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arxiv: 2605.28590 · v1 · pith:OQO2QWAMnew · submitted 2026-05-27 · ✦ hep-ph

Two-loop QCD corrections to H rightarrow b + bar{b} + g at higher powers in the dimensional regulator

Pulak Banerjee , Chinmoy Dey , M. C. Kumar , Vaibhav Pandey , V. Ravindran This is my paper

Pith reviewed 2026-06-29 11:39 UTC · model grok-4.3

classification ✦ hep-ph
keywords two-loop QCDHiggs decaydimensional regularizationhigher powers of epsilonform factorsH to b bbar gvirtual correctionsQCD amplitudes
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0 comments X

The pith

The two-loop massless QCD corrections to the amplitude for Higgs decay H to b plus anti-b plus gluon are computed to higher powers in the dimensional regulator epsilon.

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

This paper computes the two-loop massless QCD corrections to the amplitude for the decay H to b plus b-bar plus g while retaining higher powers of the dimensional regularization parameter epsilon. The work proceeds by projecting the amplitude onto the appropriate Lorentz structures for the process and presents numerical checks of the resulting form factors at sample phase-space points. These amplitudes are required as ingredients for three-loop virtual corrections to bottom-quark annihilation into Higgs plus jet production at hadron colliders. A sympathetic reader would care because such higher-order terms improve the accuracy of predictions for Higgs boson production in association with jets.

Core claim

We compute the two-loop massless QCD corrections to the amplitude of Higgs boson decay to bottom quark pair and a gluon (H to b plus b-bar plus g) in the higher powers of the dimensional regularization parameter epsilon. The calculation is performed by projecting the amplitude onto the appropriate Lorentz structures related to the process. We also show the numerical behaviour of the form factors for a few sample phase-space points. These amplitudes are necessary ingredients for computing the three-loop virtual corrections to bottom-quark annihilation to Higgs plus jet production at the hadron collisions.

What carries the argument

Projection of the amplitude onto the appropriate Lorentz structures related to the process, which extracts the form factors including higher powers of epsilon.

If this is right

  • These amplitudes serve as necessary ingredients for three-loop virtual corrections to bottom-quark annihilation to Higgs plus jet production.
  • Numerical values of the form factors are provided for several sample phase-space points.
  • The results enable more precise higher-order QCD predictions for Higgs plus jet final states at hadron colliders.

Where Pith is reading between the lines

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

  • The projection technique may extend to other two-loop amplitudes where higher epsilon powers are needed for infrared subtraction.
  • The explicit higher-order terms could be used to test conjectures about the structure of epsilon expansions in massless QCD amplitudes.

Load-bearing premise

The projection of the amplitude onto the chosen Lorentz structures remains valid and complete when higher powers of epsilon are retained.

What would settle it

An independent calculation of the form factors at one of the sample phase-space points that disagrees with the projected results on the higher-order epsilon terms would falsify the computation.

read the original abstract

We compute the two-loop massless QCD corrections to the amplitude of Higgs boson decay to bottom quark pair and a gluon ($H \rightarrow b + \bar{b} + g$) in the higher powers of the dimensional regularization parameter $\epsilon$. The calculation is performed by projecting the amplitude onto the appropriate Lorentz structures related to the process. We also show the numerical behaviour of the form factors for a few sample phase-space points. These amplitudes are necessary ingredients for computing the three-loop virtual corrections to bottom-quark annihilation to Higgs plus jet production at the hadron collisions.

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 the two-loop massless QCD corrections to the amplitude for Higgs decay H → b + ar{b} + g, retaining higher powers of the dimensional regulator ε. The amplitude is projected onto the relevant Lorentz structures, numerical values of the resulting form factors are shown at sample phase-space points, and the results are presented as inputs for three-loop virtual corrections to bar{b} → H + jet.

Significance. If correct, the calculation supplies the higher-order ε terms required for infrared cancellation when combining virtual and real contributions at three loops in Higgs-plus-jet production. This is a standard and useful ingredient for precision LHC phenomenology. The projection technique is conventional in the field, and the provision of numerical checks is a positive feature for reproducibility.

minor comments (2)
  1. [Abstract] The abstract and introduction should state explicitly the highest power of ε retained in the form factors (e.g., up to ε^3 or ε^4).
  2. [Method] A brief statement confirming that the chosen Lorentz basis remains complete and linearly independent when higher powers of ε are kept would strengthen the method section.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, including its significance for three-loop virtual corrections in Higgs-plus-jet production, and for recommending minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; direct perturbative computation

full rationale

The paper reports a concrete two-loop QCD amplitude computation for H→bbg at higher orders in ε, performed by projecting the amplitude onto Lorentz structures followed by numerical checks. No load-bearing steps reduce by definition, by fitting, or by self-citation chain to the target result itself. The derivation is a standard Feynman-diagram evaluation whose validity rests on external perturbative QCD methods rather than internal redefinition or renaming of inputs. The central claim therefore remains independent of the patterns that would trigger a positive circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; computation relies on standard perturbative QCD techniques whose details are not visible.

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discussion (0)

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Reference graph

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