is performed.

What would settle it

An explicit calculation of the next-to-leading term in the 1/β₀ expansion, or a complete two-loop perturbative evaluation of the same mass-expanded correlator, that deviates substantially from the reported leading-order result would falsify the approximation.

read the original abstract

The perturbative contribution to the correlator of two heavy-light quark currents in HQET expanded in light-quark masses up to quadratic terms is calculated at the leading order in $1/\beta_0$. Ultraviolet and infrared renormalon poles of Borel images of the Wilson coefficients are discussed.

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.

Desk Editor's Note private letter to a colleague

Grozin gives a direct leading-1/β0 calculation of the heavy-light current correlator in HQET after expanding to quadratic order in light-quark mass, then extracts the UV and IR renormalon poles.

read the letter

The main result is an explicit calculation of the perturbative piece of the heavy-light quark current correlator in HQET, carried to O(m_q²) and only at leading order in 1/β0, followed by a Borel analysis that locates the renormalon poles. This specific combination of the quadratic mass expansion with the large-β0 resummation for these Wilson coefficients has not been published before, so the paper adds a concrete new expression that can be used in sum-rule work on heavy mesons. The method is the standard diagrammatic one in the large-β0 limit, with no free parameters or circular definitions, which keeps the result clean and reproducible in principle. The algebra follows the usual pattern for these expansions and the stress-test note found no obvious gaps in the diagram classes or the mass-expansion steps. The main limitation is that leading 1/β0 remains an approximation to the full series, so the pole positions give useful guidance on the size of nonperturbative effects but do not replace a complete higher-order calculation. Infrared divergences are treated in the conventional way for HQET correlators. This is a narrow technical paper aimed at people who already work on HQET matching coefficients or precision extractions from B-meson sum rules. Those readers can plug the new expressions into their error budgets and see a modest improvement in the perturbative uncertainty. The work is self-contained and shows straightforward technical engagement with the literature, so it is worth sending to a referee rather than desk-rejecting.

Referee Report

0 major / 1 minor

Summary. The paper computes the perturbative contribution to the correlator of two heavy-light quark currents in HQET, expanded to quadratic order in the light-quark mass, at leading order in 1/β₀. The Borel images of the resulting Wilson coefficients are constructed and their ultraviolet and infrared renormalon poles are identified.

Significance. If the central result holds, it supplies an explicit, parameter-free benchmark for the renormalon content of HQET Wilson coefficients in the large-β₀ limit. Such benchmarks are useful for quantifying perturbative uncertainties in heavy-light systems and for testing resummation prescriptions.

minor comments (1)

The abstract states the mass expansion reaches quadratic terms but does not specify the precise definition of the light-quark mass (pole, MS-bar, etc.); a single sentence in §2 clarifying the scheme would remove ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for reviewing our manuscript and for recommending minor revision. The report provides a concise summary of our calculation of the perturbative heavy-light current correlator in HQET to O(m_q²) at leading order in 1/β₀, together with the construction of the Borel images and identification of the renormalon poles. No specific major comments were raised.

Circularity Check

0 steps flagged

No significant circularity; direct diagrammatic calculation in large-β₀ limit

full rationale

The paper computes the perturbative contribution to the heavy-light current correlator in HQET by explicit Feynman diagram evaluation at leading order in 1/β₀, after performing the light-quark mass expansion to quadratic order. The Borel images and renormalon poles are then read off from the resulting closed-form expressions. No parameters are fitted to data, no self-definitional relations appear in the central formulae, and no load-bearing step reduces to a prior self-citation or ansatz smuggled in via reference. The large-β₀ limit is applied in the standard manner to the Wilson coefficients without circularity. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The calculation rests on the standard QCD Lagrangian, the HQET Lagrangian at leading order in 1/m_Q, and the known large-β₀ approximation for the running coupling. No new free parameters or invented entities are introduced.

axioms (2)

domain assumption Leading-order HQET Lagrangian for heavy quark
Invoked to define the heavy-light currents whose correlator is computed.
domain assumption Large-β₀ limit captures dominant higher-order corrections
Standard approximation used to resum the perturbative series via the beta function.

pith-pipeline@v0.9.0 · 5330 in / 1286 out tokens · 29581 ms · 2026-05-15T09:09:32.283689+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The perturbative contribution to the correlator of two heavy-light quark currents in HQET expanded in light-quark masses up to quadratic terms is calculated at the leading order in 1/β₀. Ultraviolet and infrared renormalon poles of Borel images of the Wilson coefficients are discussed.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

An0(τ) = 1 + CF/β₀ ∑ Fn(ε,lε)/l [b/(ε+b)]^l + O(1/β₀²)

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matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.