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arxiv: 2606.21702 · v1 · pith:4BDY3KCAnew · submitted 2026-06-19 · ✦ hep-ph · hep-ex

Analytic results for heavy-quark contributions to charged-current DIS at NNLO

Fabrizio Caola , Giulio Gambuti , Martin Link This is my paper

Pith reviewed 2026-06-26 13:30 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords heavy quarkscharged-current DISNNLO QCD correctionscoefficient functionsGoncharov polylogarithmscharm mass dependencedeep inelastic scattering
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0 comments X

The pith

NNLO QCD corrections to heavy-quark production in charged-current DIS are computed analytically with exact charm mass dependence.

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

The paper computes the complete partonic coefficient functions at next-to-next-to-leading order for the structure functions F2, FL, and F3 in charged-current deep-inelastic scattering, keeping the exact dependence on the charm quark mass. This includes contributions from up to three heavy quarks in the final state, expressed in terms of Goncharov polylogarithms for cases with at most two heavy quarks and Chen iterated integrals or series expansions for the three-heavy-quark case. A sympathetic reader would care because these results allow for precise and efficient numerical evaluations in the relevant energy range, improving predictions for experiments involving charm quarks without relying on mass approximations or massless limits.

Core claim

We present analytic results for the NNLO QCD corrections to heavy-quark production in charged-current deep-inelastic scattering, retaining the exact dependence on the charm quark mass. We compute the complete partonic coefficient functions for the structure functions F2, FL, and F3 in the quark and gluon channels, including contributions with up to three heavy quarks in the final state. Contributions with at most two final-state heavy quarks are expressed in terms of manifestly real Goncharov polylogarithms, while the three-heavy-quark contribution involves elliptic structures represented via Chen iterated integrals and rapidly convergent expansions valid for Q greater than or equal to 5 GeV

What carries the argument

The reverse-unitarity framework combined with integration-by-parts reduction and canonical differential equations, which reduces the integrals to Goncharov polylogarithms or Chen iterated integrals.

If this is right

  • The analytic expressions enable robust numerical evaluation without encountering numerical instabilities from elliptic sectors in most cases.
  • Results agree with known exact results at lower perturbative orders and in the massless limit.
  • The expansions provide flexible and fast evaluation in the perturbative region Q ≳ 5 GeV.
  • These coefficient functions can be used directly in phenomenological studies of heavy-quark contributions to DIS.

Where Pith is reading between the lines

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

  • Such analytic control over mass dependence may allow similar techniques to be applied to other processes like neutral-current DIS or hadron collider observables involving heavy quarks.
  • The separation into polylog and elliptic parts highlights where higher transcendental functions become necessary in QCD calculations.
  • The provided expansions could be implemented in public codes for fast convolution with parton distributions.

Load-bearing premise

All two-heavy-quark contributions can be reduced to manifestly real Goncharov polylogarithms without irreducible elliptic sectors.

What would settle it

A numerical comparison showing disagreement between the computed coefficient functions and existing leading-power expansions in the high-Q limit, or with known NNLO massless results, would indicate an error in the analytic expressions.

read the original abstract

We present analytic results for the next-to-next-to-leading-order QCD corrections to heavy-quark production in charged-current deep-inelastic scattering, retaining the exact dependence on the charm quark mass. We compute the complete partonic coefficient functions for the structure functions $F_2$, $F_L$, and $F_3$ in the quark and gluon channels, including contributions with up to three heavy quarks in the final state. Working within the reverse-unitarity framework, we use integration-by-parts and canonical differential-equations techniques to express all contributions with at most two final-state heavy quarks in terms of manifestly real Goncharov polylogarithms which allow for a robust and efficient numerical evaluation. The three-heavy-quark contribution involves elliptic structures for which we give a general representation in terms of Chen iterated integrals, as well as expressions in terms of rapidly convergent expansions that are valid in the perturbative $Q\gtrsim 5~{\rm GeV}$ region and also allow for a flexible and fast numerical evaluation. We validate our results against known exact results at lower orders, massless NNLO coefficient functions, and existing leading-power expansions in the asymptotic limit where the virtuality $Q$ is much larger than the charm mass.

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

0 major / 2 minor

Summary. The manuscript computes analytic next-to-next-to-leading-order QCD corrections to heavy-quark production in charged-current deep-inelastic scattering, retaining exact charm-quark mass dependence. It derives the complete partonic coefficient functions for F2, FL, and F3 in the quark and gluon channels, including final states with up to three heavy quarks. Using reverse unitarity, integration-by-parts, and canonical differential equations, contributions with at most two heavy quarks are reduced to manifestly real Goncharov polylogarithms, while the three-heavy-quark sector is expressed via Chen iterated integrals and rapidly convergent series valid for Q ≳ 5 GeV. Results are validated against exact lower-order expressions, massless NNLO limits, and high-Q asymptotic expansions.

Significance. If the results hold, this delivers the first complete analytic NNLO coefficient functions for massive charm in CC DIS structure functions. The explicit separation of polylogarithmic and elliptic sectors, together with the provision of both polylog and convergent-series representations, enables robust numerical evaluation for phenomenology. The validation against known lower-order exact results, massless NNLO coefficient functions, and leading-power expansions constitutes a concrete strength of the work.

minor comments (2)
  1. [Abstract] The abstract states that the two-heavy-quark contributions reduce to 'manifestly real Goncharov polylogarithms'; a short paragraph in §3 or §4 clarifying the branch-cut handling that guarantees reality would aid readers implementing the expressions.
  2. Table or figure captions for the numerical comparisons (e.g., against massless NNLO limits) could explicitly list the kinematic ranges and the number of terms retained in the asymptotic expansions to facilitate direct reproduction.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the positive assessment, including the recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained against external benchmarks

full rationale

The paper computes explicit analytic NNLO coefficient functions for massive charm in charged-current DIS using reverse-unitarity + IBP + canonical DEs, expressing results in Goncharov polylogarithms (≤2 heavy quarks) or Chen integrals/expansions (3 heavy quarks). Validation is performed against independent lower-order exact results, massless NNLO limits, and high-Q expansions. No step reduces a claimed prediction to a fitted input by construction, no load-bearing self-citation chain is invoked to justify uniqueness or ansatz, and no renaming of known results occurs. The central claim is the new explicit expressions themselves, which remain falsifiable against external data and prior calculations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The calculation rests on standard perturbative QCD and established integral-reduction techniques; no free parameters are fitted to data, no new axioms beyond domain-standard assumptions, and no invented entities are introduced.

axioms (2)
  • domain assumption Reverse-unitarity framework applies to the relevant Feynman integrals in charged-current DIS
    Invoked to reduce the integrals to polylogarithms and Chen integrals.
  • domain assumption Canonical differential equations exist and can be solved for the two-heavy-quark sectors
    Central to expressing results in Goncharov polylogarithms.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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