REVIEW
Absence of linear power corrections in heavy-quark pair production in a non-Abelian gauge theory
High Energy Physics - Phenomenology · Submitted 26 Oct 2026 · 74 references
Pith's verdict: Solid NNLO cancellation in a toy model, well executed; limitations are clear and candid.
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Referee report
The paper
The paper claims
Terms linear in the gluon mass cancel in heavy-quark pair production through NNLO, when the quark mass is a short-distance mass — the first non-Abelian evidence for a proposed extension of the KLN theorem.
The reading
What carries the argument
The mechanism that carries the argument is a residue rewriting of soft-soft double-virtual integrals: instead of computing master integrals, the authors integrate over loop energies by Cauchy's theorem and relate each double-virtual integral to real-virtual and double-real ones, keeping only the real parts the cross section requires. Representative identities are $\mathrm{Re}\,I_{VV}^{(4)} = \mathrm{Re}\,I_{RV}^{(8)} - I_{RR}^{(7)}$ and $\mathrm{Re}\,I_{VV}^{(1)} = \mathrm{Re}\,I_{RV}^{(1)} + \mathrm{Re}\,I_{RV}^{(2)} - I_{RR}^{(1)} - I_{RR}^{(2)}$, with the full set in Eq. (6.52). Two auxiliary devices support it: a momentum redefinition (Eq. (4.8), extended to $\mathcal{O}(k^2)$ in Appendix A) that maps each real-emission phase space onto the Born phase space with $\mathcal{O}(m_g)$ accuracy, and the replacement of the pole mass by a short-distance mass, whose one-loop linear shift (proportional to the single master integral $I_R$) removes precisely the residual $\mathcal{O}(m_g)$ terms. Integration-by-parts reduction with reverse unitarity collapses every contribution into the master integrals of Table 1, so the coefficients of $m_g$ cancel algebraically in five independent classes.
Extended reading notes
Core claim
The paper's central claim, Eq. (8.3), is that the differential cross section for $t\bar{t}$ production by a color-neutral vector current satisfies $T_{m_g}\big[d\sigma_{t\bar{t}}/d\Omega_t\big] = \mathcal{O}(m_g\,\alpha_s^3)$ through NNLO, provided it is written in terms of a short-distance heavy-quark mass: no term linear in the gauge-boson mass survives. The raw ingredients — two-loop virtual corrections, real-virtual and double-real emissions, on-shell wave-function and mass renormalization constants, and the mass shift of tree-level and one-loop amplitudes — all individually contain such linear terms. The authors arrange the contributions into five classes (A through E) that vanish independently once the double-virtual integrals are rewritten as combinations of real-virtual and double-real integrals via loop-energy residues, so the cancellation is algebraic rather than numerical. The authors stress that the result is obtained in the spontaneously broken SU(2) theory described in Section 2, and not in QCD; its significance is as the first strong indication that the cancellation of linear power corrections, previously established in Abelianized models, extends to the non-Abelian sector.
Load-bearing premise
The load-bearing premise is that the spontaneously broken SU(2) theory with a small gluon mass faithfully mirrors the infrared structure of full QCD for linear power corrections; the authors prove the cancellation only in this model, not in QCD, and state so explicitly at the end of Section 8.
Editorial extensions
If this is right
- Through NNLO, $t\bar{t}$ production in this non-Abelian model has no linear $m_g$ dependence when the cross section is expressed through a short-distance heavy-quark mass; linear infrared sensitivity can survive only inside observables that are themselves linearly sensitive.
- The calculation is a concrete non-Abelian example of the proposed extension of the Kinoshita-Lee-Nauenberg theorem to linear infrared terms, going beyond the Abelianized cases studied earlier.
- Because the cancellation is established before any master integral is evaluated, the conclusion is independent of the detailed values of the two-loop integrals; any consistent evaluation must reproduce Eq. (8.3).
- The residue relations of Eq. (6.52) offer a template for probing linear power corrections in other processes without explicit integral evaluation.
- Observables with their own linear sensitivity spoil the cancellation, so identifying infrared-safe observables that preserve it — flagged by the authors as beyond this paper's scope — is the natural next step.
Reading between the lines
- The paper itself notes the dispersion-relation flavor of the residue identities; pushed further, such analyticity arguments might replace integration-by-parts reductions altogether and extend the cancellation to higher orders.
- A concrete test: apply the same machinery to the $Q_{\rm veto}$-dependent terms the authors set aside, or to processes with initial-state massless partons; a surviving linear term there would localize where non-perturbative sensitivity enters hadron-collider observables.
- The independent vanishing of Class B suggests the linear $m_g$ parts of the two-loop wave-function and mass renormalization constants are locked to real-emission phase-space integrals by the on-shell conditions; deriving that relation from heavy-quark effective theory would make the cancellation a theorem rather than a calculation.
- Within the model one can stress-test the claim by choosing a coupling renormalization constant $Z_g^{(1)}$ that depends on $m_g$; the paper's Class E argument indicates the $\mathcal{O}(m_g)$ terms still cancel, although the paper itself only considers $m_g$-independent schemes.
Original abstract
We study the infrared sensitivity of heavy-quark pair production by a color-neutral vector current in perturbation theory. We work in a spontaneously broken SU(2) gauge theory where, by tuning parameters to make the gauge-boson mass $m_g$ small, we use it as a probe of infrared physics. We find that, through next-to-next-to-leading order, terms linear in $m_g$ cancel in the differential cross section, provided that it is expressed through a short-distance heavy-quark mass. Interestingly, we establish this cancellation without evaluating any integrals explicitly, by relating virtual integrals to real-emission ones through loop-energy residues, with a suitable redefinition of the real-emission momenta. Our result is the first strong indication that the cancellation of non-perturbative linear power corrections in the corresponding QCD process extends to the non-Abelian sector. It is also a concrete non-Abelian example of the extension of the Kinoshita-Lee-Nauenberg theorem to linear infrared terms for sufficiently inclusive observables.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We study the infrared sensitivity of heavy-quark pair production by a color-neutral vector current in perturbation theory. We work in a spontaneously broken SU(2) gauge theory where, by tuning parameters to make the gauge-boson mass $m_g$ small, we use it as a probe of infrared physics. We find that, through next-to-next-to-leading order, terms linear in $m_g$ cancel in the differential cross section, provided that it is expressed through a short-distance heavy-quark mass. Interestingly, we establish this cancellation without evaluating any integrals explicitly, by relating virtual integrals to real-emission ones through loop-energy residues, with a suitable redefinition of the real-emission momenta. Our result is the first strong indication that the cancellation of non-perturbative linear power corrections in the corresponding QCD process extends to the non-Abelian sector. It is also a concrete non-Abelian example of the extension of the Kinoshita-Lee-Nauenberg theorem to linear infrared terms for sufficiently inclusive observables.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the infrared sensitivity of heavy-quark pair production by a color-neutral vector current in perturbation theory. | contribution 0.86 | 0.87 | 0.03 | unclear 0.55 |
| s1 | We work in a spontaneously broken SU(2) gauge theory where, by tuning parameters to make the gauge-boson mass $m_g$ small, we use it as a probe of infrared physics. | method 0.99 | 0.86 | 0.02 | asserted 0.97 |
| s2 | We find that, through next-to-next-to-leading order, terms linear in $m_g$ cancel in the differential cross section, provided that it is expressed through a short-distance heavy-quark mass. | result 1.00 | 0.97 | 0.77 | asserted 1.00 |
| s3 | Interestingly, we establish this cancellation without evaluating any integrals explicitly, by relating virtual integrals to real-emission ones through loop-energy residues, with a suitable redefinition of the real-emission momenta. | method 0.98 | 0.96 | 0.07 | asserted 1.00 |
| s4 | Our result is the first strong indication that the cancellation of non-perturbative linear power corrections in the corresponding QCD process extends to the non-Abelian sector. | interpretation 1.00 | 0.80 | 0.64 | hedged possibility 0.91 |
| s5 | It is also a concrete non-Abelian example of the extension of the Kinoshita-Lee-Nauenberg theorem to linear infrared terms for sufficiently inclusive observables. | interpretation 1.00 | 0.79 | 0.19 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
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- relations to other papers
- P abstract
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Figures
Figures reproduced from arXiv:2610.36065 by the authors.
References
Discussion
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